A Sound and Complete Semantics for a Version of Negation as Failure

Abstract Negation as failure is sound both for the closed world assumption and the completed database or completion, comp ( P ) of a program P . In general it is not complete for either of these declarative semantics. Indeed there can be no semantics for which it is both sound and complete, for all programs and queries, because non-ground negative literals cannot be dealt with, and cause floundering. By extending the negation as failure rule we exclude floundering and we give a semantics T ω ( P ) for which the extended rule is both sound and complete. T ω ( P ) is a weak version of comp ( P ) based on an iterative construction. We show that the soundness and completeness results still hold if the classical consequence relation ⊢ is replaced by a weaker relation ⊢ 31 which is sound for both 3-valued logic and intuitionistic logic.

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