Abstract
Two natural ways to specify the declarative semantics of logic programs and deductive databases are the fixpoint theory of Van Emden and Kowalski [11] and Clark's predicate completion [2]. The fixpoint theory does not apply to general programs with negation; a generalization of the theory can be defined [1,12] only if the programs are stratified. Clark's predicate completion is defined for logic programs with negation. In general, it fails to capture their intended semantics [7,8,9].
In this paper, we introduce a new notion of quasi-interpretation as a set of ground clauses of the form A ← ¬ B 1, ..., ← B n and extend the classic fixed point theory in [11] to quasi-interpretations. The semantics of a logic program P is defined by Clark's predicate completion of the least fixpoint of a continuous operator T P on quasi-interpretations. It is called the fixpoint completion of P, fixcomp(P). We then discuss the relations between fixcomp(P) and other approaches [5,7,8,9].
On leave from Institute of Computer Science and Cybernetics, National Center for Scientific Research of Vietnam, Lieugiai, Badinh, Hanoi, Vietnam.
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Dung, P.M., Kanchanasut, K. (1989). A natural semantics for logic programs with negation. In: Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1989. Lecture Notes in Computer Science, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52048-1_34
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DOI: https://doi.org/10.1007/3-540-52048-1_34
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