How to Synthesize a Tableau
نویسنده
چکیده
We synthesize a refutationally complete tableau calculus for propositional logic by a new method, using ordered resolution as a procedural framework at the meta level. Algebraically, the calculus solves the word problem for free distributive lattices. Goal-directedness of the construction is enforced by a ne-tuned well-founded ordering on terms, atoms and clauses. The synthesis is performed in two steps, transforming a natural distributive-lattice axiomatization to a resolution basis and deriving the tableau rules from the interaction of the basis with queries of the word problem. This supports an algebraic analysis of the r^ ole of distributivity and cut in tableaux and sequent calculi.
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