L18predlogic(2)

L18predlogic(2) - Predicate Logic PART 2 CSE 352 Artificial...

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Predicate Logic PART 2 CSE 352 Artificial Intelligence Professor Anita Wasilewska Lecture Notes
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Predicate Logic Part 2 PREDICATE LOGIC TAUTOLOGIES BASIC LAWS OF QUANTIFIERS
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Basic Laws of Quantifiers (Predicate Logic Tautologies) De Morgan Law ¬ x A(x) ≡ x ¬A(x) ¬ x A(x) ≡ x ¬A(x) where A(x) is any formula with free variable x ≡ means “logically equivalently” Definability: ¬ x A(x) ≡ x ¬A(x) ¬ x A(x) ≡ x ¬A(x) Application Example : A(x) is ((Px) ¬R(x)) ¬ Q( x,y) ) x(P(x) ¬R(X) ¬Q( x,y))
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