The nomore + + Approach to Answer Set Solving

Anger, Christian; Gebser, Martin; Linke, Thomas; Neumann, Anke; Schaub, Torsten

doi:10.1007/11591191_8

Cited by 22 publications

(25 citation statements)

References 14 publications

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“…About splitting heuristic, we have to note that, in their real implementations, cmodels, assat, clasp and NoMore++ can also choose atoms which represent bodies: following [2,3,18], this fact can lead to significant improvements w.r.t. the setting we have analyzed in the paper.…”

Section: Results Application To Other Asp Systemsmentioning

confidence: 99%

“…cmodels, if not restricted to choose on the atoms in , can be implicitly seen as a procedure which allows the decision of the heuristic not only on atoms, but also on bodies, if an atom n r is selected. Given this, [2,3] and, in particular, Corollary 1 in [18] show that by not restricting to the atoms in can significantly contribute to the efficiency of the procedure.…”

Section: Branches(smodels( )) = Branches(cmodels( ))mentioning

confidence: 94%

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On the relation among answer set solvers

Giunchiglia

Leone

Maratea

2008

Ann Math Artif Intell

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In this paper, we study the relation among Answer Set Programming (ASP) systems from a computational point of view. We consider smodels, dlv, and cmodels ASP systems based on stable model semantics, the first two being native ASP systems and the last being a SAT-based system. We first show that smodels, dlv, and cmodels explore search trees with the same branching nodes (assuming, of course, a same branching heuristic) on the class of tight logic programs. Leveraging on the fact that SAT-based systems rely on the deeply studied Davis-LogemannLoveland (dll) algorithm, we derive new complexity results for the ASP procedures. We also show that on nontight programs the SAT-based systems are computationally different from native procedures, and the latter have computational advantages. Moreover, we show that native procedures can guarantee the "correctness" of a reported solution when reaching the leaves of the search trees (i.e., no stability check is needed), while this is not the case for SAT-based procedures on nontight programs. A similar advantage holds for dlv in comparison with smodels if the "well-founded" operator is disabled and only Fitting's operator is used for negative inferences. We finally study the "cost" of achieving such advantages and comment on to what extent the results presented extend to other systems.A preliminary version of a part of the results presented in this work has been published in [25].

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Section: Results Application To Other Asp Systemsmentioning

confidence: 99%

Section: Branches(smodels( )) = Branches(cmodels( ))mentioning

confidence: 94%

On the relation among answer set solvers

Giunchiglia

Leone

Maratea

2008

Ann Math Artif Intell

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“…As argumented in [7], current ASP solver implementations are tightly related to ASP-T, with the intuition that the cut rule is determinised with decision heuristics, while the deduction rules describe the propagation mechanism in ASP solvers. For instance, the noMore++ system [2] is a determinisation of the rules (a)-(g),(h §),(h †),(i §), while smodels [1] applies the same rules with the cut rule restricted to atoms(Π). …”

Section: Asp Tableauxmentioning

confidence: 99%

“…However, there has been an evident lack of theoretical studies into the reasons for the efficiency of current ASP solvers (e.g. [1,2,3,4]). Solver implementations and their inference techniques can be seen as determinisations of the underlying rule-based proof systems.…”

Section: Introductionmentioning

confidence: 99%

Extended ASP Tableaux and Rule Redundancy in Normal Logic Programs

Järvisalo

Oikarinen

Logic Programming

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Abstract. We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for clause sets, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial length proof of a family of normal logic programs {Πn} for which ASP Tableaux has exponential length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the length of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving.

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“…It follows that computing the relevant instances of a rule is a difficult problem, with no polynomial time algorithms, unless P = NP. 2 However, rule instantiation is crucial for the performance of the instantiator and of the overall DLP system, and we thus need a clever algorithm to compute the relevant instances of rules efficiently. Indeed, even if exponential-time in the worst case, a good algorithm may avoid the generation of exponentially-many useless full instantiations.…”

Section: Introductionmentioning

confidence: 99%

Enhancing DLV instantiator by backjumping techniques

Perri

Scarcello

Catalano

et al. 2007

Ann Math Artif Intell

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Disjunctive logic programming (DLP) is a powerful formalism for knowledge representation and reasoning. The high expressiveness of DLP language, together with the recent availability of some efficient DLP system, has favoured the application of DLP in emerging areas like Knowledge Management and Information Integration. These applications have often to deal with huge input data, and have evidenced the need to improve the efficiency of DLP instantiators. Program instantiation is the first phase of a DLP computation; in this phase, variables are replaced by constants to generate a ground program which is then evaluated by propositional algorithms in the second phase of the computation. The instantiation process may be computationally expensive, and in fact its efficiency has been recognized to be a key issue for solving real-world problems by using disjunctive logic programming. Given a program P, a good instantiation for P is a ground program P having precisely the same answer sets as P and such that: (1) P can be computed efficiently from P, and (2) P does not contain "useless" rules, (P is as small as possible) and can thus be evaluated efficiently. In this paper, we present a structure-based backjumping algorithm for the instantiation of disjunctive logic programs, that meets the above requirements. In particular, given a rule r to be grounded, our algorithm exploits A preliminary version of part of this work has been presented at the 10th International Workshop on Non-Monotonic Reasoning (NMR 2004). 196 S. Perri et al. both the semantical and the structural information about r for computing efficiently the ground instances of r, avoiding the generation of "useless" rules. That is, from each general rule r, we compute only a relevant subset of its ground instances, avoiding the generation of "useless" instances, while fully preserving the semantic of the program. We have implemented this algorithm in DLV-the state-of-theart implementation of DLP-and we have carried out an experimentation activity on an ample collection of benchmark problems. The experimental results are very positive: the new technique improves sensibly the efficiency of the DLV system on many program classes.

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The nomore + + Approach to Answer Set Solving

Cited by 22 publications

References 14 publications

On the relation among answer set solvers

On the relation among answer set solvers

Extended ASP Tableaux and Rule Redundancy in Normal Logic Programs

Enhancing DLV instantiator by backjumping techniques

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