Propositional and Predicate Calculus - Carleton University

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51/77 Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Introduction Some Definitions Inference Rules Example Introduction Inference Rule (IR) Is a “mechanical” means Can produce new predicate sentence from other sentences Inference Rules: Classified as being Sound or Complete. Sound Inference Rule: Expression produced by the IR logically follows from S Complete Inference Rule: It has the ability to produce every expression that logically follows from S
52/77 Definitions Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Introduction Some Definitions Inference Rules Example DEFINITION: SATISFY, MODEL, VALID, INCONSISTENT For a predicate calculus expression X and interpretation I, If X has a value of T under I and a particular variable assignment, then I said to satisfy X If I satisfies X for all variable assignments, then I is a model of X X is satisfiable if and only of there exist an interpretation and variable assignment that satisfy it; otherwise, it is unsatisfiable A set of expressions is satisfiable if and only if there exist an interpretation and variable assignment that satisfy ever element If a set of expressions is not satisfiable, it is said to be inconsistent If X has a value T for all possible interpretations, X is said to be valid
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Propositional and Predicate Calculus - Carleton University

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