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INTRO LOGICINTRO LOGICDAY 20DAY 20

Translations in PLTranslations in PL66

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EXAM #3EXAM #3

25 translations from English

into Predicate Logic

4 points each

Only final formula is graded.

Do intermediate work on scratch paper.

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EXAM TOPICS 1EXAM TOPICS 1

if anyone is F, then everyone is H16i‘any’

if everyone is F, then everyone is H36hmultiple quantification

every A and B is C16gdisjunctive combinations

every F S is HAPPY16econjunctive combinations

only SENIORS are HAPPY16f‘only’

every SENIOR is HAPPY26cspecified quantifiers

everyone is HAPPY 26bsimple quantifiers

JAY and KAY are HAPPY26aun-quantified formulas

example#HWChapter 6

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EXAM TOPICS 2EXAM TOPICS 2

every F RESPECTS some G27d2 quantifiers, 3 predicates

no STUDENT RESPECTS everyone27c2 quantifiers, 2 predicates

everyone RESPECTS someone27b2 quantifiers, 1 predicate

KAY RESPECTS every STUDENT21 quantifier, 2 predicates

everyone RESPECTS KAY27a1 quantifier, 1 predicate

Example#HWChapter 7

every one who RESPECTS every F RESPECTS every G

27ecomplex predicates

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Review – 1 Quantifier, 1 PredicateReview – 1 Quantifier, 1 Predicate

x Rxjno-one respects Jay

x Rxkevery one respects Kay

x RjxJay respects some one

ReviewReview – 1 Quantifier, 2 Predicates – 1 Quantifier, 2 Predicates

x ( Fx & Rxj )no F respects Jay

x ( Fx Rxk )every F respects Kay

x ( Fx & Rjx )Jay respects some F

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Review – 2 Review – 2 QuantifiersQuantifiers, 1 Predicate, 1 Predicate

x y Ryxthere is someone whom no-one respects

x y Rxythere is someone who respects no-one

x y Ryxthere is someone whom everyone R’s

x y Rxyeveryone respects someone (or other)

x y Ryxno-one is respected by everyone

x y Rxyno-one respects everyone

x y Rxysomeone respects someone

x y Rxyeveryone respects everyone

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Review – 2 Quantifiers, 2 PredicatesReview – 2 Quantifiers, 2 Predicates

x y ( Gy & Rxy )there is someone who R’s no G

x ( Fx & yRxy )there is some F who R’s everyone

x y ( Gy Rxy )no one respects every G

x ( Fx yRxy )every F respects someone (or other)

x y ( Gy & Rxy )some one respects some G

x ( Fx yRxy )every F respects everyone

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Review – 2 Quantifiers, 3 PredicatesReview – 2 Quantifiers, 3 Predicates

x ( Fx & y(Gy & Rxy) )there is some F who R’s no G

x ( Fx & y(Gy Rxy) )there is some F who R’s every G

x ( Fx & y(Gy Rxy) )no F respects every G

x ( Fx y(Gy & Rxy) )every F respects some G (or other)

x ( Fx & y(Gy & Rxy) )some F respects some G

x ( Fx y(Gy Rxy) )every F respects every G

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new material new material for day 5for day 5

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Complex PredicatesComplex Predicates

Simple Predicates

Pxx is a Politician

no further analysis required

Cxx is a Citizen

Complex Predicates

no Citizen Respects x

Jay Respects x

x Respects everyone must be further analyzed

x

x Respects him/herself

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Example AnalysesExample Analyses

y ( Cy & Ryx )no Citizen Respects x

y ( Cy Ryx )every Citizen Respects x

y ( Py Rxy )x Respects every Pol

y ( Py & Rxy )x Respects at least one Pol

y Ryxsomeone Respects x

y Rxyx Respects everyone

Rxxx Respects him/herself

RjxJay Respects x

Rxkx Respects Kay

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Example 1Example 1

y ( Py & Rxy )

x R’s at least one P

xCxx

every citizen respects at least one politician

x { Cx y ( Py & Rxy ) }

respects at least one politicianevery citizen

isevery C

{ }

then you if you are C you are

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x

Example 2Example 2

no politician is respected by every citizen

y ( Cy Ryx )

every C Respects x

x is R’ed by every C

}&Pxx

x { Px & y ( Cy Ryx ) }

respected by every citizenno politician

no P is

is

there is no one who is P and who is

{

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Example 3Example 3

every one who respects every pol is a moron

y ( Py Rxy )

x R’s every Politician

Mxx{x

Misevery

x { y(Py Rxy) Mx }

a moronisone who respects every Pevery

}

you are Mthenif you are you

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Example 4Example 4

x { y(Py Rxy) y(Py Ryx) }

respected by every P

every one who respects every Pol is respected by every Pol

y ( Py Ryx )y ( Py Rxy )

x is R’ed by every Px R’s every P

xx{x

is every

}

one who R’s every Pevery is

you are then if you are you

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x

Example 5Example 5

x { y ( Py Rxy ) & Rxx }

who is and who is there is no one

no one who respects every pol respects him/herself

Rxxy (Py Rxy )

x R’s him/herselfx R’s every P

}&x{x

x is x is there is no x :

isno

respects him/herselfone who R’s every Pno

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THE ENDTHE END