Relativized hyperequivalence of logic programs for modular programming

Truszczyński, Mirosław; Woltran, Stefan

doi:10.1017/s1471068409990159

Cited by 8 publications

(4 citation statements)

References 27 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It allows for specifying, on the one hand, the atoms which are permitted to occur in the rule heads of context programs and, on the other hand, the atoms allowed in the rule bodies. Besides generalising various equivalence notions, hyperequivalence can be parametrised for application-specific equivalence tests [6].…”

Section: Introductionmentioning

confidence: 99%

Elimination of Disjunction and Negation in Answer-Set Programs under Hyperequivalence

2008

Self Cite

View full text Add to dashboard Cite

Abstract. The study of different notions of equivalence is one of the cornerstones of current research in answer-set programming. This is mainly motivated by the needs of program simplification and modular programming, for which ordinary equivalence is insufficient. A recently introduced equivalence notion in this context is hyperequivalence, which includes as special cases strong, uniform, and ordinary equivalence. We study in this paper the question of replacing programs by syntactically simpler ones preserving hyperequivalence (we refer to such a replacement as a casting). In particular, we provide necessary and sufficient semantic conditions under which the elimination of disjunction, negation, or both, in programs is possible, preserving hyperequivalence. In other words, we characterise in model-theoretic terms when a disjunctive logic program can be replaced by a hyperequivalent normal, positive, or Horn program, respectively. Furthermore, we study the computational complexity of the considered tasks and, based on similar results for strong equivalence developed in previous work, we provide methods for constructing the respective hyperequivalent programs. Our results contribute to the understanding of problem settings in logic programming in the sense that they show in which scenarios the usage of certain constructs are superfluous or not.

show abstract

Section: Introductionmentioning

confidence: 99%

Elimination of Disjunction and Negation in Answer-Set Programs under Hyperequivalence

2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…Thus, even if just one atom from At is forbidden from appearing in heads of rules in context programs, the complexity jumps one level up. For a detailed analysis of this behavior we refer to (Truszczyński & Woltran 2008).…”

Section: Discussionmentioning

confidence: 99%

Hyperequivalence of logic programs with respect to supported models

Truszczyński

Woltran

2008

Ann Math Artif Intell

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…This concept, also termed hyperequivalence (Truszczyński & Woltran, 2009), allows for a common characterisation of strong and uniform equivalence and thus to understand the difference between these notions on model-theoretic grounds. More specifically, two programs P and Q over A are hyperequivalent relative to H and B, if, for each DLP R such that r∈P H(r) ⊆ H and r∈P (B + (r) ∪ B − (r)) ⊆ B, it holds that AS(P ∪ R) = AS(Q ∪ R).…”

Section: Generalisationsmentioning

confidence: 99%

Model-based recasting in answer-set programming

Eiter

Fink

Pührer

et al. 2013

Journal of Applied Non-Classical Logics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Relativized hyperequivalence of logic programs for modular programming

Cited by 8 publications

References 27 publications

Elimination of Disjunction and Negation in Answer-Set Programs under Hyperequivalence

Elimination of Disjunction and Negation in Answer-Set Programs under Hyperequivalence

Hyperequivalence of logic programs with respect to supported models

Model-based recasting in answer-set programming

Contact Info

Product

Resources

About