Transcription of Propositional logic: Horn clauses
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Propositional logic: Horn clauses
1CS 2740 Knowledge RepresentationM. HauskrechtCS 2740 Knowledge RepresentationLecture 6 Milos Sennott SquarePropositional logic: horn clauses CS 2740 Knowledge RepresentationM. HauskrechtAdministration Homework assignment 2 Propositional logic exercises Programming a resolution solver2CS 2740 Knowledge RepresentationM. HauskrechtLogical inference problemLogical inference problem: Given: a knowledge base KB (a set of sentences) and a sentence (called a theorem), Does a KB semantically entail?In other words: In all interpretations in which sentences in the KB are true, is also true? =|KB? CS 2740 Knowledge RepresentationM. HauskrechtSolving logical inference problemIn the following:How to design the procedure that answers: Three approaches: Truth-table approach Inference rules Conversion to the inverse SAT problem Resolution-refutation =|KB?3CS 2740 Knowledge RepresentationM. HauskrechtKB in restricted formsIf the sentences in the KB are restricted to some special forms some of the sound inference rules may become completeExample: horn form ( horn normal form) Two inference rules that are sound and complete with respect to Propositional symbolsfor KBs in the horn normal form: Resolution (positive unit resolution) Modus ponens)()(DCABA ))(()(DCAAB Can be written also as:CS 2740 Knowledge RepresentationM.
• Horn form (Horn normal form) • Two inference rules that are sound and complete with respect to propositional symbols for KBs in the Horn normal form: – Resolution (positive unit resolution) – Modus ponens (A∨¬B) ∧(¬A∨¬C ∨D) Can be written also as: (B ⇒ A) ∧(( A ∧C) ⇒ D) CS 2740 Knowledge Representation M. Hauskrecht ...
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