Hyperequivalence of logic programs with respect to supported models.

Annals of Mathematics and Artificial Intelligence (Impact Factor: 0.49). 01/2008; 53:331-365. DOI: 10.1007/s10472-009-9119-8
Source: DBLP

ABSTRACT Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here
as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative
to the stable-model semantics. However, other semantics for logic programs are also of interest, especially the semantics
of supported models which, when properly generalized, is closely related to the autoepistemic logic of Moore. In this paper,
we consider a family of hyperequivalence relations for programs based on the semantics of supported and supported minimal models. We characterize these relations
in model-theoretic terms. We use the characterizations to derive complexity results concerning testing whether two programs
are hyperequivalent relative to supported and supported minimal models.

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    ABSTRACT: Over the years, the stable-model semantics has gained a position of the correct (two-valued) interpretation of default negation in programs. However, for programs with aggregates (constraints), the stable-model semantics, in its broadly accepted generalization stemming from the work by Pearce, Ferraris and Lifschitz, has a competitor: the semantics proposed by Faber, Leone and Pfeifer, which seems to be essentially different. Our goal is to explain the relationship between the two semantics. Pearce, Ferraris and Lifschitz's extension of the stable-model semantics is best viewed in the setting of arbitrary propositional theories. We propose an extension of the Faber-Leone-Pfeifer semantics, or FLP semantics , for short, to the full propositional language, which reveals both common threads and differences between the FLP and stable-model semantics. We establish several properties of the FLP semantics. We apply a similar approach to define supported models for arbitrary propositional theories.
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    ABSTRACT: In Answer-Set Programming different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied and characterized by various selections of models in the logic of Here-and-There (HT). For uniform equivalence however, correct characterizations in terms of HT-models can only be obtained for finite theories, respectively programs. In this paper, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HT-models and countermodels (so-called equivalence interpretations), which are lifted to first-order theories under a very general semantics given in terms of a quantified version of HT. We show that countermodels exhibit expedient properties like a simplified treatment of extended signatures, and provide further results for non-ground logic programs. In particular, uniform equivalence coincides under open and ordinary answer-set semantics, and for finite non-ground programs under these semantics, also the usual characterization of uniform equivalence in terms of maximal and total HT-models of the grounding is correct, even for infinite domains, when corresponding ground programs are infinite.
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    ABSTRACT: Equivalence and generality relations over logic programs have been proposed in answer set programming to semantically compare information contents of logic programs. In this paper, we overview previous relations of answer set programs, and propose a general framework that subsumes previous relations. The proposed framework allows us to compare programs possibly having non-minimal answer sets as well as to explore new relations between programs. Such new relations include relativized variants of generality relations over logic programs. By selecting contexts for comparison, the proposed framework can represent weak, strong and uniform variants of generality, inclusion and equivalence relations. These new relations can be applied to comparison of abductive logic programs and coordination of multiple answer set programs.
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Miroslaw Truszczynski