Encodings for Equilibrium Logic and Logic Programs with Nested Expressions

Pearce, David; Tompits, Hans; Woltran, Stefan

doi:10.1007/3-540-45329-6_31

Cited by 44 publications

(57 citation statements)

References 15 publications

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“…One can observe that this encoding is related to encodings for computing stable models via QBFs, as discussed by Egly et al [6] and Pearce et al [24]. Indeed, taking the two main conjuncts from S Π (V 1 ), Φ = P 1,1 ∧∀V 2 (V 2 < V 1 ) → ¬P 2,1 and Ψ = Q 1,1 → ∃V 4 (V 4 < V 1 ) ∧ Q 4,1 ) , we get, for any assignment Y 1 ⊆ V 1 , Y 1 |= Φ iff Y is an answer set of P , and Y 1 |= Ψ iff Y is not an answer set of Q.…”

Section: Special Casesmentioning

confidence: 94%

“…, amounts to a propositional unsatisfiability test, witnessing the coNP-completeness complexity for checking strong equivalence [24]. One can show that the reductions due to Pearce et al [24] and Lin [21] for testing strong equivalence in terms of propositional logic are simple variants thereof.…”

Section: Special Casesmentioning

confidence: 99%

“…One can show that the reductions due to Pearce et al [24] and Lin [21] for testing strong equivalence in terms of propositional logic are simple variants thereof. For strong equivalence relative to a set A of atoms [28], i.e., for Π being of form (P, Q, P A , = B ) with B = U but with arbitrary A, our encodings T Π (V 1 ) and T Π (V 1 ) can still be simplified since V A∪B 3 = ∅.…”

Section: Special Casesmentioning

confidence: 99%

See 2 more Smart Citations

Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Tompits

Woltran

2005

Logic Programming

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Abstract. In recent work, a general framework for specifying program correspondences under the answer-set semantics has been defined. The framework allows to define different notions of equivalence, including the well-known notions of strong and uniform equivalence, as well as refined equivalence notions based on the projection of answer sets, where not all parts of an answer set are of relevance (like, e.g., removal of auxiliary letters). In the general case, deciding the correspondence of two programs lies on the fourth level of the polynomial hierarchy and therefore this task can (presumably) not be efficiently reduced to answerset programming. In this paper, we describe an approach to compute program correspondences in this general framework by means of linear-time constructible reductions to quantified propositional logic. We can thus use extant solvers for the latter language as back-end inference engines for computing program correspondence problems. We also describe how our translations provide a method to construct counterexamples in case a program correspondence does not hold.

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Section: Special Casesmentioning

confidence: 94%

Section: Special Casesmentioning

confidence: 99%

Section: Special Casesmentioning

confidence: 99%

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Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Tompits

Woltran

2005

Logic Programming

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“…In particular, whenever P occurs as a subprogram in the context of another program, we can replace P without changing the semantics (i.e., without changing the answer sets of the overall program) only by programs which are strongly equivalent to P. Note that due to the non-monotonic semantics such a replacement property cannot be obtained by just comparing the answer sets of the subprograms which are subject to replacement. The replacement property is important for modularization and optimization of logic programs, and its semantic and complexity properties have been investigated for ground and nonground programs [16,18,19,38,55,66].…”

Section: Strong Equivalencementioning

confidence: 99%

Complexity results for answer set programming with bounded predicate arities and implications

Eiter

Faber

Fink

et al. 2007

Ann Math Artif Intell

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Answer set programming is a declarative programming paradigm rooted in logic programming and non-monotonic reasoning. This formalism has become a host for expressing knowledge representation problems, which reinforces the interest in efficient methods for computing answer sets of a logic program. The complexity of various reasoning tasks for general answer set programming has been amply studied and is understood quite well. In this paper, we present a language fragment in which the arities of predicates are bounded by a constant. Subsequently, we analyze the complexity of various reasoning tasks and computational problems for this fragment, comprising answer set existence, brave and cautious reasoning, and strong equivalence. Generally speaking, it turns out that the complexity drops significantly with respect to the full non-ground language, but is still harder than for the respective ground or propositional languages. These results have several implications, most importantly for solver implementations: Virtually all currently available solvers have exponential (in the size of the input) space requirements even for programs with bounded predicate arities, while our results indicate that for those programs polynomial space should be sufficient. This can be seen as a manifestation of the "grounding bottleneck" (meaning that programs are first instantiated and then solved) from which answer set programming solvers currently suffer. As a final contribution, we provide a sketch of a method that can avoid the exponential space requirement for programs with bounded predicate arities.

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“…Our elaboration of paraconsistent reasoning is part of an encompassing research program, analysing a large spectrum of reasoning mechanisms in Artificial Intelligence, among them nonmonotonic reasoning [8], (nonmonotonic) modal logics [10], logic programming [7,17], abductive reasoning [9], and belief revision [6].…”

Section: Introductionmentioning

confidence: 99%

Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems

Besnard

Schaub

Tompits

et al. 2002

Logics in Artificial Intelligence

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Abstract. Signed systems were introduced as a general, syntaxindependent framework for paraconsistent reasoning, that is, nontrivialised reasoning from inconsistent information. In this paper, we show how the family of corresponding paraconsistent consequence relations can be axiomatised by means of quantified Boolean formulas. This approach has several benefits. First, it furnishes an axiomatic specification of paraconsistent reasoning within the framework of signed systems. Second, this axiomatisation allows us to identify upper bounds for the complexity of the different signed consequence relations. We strengthen these upper bounds by providing strict complexity results for the considered reasoning tasks. Finally, we obtain an implementation of different forms of paraconsistent reasoning by appeal to the existing system QUIP.

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Encodings for Equilibrium Logic and Logic Programs with Nested Expressions

Cited by 44 publications

References 15 publications

Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Complexity results for answer set programming with bounded predicate arities and implications

Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems

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