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Propositional Calculus II:Two more Rules of Inference/Inference Schemata
(conditional elim = modus ponens, proof by cases), Application to Additional Motivating Problems
Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science
Lally School of Management & TechnologyRensselaer Polytechnic Institute (RPI)
Troy, New York 12180 USA
Intro to Logic2/3/2020
Selmer Bringsjord
No, it’s not logical to throw a bomb from the Kansas City 49-yard line @ 3rd and 10, with 1:49 to go.
Re-re-re…orientation w.r.t. web pages …
The Starting Code to Purchase in Bookstore
The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The email address you enter is case-sensitive!
The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The email address you enter is case-sensitive!Your OS and browser must be fully up-to-date; Chrome is the best choice, browser-wise (though I use Safari).
The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The email address you enter is case-sensitive!Your OS and browser must be fully up-to-date; Chrome is the best choice, browser-wise (though I use Safari).Watch that the link doesn’t end up being classified as spam.
The Starting Code Purchased in Bookstore Should By Now’ve Been Used to Register & Subsequently Sign In
First batch of prop. calc. (Homework) Problems in;easiest starting place: switching_conjuncts_fine.
E-Housekeeping Pts, Redux
E-Housekeeping Pts, Redux
• Must input your RIN.
E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
• Make sure browser fully up-to-date.
E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
• Make sure browser fully up-to-date.
• Chrome best (but I use Safari).
E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
• Make sure browser fully up-to-date.
• Chrome best (but I use Safari).
• Always work in the same browser window with multiple tabs; must do this with email and HyperGraderTM & HyperSlateTM.
Propositional Calculus II:More Rules of Inference
(conditional elim = modus ponens, proof by cases), Application to Additional Motivating Problems
Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science
Lally School of Management & TechnologyRensselaer Polytechnic Institute (RPI)
Troy, New York 12180 USA
Intro to Logic2/3/2020
Selmer Bringsjord
Last time we introduced and and lauded the power of oracles, and questions … and now … picking up where we left off …
“NYS 3” RevisitedGiven the statements¬¬cc → a¬a ∨ bb → d¬(d ∨ e)
which one of the following statements must also be true?
¬ceh¬aall of the above
“NYS 3” RevisitedGiven the statements¬¬cc → a¬a ∨ bb → d¬(d ∨ e)
which one of the following statements must also be true?
¬ceh¬aall of the above
“NYS 3” RevisitedGiven the statements¬¬cc → a¬a ∨ bb → d¬(d ∨ e)
which one of the following statements must also be true?
¬ceh¬aall of the above
After last class, should have done …Exercise: Show in HyperSlateTM that each of the first four options can be proved using the PC entailment oracle.
(and (not C) E H (not A))
(and (not C) E H (not A))
(and (not C) E H (not A))
(and (not C) E H (not A))
(and (not C) E H (not A))
(and (not C) E H (not A))
(and (not C) E H (not A))
Proof Plan …
Proof Plan …
Proof Plan …
Proof Plan …
Proof Plan …
Sub-Proof
Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
conditional elima.k.a., modus ponens
Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
conditional elima.k.a., modus ponens
The Universe of Logics
Infinitary Finitary
Intensional ExtensionalDeductive InductiveDeductive Inductive
Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram
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L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
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modus ponens
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Next problem(King-Ace) …
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.NO!
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
King-Ace Solved
Proposition: There is not an ace in the hand.
Proof: We know that at least one of the if-thens (i.e., at least one of the conditionals) is false. So we have two cases to consider, viz., that K => A is false, and that ¬K => A is false. Take first the first case; accordingly, suppose that K => A is false. Then it follows that K is true (since when a conditional is false, its antecedent holds but its consequent doesn’t), and A is false. Now consider the second case, which consists in ¬K => A being false. Here, in a direct parallel, we know ¬K and, once again, ¬A. In both of our two cases, which are exhaustive, there is no ace in the hand. The proposition is established. QED
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO!
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Study the S-expression
Study the S-expression
We need another rule of inference to crack this problem … …
We need another rule of inference to crack this problem … …
disjunction elimination
From ~ p. 54 in LAMA-BDLA
From ~ p. 54 in LAMA-BDLA
From ~ p. 54 in LAMA-BDLA
From ~ p. 54 in LAMA-BDLA
?
From ~ p. 54 in LAMA-BDLA
?
From ~ p. 54 in LAMA-BDLA
?
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Exercise (on HyperGraderTM): Finish the proof in HyperSlateTM — with no remaining use of an oracle.
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