Graphs and colorings for answer set programming

Konczak, Kathrin; Linke, Thomas; Schaub, Torsten

doi:10.1017/s1471068405002528

Cited by 14 publications

(20 citation statements)

References 45 publications

(76 reference statements)

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“…We have Cn(GR P (X) ∅ ) = head(GR P (X)), then X = Cn(GR P (X) ∅ ) and, according to (Konczak et al 2006), X is an answer set of P .…”

Section: Resultsmentioning

confidence: 99%

“…(Konczak et al 2006) Let R be a set of rules. R is grounded if there exists an enumeration r i i∈[1.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…(Konczak et al 2006) Let P be a normal logic program and X be an atom set. Then, X is an answer set of P if and only if X = head(GR P (X)) and GR P (X) is grounded.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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`ASPeRiX`, a first-order forward chaining approach for answer set computing

Lefèvre¹,

Béatrix²,

Stéphan³

et al. 2017

Theory and Practice of Logic Programming

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The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first order logic program with default negation. In a preliminary step this program with variables is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the solver. This last one computes (if they exist) one or many answer sets (stable models) of the program, each answer set encoding one solution of the initial problem. Until today, almost all ASP systems apply this two steps computation.In this article, the project ASPeRiX is presented as a first order forward chaining approach for Answer Set Computing. This project was amongst the first to introduce an approach of answer set computing that escapes the preliminary phase of rule instantiation by integrating it in the search process. The methodology applies a forward chaining of first order rules that are grounded on the fly by means of previously produced atoms. Theoretical foundations of the approach are presented, the main algorithms of the ASP solver ASPeRiX are detailed and some experiments and comparisons with existing systems are provided.

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“…We have Cn(GR P (X) ∅ ) = head(GR P (X)), then X = Cn(GR P (X) ∅ ) and, according to (Konczak et al 2006), X is an answer set of P .…”

Section: Resultsmentioning

confidence: 99%

“…(Konczak et al 2006) Let R be a set of rules. R is grounded if there exists an enumeration r i i∈[1.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

`ASPeRiX`, a first-order forward chaining approach for answer set computing

Lefèvre¹,

Béatrix²,

Stéphan³

et al. 2017

Theory and Practice of Logic Programming

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“…In Anger et al (2005) and Konczak et al (2006), rule dependency graphs (a.k.a. In Anger et al (2005) and Konczak et al (2006), rule dependency graphs (a.k.a.…”

Section: Justifications and Debugging Of Prolog Programsmentioning

confidence: 99%

Justifications for logic programs under answer set semantics

Pontelli¹,

Son²,

Elkhatib³

2009

Theory and Practice of Logic Programming

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Link to this article: http://journals.cambridge.org/abstract_S1471068408003633How to cite this article: ENRICO PONTELLI, TRAN CAO SON and OMAR ELKHATIB (2009). Justications for logic programs under answer set semantics. AbstractThe paper introduces the notion of offline justification for answer set programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom with respect to a given answer set. The paper extends also this notion to provide justification of atoms during the computation of an answer set (on-line justification) and presents an integration of online justifications within the computation model of Smodels. Offline and online justifications provide useful tools to enhance understanding of ASP, and they offer a basic data structure to support methodologies and tools for debugging answer set programs. A preliminary implementation has been developed in ASP − PROLOG.Proof. The result is obvious from the definition of offline e-graph and from the fact that J − ∩ TA P (M) ⊆ TA P (M). Proposition 4. Let M 0 , . . . , M k be a general complete computation and S(M 0 ), . . . , S(M k ) be an online justification of the computation. Then, for each atom a in M k , the egraph of a in S(M k ) is an offline justification of a w.r.t. M k and TA P (M k ).Proof. This follows immediately from Lemma 5.2, the construction of the snapshots S(M i ), the fact that M i M k for every k, and M k being an answer set of P .

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“…[Beame and Pitassi 1998;Beame et al 2004;Pipatsrisawat and Darwiche 2011]), ASP lacks formal frameworks for describing inferences conducted by ASP solvers. This has led to great heterogeneity in the description of algorithms for ASP solving, ranging over operational [Anger et al 2005;Calimeri et al 2006;Faber 2002;Konczak et al 2006;Simons et al 2002] and procedural [Gebser et al 2007a;Giunchiglia et al 2006Giunchiglia et al , 2008Lin and Zhao 2004;Lin et al 2006;Ward and Schlipf 2004] characterizations, which complicates identifying fundamental properties of algorithms (such as soundness and completeness) as well as formal comparisons between them.…”

Section: Introductionmentioning

confidence: 99%

Tableau Calculi for Logic Programs under Answer Set Semantics

Gebser

Schaub

2013

ACM Trans. Comput. Logic

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We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions. ACM Reference Format:Gebser, M. and Schaub, T. 2013. Tableau calculi for logic programs under answer set semantics. ACM Trans.

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Graphs and colorings for answer set programming

Cited by 14 publications

References 45 publications

`ASPeRiX`, a first-order forward chaining approach for answer set computing

`ASPeRiX`, a first-order forward chaining approach for answer set computing

Justifications for logic programs under answer set semantics

Tableau Calculi for Logic Programs under Answer Set Semantics

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Graphs and colorings for answer set programming

Cited by 14 publications

References 45 publications

ASPeRiX, a first-order forward chaining approach for answer set computing

ASPeRiX, a first-order forward chaining approach for answer set computing

Justifications for logic programs under answer set semantics

Tableau Calculi for Logic Programs under Answer Set Semantics

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Product

Resources

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`ASPeRiX`, a first-order forward chaining approach for answer set computing

`ASPeRiX`, a first-order forward chaining approach for answer set computing