Negation As Refutation

Abstract

A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilattice notion. An efficient implementation based on semantic tableaux is sketched; it reduces to SLD resolution when negations are not involved. The resulting system can give reasonable answers to queries that involve both negation and free variables. Also it gives the same results as Prolog when there are no negations. Finally, an implementation in Prolog is given.

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2010-12-22

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Author's Profile

Melvin Fitting
CUNY Graduate Center

References found in this work

Four valued semantics and the liar.Albert Visser - 1984 - Journal of Philosophical Logic 13 (2):181 - 212.
Query.[author unknown] - 1989 - Newsletter of the Society for the Advancement of American Philosophy 17 (52):9-9.

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