Hyperequivalence of logic programs with respect to supported models

Truszczyński, Mirosław; Woltran, Stefan

doi:10.1007/s10472-009-9119-8

Cited by 9 publications

(32 citation statements)

References 27 publications

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“…Thus, the conditions (1), (2) and (5) Table 1 summarizes the results. It shows that the problems concerning supp-equivalence (no normality restriction), and stable-equivalence for normal programs are all coNP-complete (as are the corresponding direct-direct problems, studied in [24] and here). The situation is more diversified for suppmin-equivalence and stable-equivalence (no normality restriction) with some problems being coNP-and others Π P 2 -complete.…”

Section: Lemma 4 Let P Q Be Programs Andmentioning

confidence: 69%

Relativized hyperequivalence of logic programs for modular programming

Truszczyński¹,

Woltran²

2009

Theory and Practice of Logic Programming

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Abstract.A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, independently of each other, the head and body alphabets in context programs. We study relativized hyperequivalence for the three semantics of logic programs given by stable, supported and supported minimal models. For each semantics, we identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyperequivalence relative to contexts where the head and body alphabets are specified directly has been studied before. In this paper, we establish the complexity of deciding relativized hyperequivalence wrt the three other types of context programs.

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Section: Lemma 4 Let P Q Be Programs Andmentioning

confidence: 69%

Relativized hyperequivalence of logic programs for modular programming

Truszczyński¹,

Woltran²

2009

Theory and Practice of Logic Programming

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“…Work on the latter could profit from previous results on the relation of loops and HT -models (Gebser, Schaub, Tompits, & Woltran, 2008). Strong equivalence has also been studied under other semantics, including well-founded semantics (Cabalar, Odintsov, & Pearce, 2006;Nomikos, Rondogiannis, & Wadge, 2005) and supported model semantics (Truszczyński & Woltran, 2008). It could also be worthwhile to study program recasting in these settings.…”

Section: Resultsmentioning

confidence: 99%

Model-based recasting in answer-set programming

Eiter

Fink

Pührer

et al. 2013

Journal of Applied Non-Classical Logics

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Abstract. As well-known, answer-set programs do not satisfy the replacement property in general, i.e., programs P and Q that are equivalent may cease to be so when they are put in the context of some other program R, i.e., R ∪ P and R ∪ Q may have different (sets of) answer sets. Pearce et al. thus introduced strong equivalence for context-independent equivalence, and proved that such equivalence holds between given programs P and Q iff P and Q are equivalent theories in the monotonic logic of here-and-there. In this article, we consider a related question: given a program P , does there exist some program Q from a certain class C of programs such that P and Q are equivalent under a given notion of equivalence? Furthermore, if the answer to this question is positive, how can we recast P to an equivalent program from C (i.e., construct such a Q)? In particular, we consider classes of programs that emerge by (dis)allowing disjunction and/or negation, and as equivalence notions we consider strong, uniform, and ordinary equivalence. Based on general model-theoretic properties and a novel form of canonical programs, we develop semantic characterisations for the existence of such a program Q, determine the computational complexity of checking existence, and provide (local) rewriting rules for recasting.

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“…The term 'hyperequivalence' has been coined in the context of ASP, as a general expression for different forms of equivalence, which guarantee that the semantics is preserved under the addition of arbitrary programs (called contexts) from a particular class of programs [36]. Relativized hyperequivalence emanates from the study of relativized notions of equivalence by restricting contexts to particular alphabets (see e.g., [8,28]).…”

Section: Relativized Hyperequivalence For Propositional Theoriesmentioning

confidence: 99%

“…A further refinement distinguishes the alphabet for atoms allowed in rule heads of an addition from the alphabet for atoms allowed in rule bodies [38]. The various notions of equivalence that can be formalized this way have recently been called relativized hyperequivalence [36,37].…”

Section: Introductionmentioning

confidence: 99%

Equivalences in Answer-Set Programming by Countermodels in the Logic of Here-and-There

Fink

2008

Logic Programming

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Abstract. Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in Answer-Set Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. Such semantic comparisons are usually 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 article, 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). Moreover, we generalize the so-called notion of relativized hyperequivalence for programs to propositional theories, and apply the same methodology in order to obtain a semantic characterization which is amenable to infinite settings. This allows for a lifting of the results to first-order theories under a very general semantics given in terms of a quantified version of HT. We thus obtain a general framework for the study of various notions of equivalence for theories under answer-set semantics. Moreover, we prove an expedient property that allows for 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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Hyperequivalence of logic programs with respect to supported models

Cited by 9 publications

References 27 publications

Relativized hyperequivalence of logic programs for modular programming

Relativized hyperequivalence of logic programs for modular programming

Model-based recasting in answer-set programming

Equivalences in Answer-Set Programming by Countermodels in the Logic of Here-and-There

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