Artificial.intelligence_0176 - Suppose a b is valid For any...

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• Suppose a b is valid: - For any model m, if a is true in m, b must be true in m. Therefore, a |= b. Satisfiability • A sentence is satisfiable/consistent if it is true in at least one model: - m is a model of a, or m satisfies a. • A sentence is unsatisfiable/inconsistent if there exists no model that satisfies it. • Contradiction theorem: a |= b iff the sentence (a and not b ) is unsatisfiable. Also called proof by contradiction or refutation . Proof of Deduction Theorem (Continued) • To show that (a and not b) is
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