Propositional and Predicate Calculus - Carleton University

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55/77 Unification 2 Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Introduction Some Definitions Inference Rules Example DEFINITION: MODUS PONENS, MODUS TOLLENS, AND ELIMINATION, AND INTRODUCTION, and UNIVERSAL INSTANTIATION If the sentences P and P → Q are known to be true, then modus ponens lets us infer Q Under the inference rule modus tollens, if P → Q known to be true and Q is known to be false, we can infer ¬P And Elimination allows us to infer the truth of either of the conjuncts from the truth of a conjunctive sentence For instance, P∧Q lets us conclude P and Q are true And Introduction allows us to infer the truth of the conjunction from the truth of the conjuncts For instance, if P and Q are true, then P∧Q is true Universal Instantiation states that if any universally quantified variable in a true sentence is replaced by any appropriate term from the domain, the result is a true sentence. Thus, if a is from the domain of X, then ∀X p(X) lets us infer p(a).
56/77 Inference Rules Outline and Introduction Propositional Calculus Predicate Calculus Inference Rules Unification Resolution Theorem Proving Introduction Some Definitions Inference Rules Example Modus Ponens Modus Tollens P → Q P → Q P ¬Q −−−−− −−−−− Q ¬P And Elimination P ∧ Q −−−−− P Q And Introduction P Q −−−−− P ∧ Q
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Propositional and Predicate Calculus - Carleton University

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