Tableau Methods for Classical Propositional Logic

Traditionally, a mathematical problem was considered ‘closed’ when an algorithm was found to solve it ‘in principle’. In this sense the deducibility problem of classical propositional logic was already ‘closed’ in the early 1920’s, when Wittgenstein and Post independently devised the well-known decision procedure based on the truth-tables. As usually happens this positive result ended up killing any theoretical interest in the subject. In contrast, first order logic was spared by a negative result. Its undecidability, established by Church and Turing in the 1930’s, made it an ‘intrinsically’ interesting subject forever. If no decision procedure can be found, that is all decision procedures have to be partial, the problem area is in no danger of saturation: it is always possible to find ‘better’ methods (at least for certain purposes).

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