lecture 3- pedicate calculus (AI).ppt

8/16/2019 lecture 3- pedicate calculus (AI).ppt

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Artificial Intelligence

Lecture 3: The Predicate

Calculus-I


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Today

The Propositional Calculus

The Predicate Calculus


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Declarative vs. Procedural

Declarative programming Design representation language maing it

easy to e!press no"ledge

#implify construction of solution Procedural programming

$no"ledge is em%odied in the algorithms and

program code itself Potentially more efficient& %ut more difficult to

develop solution


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Propositional Logic

A very simple logic

#ynta!& #emantics& Inference algorithm

Centered around propositions #tatements a%out the "orld that may %e true

or false

e.g.& 'rass is green( )ater is "et( It sno"ed

last Tuesday.


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#ym%ols


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#entences


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#emantics


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For propositional expressions P, Q and R :

Proposition *+uivalence


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Truth table for the

operator ∧.

Truth Ta%le

Truth table demonstrating theequivalence of and .


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Today

The Propositional Calculus

The Predicate Calculus


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Predicate Logic

At a high level, Predicate Logic allo"s you to represent

o%ects&

properties of o%ects& and relations among o%ects


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Predicate logic

)hereas propositional logic assumes the "orld containsfacts that are true or false/

Predicate logic lie natural language/ assumes the"orld contains 0%ects: people& houses& num%ers& colors& %ase%all games&

"ars& ,

1elations: red& round& prime& %igger than& part of& comes%et"een& ,

2unctions: father of& %est friend& one more than& plus& ,


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#ynta!

Constants dept0fC#& cA#PA...

Predicates %rother& near& loves&...

2unctions s+rt& father0f&...

4aria%les 5& 6& A& 7&... Connectives ¬& ⇒& ∧& ∨

*+uality 8

9uantifiers ∀& ∃


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#ym%ols


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#ym%ols cont.


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Terms


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Atomic #entences


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#entences


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Interpretation


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Interpretation cont.


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Interpretation cont.


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*+uivalence

2or predicates p and +& and varia%les 5

and 6

¬∃5p5/ ≡ ∀5¬p5/

¬∀5p5/ ≡ ∃5¬p5/

∃5p5/ ≡ ∃6p6/

∀5p5/ ≡ ∀6p6/

∀5p5/∧+5// ≡ ∀5p5/∧∀6+6//

∃5p5/∨+5// ≡ ∃5p5/∨∃6+6/ /

lecture 3- pedicate calculus (AI).ppt

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