Propositional and Predicate Calculus - Carleton University

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35/77 Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Predicates and Atomic Sentences Introduction Predicates and Sentences: Syntax General Important Notes Atomic Sentences Predicate Calculus: Semantics Predicate Equivalences Some Examples Consider: ∀X likes(X, cake) This sentence will be true when all of the values of the variable (that belong to the disclosure domain) satisfy this predicate Consider: ∃X friends(X, sara) This sentence will be true when there is at least one value of the variable (that belongs to the disclosure domain) that satisfies this predicate
36/77 Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Predicates Calculus Sentences DEFINITION PREDICATE CALCULUS SENTENCES Every atomic sentence is a sentence. 1. If s is a sentence, so is its negation, ¬s Introduction Predicates and Sentences: Syntax General Important Notes Atomic Sentences Predicate Calculus: Semantics Predicate Equivalences Some Examples 2. If s 1 and s 2 are sentences, then so is their conjunction s 1 ∧ s 2 3. If s 1 and s 2 are sentences, then so is their disjunction s 1 ∨ s 2 4. If s 1 and s 2 are sentences, then so is their implication s 1 → s 2 5. If s 1 and s 2 are sentences, then so is their equivalence s 1 ≡ s 2 6. If X is a variable and s a sentence, then ∀X s is a sentence. 7. If X is a varaible and s a sentence, then ∃X s is a sentence.
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Propositional and Predicate Calculus - Carleton University

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