Uniform Equivalence for Equilibrium Logic and Logic Programs

Pearce, David; Valverde, Agustín

doi:10.1007/978-3-540-24609-1_18

Cited by 24 publications

(34 citation statements)

References 12 publications

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“…Note that this generalizes an observation reported in [49] to relativized notions of equivalence, namely that uniform and strong equivalence are the only forms of equivalence obtained by varying the logical form of expressions in the extension.…”

Section: Corollary 3 For Programs P Q and A Set Of Atomssupporting

confidence: 86%

“…Programs with nested expressions [38] (also called nested logic programs) extend DLPs in such a way that arbitrarily nested formulas, formed from literals using negation as failure, conjunction, and disjunction, constitute the heads and bodies of rules. Our characterizations for uniform equivalence are well suited for this class as was shown in [49]. Since the proofs of our main results are generic in the use of reducts, we expect that all results (including relativized notions of equivalence) can be carried over to nested logic programs without any problems.…”

Section: Example 17mentioning

confidence: 82%

“…Moreover, we show that relativized strong equivalence shares an important property with strong equivalence: constraining possible program extensions to sets of rules of the form A ← B , where A and B are atoms, does not lead to a different concept (Corollary 3). The observation of Pearce and Valverde [49] that uniform and strong equivalence are essentially the only concepts of equivalence obtained by varying the logical form of the program extensions therefore generalizes to relative equivalence.…”

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Semantical characterizations and complexity of equivalences in answer set programming

Eiter

Fink

Woltran

2007

ACM Trans. Comput. Logic

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Abstract. In recent research on non-monotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens equivalence of P and Q with respect to answer sets (which is the particular case for R = ∅), and has its applications in program optimization, verification, and modular logic programming. In this paper, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence, where R is a set of facts rather than a set of rules. This notion, which is well known in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence, where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case, as well as some restricted classes, provide semantical characterizations and analyze the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for input-based problem solving.

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Section: Corollary 3 For Programs P Q and A Set Of Atomssupporting

confidence: 86%

Section: Example 17mentioning

confidence: 82%

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Semantical characterizations and complexity of equivalences in answer set programming

Eiter

Fink

Woltran

2007

ACM Trans. Comput. Logic

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show abstract

“…[PV04] argued that in the context of answer-set programming strong and uniform equivalence are the only two concepts of this type. Our results suggest that the two concepts are close to each other also in a more general algebraic setting we considered here.…”

Section: Discussionmentioning

confidence: 99%

Strong and uniform equivalence of nonmonotonic theories – an algebraic approach

Truszczyński

2007

Ann Math Artif Intell

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“…For any two theories, respectively programs, and a potential extension by Γ, we consider the following notions of equivalence which have been shown to be the only forms of equivalence obtained by varying the logical form of extensions in the propositional case in [29].…”

Section: Notions Of Equivalencementioning

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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Uniform Equivalence for Equilibrium Logic and Logic Programs

Cited by 24 publications

References 12 publications

Semantical characterizations and complexity of equivalences in answer set programming

Semantical characterizations and complexity of equivalences in answer set programming

Strong and uniform equivalence of nonmonotonic theories – an algebraic approach

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

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