Simplifying Logic Programs Under Answer Set Semantics

Pearce, David

doi:10.1007/978-3-540-27775-0_15

Cited by 11 publications

(10 citation statements)

References 31 publications

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“…In fact there is an effective method to transform a program into a logically equivalent one in which the decidable literals in Neg( ) have been eliminated, [79].…”

Section: Proposition 10 ([79]) Every Generalised Disjunctive Program mentioning

confidence: 99%

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Equilibrium logic

Pearce

2006

Ann Math Artif Intell

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141

108

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“…In fact there is an effective method to transform a program into a logically equivalent one in which the decidable literals in Neg( ) have been eliminated, [79].…”

Section: Proposition 10 ([79]) Every Generalised Disjunctive Program mentioning

confidence: 99%

“…Here I would like to correct an error in[79] where this result was mistakenly stated to hold for generalised disjunctive programs with rules of form(5). In fact the proof uses the t-minimality property of equilibrium models for disjunctive rules.…”

mentioning

confidence: 99%

Equilibrium logic

Pearce

2006

Ann Math Artif Intell

Self Cite

141

108

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show abstract

“…Two programs, P and Q, are strongly equivalent iff, for any program R, AS (P ∪ R) = AS (Q ∪ R); they are uniformly equivalent iff, for any set F of facts, AS (P ∪ F ) = AS (Q ∪ F ). While strong equivalence is relevant for program optimisation and modular programming in general [7][8][9], uniform equivalence is useful in the context of hierarchically structured program components, where lower-layered components provide input for higher-layered ones. In abstracting from strong and uniform equivalence, Eiter et al [4] introduced the notion of a correspondence problem which allows to specify (i) a context, i.e., a class of programs used to be added to the programs under consideration, and (ii) the relation that has to hold between the answer sets of the extended programs.…”

Section: System Specificsmentioning

confidence: 99%

Testing Relativised Uniform Equivalence under Answer-Set Projection in the System cc ⊤

Oetsch

Seidl

Tompits

et al. 2009

Lecture Notes in Computer Science

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Abstract.The system cc⊤ is a tool for testing correspondence between logic programs under the answer-set semantics with respect to different refined notions of program correspondence. The underlying methodology of cc⊤ is to reduce a given correspondence problem to the satisfiability problem of quantified propositional logic and to employ extant solvers for the latter language as back-end inference engines. In a previous version of cc⊤, the system was designed to test correspondence between programs based on relativised strong equivalence under answer-set projection. Such a setting generalises the standard notion of strong equivalence by taking the alphabet of the context programs as well as the projection of the compared answer sets to a set of designated output atoms into account. This paper outlines a newly added component of cc⊤ for testing similarly parameterised correspondence problems based on uniform equivalence. General InformationAn important issue in software development is to determine whether two encodings of a given problem are equivalent, i.e., whether they yield the same result on a given problem instance. Depending on the context of problem representations, different definitions of "equivalence" are useful and desirable. The system cc⊤ [1] (short for "correspondencechecking tool") is devised as a checker for a broad range of different such comparison relations defined between disjunctive logic programs (DLPs) under the answer-set semantics [2]. In a previous version of cc⊤, the system was designed to test correspondence between logic programs based on relativised strong equivalence under answerset projection. Such a setting generalises the standard notion of strong equivalence [3] by taking the alphabet of the context programs as well as the projection of the compared answer sets to a set of designated output atoms into account [4]. The latter feature ⋆

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“…While strong equivalence of logic programs under answer set semantics has been considered in a number of papers [7,11,40,37,45,47,56,57,46,48], investigations on uniform equivalence just started with preliminary parts of this work [16]. Recent papers on program transformations [20,19] already take both notions into account.…”

Section: Examplementioning

confidence: 99%

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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Simplifying Logic Programs Under Answer Set Semantics

Cited by 11 publications

References 31 publications

Equilibrium logic

Equilibrium logic

Testing Relativised Uniform Equivalence under Answer-Set Projection in the System cc ⊤

Semantical characterizations and complexity of equivalences in answer set programming

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