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Unformatted text preview: CS 440: Introduction to AI Homework 2  Part A (Part B will be available soon.) Due: September 23 11:59PM, 2010 Your answers must be concise and clear. Explain sufficiently that we can easily determine what you understand. We will give more points for a brief interesting discussion with no answer than for a bluffing answer. 1 Validity and Satisfiability Determine whether each formula is valid, satisfiable (but not valid), or unsatis fiable. 1. P ( x ) 2. ∀ x P ( x ) 3. ∃ x ∀ y P ( x,y ) 4. ∀ x ( P ( x ) ∨¬ P ( x )) 5. ∃ x ∀ y ( P ( x,y ) ⇒ ∀ w ∃ z P ( w,z )) 6. ∃ x ( P ( x ) ⇒ ¬ P ( x )) 7. ∃ x ¬ ( ¬ P ( x ) ∨ P ( x )) 8. ∀ x ∀ y ( ¬ P ( x ) ∨ P ( y )) ⇒ ( P ( x ) ⇒ P ( y )) 2 Sentence Translation This problem has two parts. In the first part, you are asked to translate some first order predicate calculus (FOPC) sentences into English sentences. The meanings of the predicates and functions in the FOPC sentences are given....
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 Spring '08
 Levinson
 Logic, Artificial Intelligence, Predicate logic, Quantification, Universal quantification, FOPC

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