Computing Equilibrium Models Using Signed Formulas

Pearce, David; Guzmán, Inman P. de; Valverde, Agustín

doi:10.1007/3-540-44957-4_46

Cited by 12 publications

(13 citation statements)

References 16 publications

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“…Answer set semantics was already generalised and extended to arbitrary propositional theories with two negations in the system of equilibrium logic, defined in [18] and further studied in [19][20][21]. Equilibrium logic is based on a simple, minimal model construction in the nonclassical logic of here-and-there (with strong negation), and admits also a natural fixpoint characterisation in the style of nonmonotonic logics.…”

Section: Introductionmentioning

confidence: 99%

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Reducing Propositional Theories in Equilibrium Logic to Logic Programs

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Pearce

Valverde

2005

Progress in Artificial Intelligence

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Abstract. The paper studies reductions of propositional theories in equilibrium logic to logic programs under answer set semantics. Specifically we are concerned with the question of how to transform an arbitrary set of propositional formulas into an equivalent logic program and what are the complexity constraints on this process. We want the transformed program to be equivalent in a strong sense so that theory parts can be transformed independent of the wider context in which they might be embedded. It was only recently established [2] that propositional theories are indeed equivalent (in a strong sense) to logic programs. Here this result is extended with the following contributions. (i) We show how to effectively obtain an equivalent program starting from an arbitrary theory. (ii) We show that in general there is no polynomial transformation if we require the resulting program to share precisely the vocabulary or signature of the initial theory. (iii) Extending previous work we show how polynomial transformations can be achieved if one allows the resulting program to contain new atoms. The program obtained is still in a strong sense equivalent to the original theory, and the answer sets of the theory can be retrieved from it.

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Section: Introductionmentioning

confidence: 99%

“…Equilibrium logic is based on a simple, minimal model construction in the nonclassical logic of here-and-there (with strong negation), and admits also a natural fixpoint characterisation in the style of nonmonotonic logics. In [21,14] it was shown that answer set semantics for nested programs [13] is also captured by equilibrium models.…”

Section: Introductionmentioning

confidence: 99%

Reducing Propositional Theories in Equilibrium Logic to Logic Programs

Cabalar

Pearce

Valverde

2005

Progress in Artificial Intelligence

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“…Deciding for some ϕ whether Π | ∼ϕ is Π p 2 -complete. The corresponding complexity classes for programs with nested expressions [23] and for propositional theories in equilibrium logic are the same, [29,30]. So complexity does not alter when the syntax is extended in this way.…”

Section: Some Complexity and Implementation Issuesmentioning

confidence: 99%

“…Any attempt is bound to fail on purely complexity-theoretic grounds. Deciding whether a literal is stable is a co-NP complete problem, while deciding whether a nested or disjunctive logic program has an answer set is Σ p 2 -complete, [12,29,30].…”

Section: But This Implies That H H |= R Which Is Impossible By the mentioning

confidence: 99%

Simplifying Logic Programs Under Answer Set Semantics

Pearce

2004

Logic Programming

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Abstract. Now that answer set programming has emerged as a practical tool for knowledge representation and declarative problem solving there has recently been a revival of interest in transformation rules that allow for programs to be simplified and perhaps even reduced to programs of 'lower' complexity. Although it has been known for some that there is a maximal monotonic logic, denoted by N5, with the property that its valid (equivalence preserving) inference rules provide valid transformations of programs under answer set semantics, with few exceptions this fact has not really been exploited in the literature. The paper studies some new transformation rules using N5-inference to simplify extended disjunctive logic programs known to be strongly equivalent to programs with nested expressions.

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“…It is defined in terms of the logic of here-and-there, which is intermediate between classical logic and intuitionistic logic. Equilibrium logic was introduced in [26] and further investigated in [27]; proof theoretic studies of the logic can be found in [29,28].…”

Section: Equilibrium Logicmentioning

confidence: 99%

A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report

et al. 2002

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Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction, disjunction, as well as the negation as failure operator in an unrestricted fashion. This provides a very flexible and compact framework for knowledge representation and reasoning. Previous results show that nested logic programs can be transformed into standard (unnested) disjunctive logic programs in an elementary way, applying the negation as failure operator to body literals only. This is of great practical relevance since it allows us to evaluate nested logic programs by means of off-the-shelf disjunctive logic programming systems, like DLV. However, it turns out that this straightforward transformation results in an exponential blow-up in the worst-case, despite the fact that complexity results indicate that there is a polynomial translation among both formalisms. In this paper, we take up this challenge and provide a polynomial translation of * This work was partially supported by the Austrian Science Fund (FWF) under grants P15068-INF and N Z29-INF. The authors would like to thank Agata Ciabattoni for pointing out some relevant references.† Affiliated with the School of Computing Science at Simon Fraser University, Burnaby, Canada. logic programs with nested expressions into disjunctive logic programs. Moreover, we show that this translation is modular and (strongly) faithful. We have implemented both the straightforward as well as our advanced transformation; the resulting compiler serves as a front-end to DLV and is publicly available on the Web.

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Computing Equilibrium Models Using Signed Formulas

Cited by 12 publications

References 16 publications

Reducing Propositional Theories in Equilibrium Logic to Logic Programs

Reducing Propositional Theories in Equilibrium Logic to Logic Programs

Simplifying Logic Programs Under Answer Set Semantics

A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report

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