Propositional and Predicate Calculus - Carleton University

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Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Predicates Calculus Sentences verify_sentence algorithm Introduction Predicates and Sentences: Syntax General Important Notes Atomic Sentences Predicate Calculus: Semantics Predicate Equivalences Some Examples function verify_sentence(expression); begin case expression is an atomic sentence: return SUCCESS expression is of the form QXs where Q is either∀ or ∃, X is a variable, and s is an expression; if verify_sentence(s) returns SUCCESS then return SUCCESS else return FAIL expression is of the form ¬s: if verify_sentence(s) returns SUCCESS then return SUCCESS else return FAIL if verify_sentence(s)returns SUCCESS then return SUCCESS else return FAIL expression is of the form s 1 op s 2 , where op is a binary logical operator: if verify_sentence(s_1)returns SUCCESS and verify_sentence(s_2)returns SUCCESS then return SUCCESS else return FAIL; otherwise: return FAIL end end 37/77
38/77 Examples Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Introduction Predicates and Sentences: Syntax General Important Notes Atomic Sentences Predicate Calculus: Semantics Predicate Equivalences Some Examples Examples: Determine whether the following is a sentence or not. plus(two,three) No equal(plus(two, three), five) Yes equal(plus(two, three), seven) Yes ∃X likes(X, ice-cream) ∧ equal(plus(two, three), five) Yes
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Propositional and Predicate Calculus - Carleton University

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