Stanford CS 157 - Propositional Logic (16 pages)

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Propositional Logic



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Propositional Logic

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Lecture Notes


Pages:
16
School:
Stanford University
Course:
Cs 157 - Logic and Automated Reasoning
Logic and Automated Reasoning Documents

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Computational Logic Lecture 2 Propositional Logic Michael Genesereth Autumn 2005 Propositional Constants Examples raining r32aining rAiNiNg rainingorsnowing Non Examples 324567 raining or snowing 9 29 05 2 1 Compound Sentences Negations raining The argument of a negation is called the target Conjunctions raining snowing The arguments of a conjunction are called conjuncts Disjunctions raining snowing The arguments of a disjunction are called disjuncts 9 29 05 3 Compound Sentences concluded Implications raining cloudy The left argument of an implication is the antecedent The right argument is the consequent Reductions cloudy raining The left argument of a reduction is the consequent The right argument of a reduction is the antecedent Equivalences cloudy raining 9 29 05 4 2 Parenthesis Removal Dropping Parentheses is good p q p q But it can lead to ambiguities p q r p q r p q r p q r 9 29 05 5 Precedence Parentheses can be dropped when the structure of an expression can be determined by precedence NB An operand associates with operator of higher precedence If surrounded by operators of equal precedence the operand associates with the operator to the right p q r p q r p q p q r p q r 9 29 05 6 3 Example p o q r s a c b o p q p q a r o b p q s o r o r c a b 9 29 05 7 Example p q r r p q p q p q 9 29 05 8 4 Propositional Interpretation A propositional interpretation is an association between the propositional constants in a propositional language and the truth values T or F p i T q i F r i T pi T qi F ri T 9 29 05 9 Sentential Interpretation A sentential interpretation is an association between the sentences in a propositional language and the truth values T or F pi T qi F ri T p q i T q r i T p q q r i T A propositional interpretation defines a sentential interpretation by application of operator semantics 9 29 05 10 5 Operator Semantics Negation T F F T For example if the interpretation of p is F then the interpretation of p is T For example if the interpretation of p q



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