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# l17bwmodbased - Entailment and Inference in Propositional...

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11/6/2005 1 Entailment and Inference in Propositional Logic Brian C. Williams Session 17 copyright Brian Wil iams 16.410-13 11/6/2005 2 Main 1 Pressure 1 Pressure 2 Val copyright Brian Wil iams How Do We Reason About Complex Systems at a Commonsense Level? Helium tank Fuel tank Oxidizer tank Engines Flow = zero = nominal = nominal Acceleration = zero Reformulated as questions of entailment in propositional logic. Is it guaranteed that opening the white ves will produce thrust? 11/6/2005 3 Outline ion Summary copyright Brian Wil iams Propositional Entailment Natural Deduction Deduction by Resolut a 1

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11/6/2005 4 Entailment and Models KB α KB α iff α in all α copyright Brian Wil iams Given knowledge base , and sentence entails is true models where KB is true Example KB = “Giants won”, “Reds won” = “Either the Giants won or the Reds won” 11/6/2005 5 Models and Entailment m l α if α i . M( α ) α ils α iff α ) M( α ) M(KB) copyright Brian Wil iams Interpretation is a mode of sentence s true given m denotes the set of all models of sentence Entailment KB enta M(KB) subset M( 11/6/2005 6 Propositional Inference: Enumeration Method α il α ? α KB C B A copyright Brian Wil iams KB = (A or C) and (B or not C) = A or B Does KB enta True True True False True True True False True False False True True True False False True False True False False False False False B or not C A or C a 2
11/6/2005 7 Propositional Inference: Enumeration Method α il α ? α KB C B A copyright Brian Wil iams KB = (A or C) and (B or not C) = A or B Does KB enta True True True True True True True True True True True False True True True False False True True False True True True True True False False True True True True True True True False True False True False False True False False False False True True False False False False True False False False False B or not C A or C 11/6/2005 8 Relating Entailment to

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l17bwmodbased - Entailment and Inference in Propositional...

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