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Algorithms for finding matrix models of propositional calculi

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Abstract

A suite of algorithms is presented for finding all matrix models for a given propositional calculus from a given search-space. The approach firstly involves finding, for each axiom schema, all minimal partial matrices for the search-space that directly fail to satisfy the axiom (i.e. allrefutations by the axiom). This essentially reduces the problem of generating matrices to a constraint satisfaction problem, albeit a more general one than previously considered in practical settings. A refutation-driven backtracking algorithm is presented for such problems. The algorithms do not rely on any special algebraic properties, although they are capable of exploiting them when available. Preliminary computational experience is reported which demonstrates the practical utility of the algorithms to the logician.

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Pritchard, P. Algorithms for finding matrix models of propositional calculi. J Autom Reasoning 7, 475–487 (1991). https://doi.org/10.1007/BF01880325

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  • DOI: https://doi.org/10.1007/BF01880325

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