Modulo Errors

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A demonstration of weaknesses in Prolog’s goal-matching method in the context of language recognition/generation. Considers decidability, term languages, statement form, arbitrary strings from a restricted alphabet.

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Two standard forms for first order predicate logic- Prenex normal form requires all the quantifiers to be at the front, whilst Skolem form further demands that only universal (forall) quantifiers are used . Gives an algorithm for finding prenex form with worked example; consideration of Skolem functions; Skolem normal form algorithm; a consideration of logical equivalence and the merits of these normal forms.

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A backward-chaining proof method for predicate logic, motivated by proof by contradiction rather than deduction. Description of the semantic tableau structure and rules, with suggested order of application. Also includes worked examples and a proof of correctness and completeness (with reference to Gödel’s theorems).