Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation

Leone, Nicola; Rullo, Pasquale; Scarcello, Francesco

doi:10.1006/inco.1997.2630

Cited by 141 publications

(192 citation statements)

References 47 publications

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“…Therefore, the next theorem immediately follows from the characterization of unfounded sets in (Leone et al 1997). …”

Section: Definition 32 (Unfounded Sets)mentioning

confidence: 91%

“…The presence of negation also complicates the proof that the rewritten program is query-equivalent to the original one. To demonstrate this result, we have exploited the characterization of stable models via unfounded sets of (Leone et al 1997), and generalized the equivalence proof of (Alviano et al 2009) to the case of programs with functions.…”

Section: Related Workmentioning

confidence: 99%

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Disjunctive ASP with functions: Decidable queries and effective computation

Alviano¹,

Faber²,

Leone³

2010

Theory and Practice of Logic Programming

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Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASP fs ). We show that query answering in this setting is decidable, if the query is finitely recursive (ASP fs fr ). Our proof yields also an effective method for query evaluation. It is done by extending the magic set technique to ASP fs fr . We show that the magic-set rewritten program is query equivalent to the original one (under both brave and cautious reasoning). Moreover, we prove that the rewritten program is also finitely ground, implying that it is decidable. Importantly, finitely ground programs are evaluable using existing ASP solvers, making the class of ASP fs fr queries usable in practice.

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“…Therefore, the next theorem immediately follows from the characterization of unfounded sets in (Leone et al 1997). …”

Section: Definition 32 (Unfounded Sets)mentioning

confidence: 91%

Section: Related Workmentioning

confidence: 99%

Disjunctive ASP with functions: Decidable queries and effective computation

Alviano¹,

Faber²,

Leone³

2010

Theory and Practice of Logic Programming

Self Cite

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show abstract

“…We express the absence of an external support in an interpretation by adapting the concept of an unfounded set [10,11] to DL-programs.…”

Section: External Support and Unfounded Sets For Dl-programsmentioning

confidence: 99%

Stepwise Debugging of Description-Logic Programs

2012

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Abstract. Description-logic programs (or DL-programs for short) combine logic programs under the answer-set semantics with description logics for semanticweb reasoning. In order for a wider acceptance of the formalism among semanticweb engineers, it is vital to have adequate tools supporting the program development process. In particular, methods for debugging DL-programs are needed. In this paper, we introduce a framework for interactive stepping through a DLprogram as a means for debugging which builds on recent results on stepping for standard answer-set programs. To this end, we provide a computation model for DL-programs using states based on the rules that a user considers as active in the program and the resulting intermediate interpretation. During the course of stepping, the interpretations of the subsequent states evolve towards an answer set of the overall program. Compared to the case of standard answer-set programs, we need more involved notions of states and computations in the presence of DL-atoms. In particular, if non-convex DL-atoms are involved, we have to allow for non-stable computations. Intuitively speaking, we realise this by allowing the user to assume the truth of propositional atoms which must be justified in subsequent states. To keep track of these additional atoms, we extend the well-known notion of an unfounded set for DL-programs.

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“…For ordinary programs, unfounded sets proved to be a fruitful approach [16], which later had been extended to programs with aggregates [11]: an interpretation is an FLP-answer set of some program, if and only if it is unfounded-free, i.e., is disjoint from every unfounded set. Thus to decide whether a candidate is an answer set, one can simply search for unfounded sets, rather than to explicitly construct the reduct and enumerate its models in search for a smaller one.…”

Section: Introductionmentioning

confidence: 99%

Exploiting Unfounded Sets for HEX-Program Evaluation

Eiter

Fink

Krennwallner

et al. 2012

Logics in Artificial Intelligence

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Abstract. HEX programs extend logic programs with external computations through external atoms, whose answer sets are the minimal models of the FaberLeone-Pfeifer-reduct. As already reasoning from Horn programs with nonmonotonic external atoms of polynomial complexity is on the second level of the polynomial hierarchy, answer set checking needs special attention; simply computing reducts and searching for smaller models does not scale well. We thus extend an approach based on unfounded sets to HEX and integrate it in a Conflict Driven Clause Learning framework for HEX program evaluation. It reduces the check to a search for unfounded sets, which is more efficiently implemented as a SAT problem. We give a basic encoding for HEX and show optimizations by additional clauses. Experiments show that the new approach significantly decreases runtime.

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Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation

Cited by 141 publications

References 47 publications

Disjunctive ASP with functions: Decidable queries and effective computation

Disjunctive ASP with functions: Decidable queries and effective computation

Stepwise Debugging of Description-Logic Programs

Exploiting Unfounded Sets for HEX-Program Evaluation

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