CS 730/830: Intro AI

■ COVID

What is KR?

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 1 / 21

asst 5 is posted

COVID

■ COVID

What is KR?

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 2 / 21

■ check your Wildcat Pass before coming to campus■ send me email if you need to isolate/quarantine

EOLQs

■ COVID

What is KR?

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 3 / 21

Introduction toKnowledge Representation

and Reasoning

■ COVID

What is KR?

■ What is KR?

■ History of Logic

■ Advice Taker

■ The PSSH

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 4 / 21

What is Knowledge Representation?

■ COVID

What is KR?

■ What is KR?

■ History of Logic

■ Advice Taker

■ The PSSH

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 5 / 21

■ Representing facts■ Reasoning with facts

Can computers be meaningful?

History of Logic

■ COVID

What is KR?

■ What is KR?

■ History of Logic

■ Advice Taker

■ The PSSH

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 6 / 21

Philo of Megara (5C BC): truth tablesAristotle (322BC): tautologies of proper argumentsGottfried Leibniz (1646-1716): inference as math-like (bogus)logicGeorge Boole (1854): The Laws of Thought (almostpropositional logic)Gottlob Frege (1879): Conceptual Notation (propositional andfirst-order logic)Dartmouth Conference (1956): ‘AI’ coinedAdvice Taker (1959): manifesto for declarative knowledgeCYCorp (1984- , www.cyc.com): slightly more complicated thanfirst-order logic

The Advice Taker (1959)

■ COVID

What is KR?

■ What is KR?

■ History of Logic

■ Advice Taker

■ The PSSH

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 7 / 21

John McCarthy: “AI”, Lisp, time-sharing

Empirical Philosophy = Science

■ COVID

What is KR?

■ What is KR?

■ History of Logic

■ Advice Taker

■ The PSSH

Prop. Logic

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 8 / 21

The Physical Symbol System Hypothesis: A physicalsymbol system has the necessary and sufficient means for generalintelligent action. (Newell and Simon)

where a

Symbol is a designating pattern that can be combined withothers to form another designating pattern

and

Designation means standing in for something in the world

Propositional Logic

■ COVID

What is KR?

Prop. Logic

■ Prop. Logic

■ Logic

■ An Example

■ Semantics

■ Break

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 9 / 21

Propositional Logic

■ COVID

What is KR?

Prop. Logic

■ Prop. Logic

■ Logic

■ An Example

■ Semantics

■ Break

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 10 / 21

itisraining

iamwet

itisraining → iamwet

x y x ∧ y

T T TT F FF T FF F F

x y x→ y

T T TT F FF T TF F T

x x→ y modusy ponens

∧,∨,¬,→ (⊃,⇒),↔

Logic

■ COVID

What is KR?

Prop. Logic

■ Prop. Logic

■ Logic

■ An Example

■ Semantics

■ Break

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 11 / 21

A logic is a formal system:

■ syntax: defines sentences■ semantics: relation to world■ inference rules: reaching new conclusions

three layers: proof, models, reality

flexible, general, principled

Encode in Propositional Logic

■ COVID

What is KR?

Prop. Logic

■ Prop. Logic

■ Logic

■ An Example

■ Semantics

■ Break

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 12 / 21

If the unicorn is mythical, then it is immortal, but if it is notmythical, then it is a mortal mammal. If the unicorn is eitherimmortal or a mammal, then it is horned. The unicorn is magicalif it is horned.

Semantics

■ COVID

What is KR?

Prop. Logic

■ Prop. Logic

■ Logic

■ An Example

■ Semantics

■ Break

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 13 / 21

Interpretation: possible world = state of affairs = truth value foreach propositionMeaning: values across all interpretationsModel of P : an interpretation in which P is trueSatisfiable: ∃ a modelEntailment: if α is true in every model of KB, then KB |= α

Valid: true in any interpretation

x y (x ∧ ¬y) z (x ∧ ¬y)→ z

T T F T TT T F F TT F T T TT F T F FF T F T TF T F F TF F F T TF F F F T

Break

■ COVID

What is KR?

Prop. Logic

■ Prop. Logic

■ Logic

■ An Example

■ Semantics

■ Break

Reasoning

Wheeler Ruml (UNH) Lecture 10, CS 730 – 14 / 21

■ asst 4■ asst 5

Reasoning

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 15 / 21

Propositional Reasoning

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 16 / 21

Entailment: if β is true in every model of α, then α |= β

computing entailmentsoundness, completeness

α |= β iff α→ β is valid

α |= β iff α ∧ ¬β is unsatisfiable

determining satisfiability is NP-completeeg, easy to test proof of yes!

Boolean Satisfiability

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 17 / 21

Given a formula of boolean logic, is there any assignment of T/Fto its variables that makes the entire formula true?

(a ∨ b ∨ c) ∧ (¬a ∨ b ∨ ¬c) ∧ (¬a ∨ ¬b ∨ c) ∧ (¬a ∨ ¬b ∨ ¬c)

The Davis-Logemann-Loveland Algorithm (1962)

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 18 / 21

DLL(φ):UnitPropagate(φ)[ PureLiterals(φ) ]if φ is empty, return SATif φ contains empty clause, return UNSATv ← choose a variableif DLL(SetVariable(φ with v =true))=SAT, return SATelse, return DLL(SetVariable(φ with v =false))

UnitPropagate(φ):as long as there is a unit clause

SetVariable according to the literal

SetVariable(φ with v = value):remove clauses where v appears as valueremove v from clauses where it appears as ¬value

WalkSAT/SKC (1994)

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 19 / 21

for 1 to maxTries

assign all variables randomlyfrom 1 to maxFlips

randomly choose an unsatisfied clause c

if one or more of c’s variables can be flipped whilebreaking nothing,randomly choose among those

elsewith probability p

randomly choose one of c’s variableselse

randomly choose among those of c’s variables thatminimize breaks

flip the variableif formula satisfied, terminate

p ≈ 0.5?

Local Search for SAT

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 20 / 21

DPLL: 50 vars = 1.4 secs, 100 vars = 2.8 min, 140 vars = 4.7hrs

Local Search for SAT

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 20 / 21

DPLL: 50 vars = 1.4 secs, 100 vars = 2.8 min, 140 vars = 4.7hrs

GSAT: 100 vars = 6 secs, 140 vars = 14 secs, 500 vars = 1.6 hrs

EOLQs

■ COVID

What is KR?

Prop. Logic

Reasoning

■ Reasoning

■ SAT

■ DLL

■ WalkSAT

■ GSAT

■ EOLQs

Wheeler Ruml (UNH) Lecture 10, CS 730 – 21 / 21

Please write down the most pressing question you have aboutthe course material covered so far and put it in the box on yourway out.Thanks!