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45
Answer set programming based on propositional satisfiability
 Journal of Automated Reasoning, 36:345–377, Gelfond
"... Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic pro ..."
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Cited by 67 (11 self)
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Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas. In this paper, we present a SATbased procedure, called ASPSAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASPSAT. From a practical perspective, we have (i) implemented ASPSAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other stateoftheart answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on “small but hard ” problems are ineffective on “big but easy” problems and vice versa.
Disjunctive Answer Set Programming via Satisfiability
 LOGIC PROGRAMMING AND NONMONOTONIC REASONING — 8TH INTERNATIONAL CONFERENCE, LPNMR’05, DIAMANTE, ITALY, SEPTEMBER 2005, PROCEEDINGS. VOLUME 3662 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answe ..."
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Cited by 36 (2 self)
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Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answer sets for disjunctive logic programs. We implement two different ways of SAT solver invocation used in nondisjunctive answer set programming. The algorithms are based on the definition of completion for disjunctive programs and the extension of loop formula to the disjunctive case. We propose the necessary modifications to the algorithms known for nondisjunctive programs in order to adapt them to the disjunctive case and demonstrate their implementation based on system CMODELS.
Loop formulas for circumscription
 Artificial Intelligence
, 2004
"... Clark’s completion is a simple nonmonotonic formalism and a special case of many nonmonotonic logics. Recently there has been work on extending completion with “loop formulas ” so that general cases of nonmonotonic logics such as logic programs (under the answer set semantics) and McCain–Turner caus ..."
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Cited by 26 (16 self)
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Clark’s completion is a simple nonmonotonic formalism and a special case of many nonmonotonic logics. Recently there has been work on extending completion with “loop formulas ” so that general cases of nonmonotonic logics such as logic programs (under the answer set semantics) and McCain–Turner causal logic can be characterized by propositional logic in the form of “completion + loop formulas”. In this paper, we show that the idea is applicable to McCarthy’s circumscription in the propositional case. We also show how to embed propositional circumscription in logic programs and in causal logic, inspired by the uniform characterization of “completion + loop formulas”.
A comparison of CLP(FD) and ASP solutions to NPcomplete problems
 In Proceedings of the Twentyfirst International Conference on Logic Programming (ICLP 2005
, 2005
"... Abstract. This paper presents experimental comparisons between declarative encodings of various computationally hard problems in both Answer Set Programming (ASP) and Constraint Logic Programming (CLP) over finite domains. The objective is to identify how the solvers in the two domains respond to di ..."
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Cited by 25 (8 self)
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Abstract. This paper presents experimental comparisons between declarative encodings of various computationally hard problems in both Answer Set Programming (ASP) and Constraint Logic Programming (CLP) over finite domains. The objective is to identify how the solvers in the two domains respond to different problems, highlighting strengths and weaknesses of their implementations and suggesting criteria for choosing one approach versus the other. Ultimately, the work in this paper is expected to lay the ground for transfer of concepts between the two domains (e.g., suggesting ways to use CLP in the execution of ASP). 1
cmodels  satbased disjunctive answer set solver
 of Lecture Notes in Computer Science
, 2005
"... Disjunctive logic programming under the stable model semantics [GL91] is a new ..."
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Cited by 21 (6 self)
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Disjunctive logic programming under the stable model semantics [GL91] is a new
Answer set programming for representing and reasoning about virtual institutions
 In Computational Logic in MultiAgent Systems (CLIMAVII
, 2006
"... Abstract. It is recognised that institutions are potentially powerful means for making agent interactions effective and efficient, but institutions will only really be useful when, as in other safetycritical scenarios, it is possible to prove that particular properties do or do not hold for all pos ..."
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Cited by 18 (10 self)
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Abstract. It is recognised that institutions are potentially powerful means for making agent interactions effective and efficient, but institutions will only really be useful when, as in other safetycritical scenarios, it is possible to prove that particular properties do or do not hold for all possible encounters. In contrast to symbolic modelchecking, answer set programming permits the statement of problems and queries in domainspecific terms as executable logic programs, thus eliminating the gap between specification and verification language. Furthermore, results are presented in the same terms. In this paper we describe the use of answer set programs as an institutional modelling technique. We demonstrate that our institutional model can be intuitively be mapped into an answer set program such that the ordered event traces of the former can be obtained as the answer sets of the latter, allowing for an easy way to query properties of models. 1
Elementary sets for logic programs
 In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI
, 2006
"... By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark’s completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the LinZhao theorem remains corr ..."
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Cited by 17 (13 self)
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By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark’s completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the LinZhao theorem remains correct even if we restrict loop formulas to a special class of loops called “elementary loops. ” In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop for nondisjunctive programs, but is simpler, and, unlike elementary loops, can be extended to disjunctive programs without producing unintuitive results. We show that the maximal unfounded elementary sets for the “relevant ” part of a program are exactly the minimal sets among the nonempty unfounded sets. We also present a graphtheoretic characterization of elementary sets for nondisjunctive programs, which is simpler than the one proposed in (Gebser & Schaub 2005). Unlike the case of nondisjunctive programs, we show that the problem of deciding an elementary set is coNPcomplete for disjunctive programs.
Multivalued Action Languages with Constraints in CLP(FD)
"... Abstract. Action description languages, such as A and B [6], are expressive instruments introduced for formalizing planning domains and problems. The paper starts by proposing a methodology to encode an action language (with conditional effects and static causal laws), a slight variation of B, using ..."
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Cited by 15 (10 self)
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Abstract. Action description languages, such as A and B [6], are expressive instruments introduced for formalizing planning domains and problems. The paper starts by proposing a methodology to encode an action language (with conditional effects and static causal laws), a slight variation of B, using Constraint Logic Programming over Finite Domains. The approach is then generalized to lift the use of constraints to the level of the action language itself. A prototype implementation has been developed, and the preliminary results are presented and discussed. 1
On the relation between answer set and SAT procedures (or, between cmodels and smodels)
 PROCEEDINGS OF THE TWENTYFIRST INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 2005
"... Answer Set Programming (ASP) is a declarative paradigm for solving search problems. Stateoftheart systems for ASP include SMODELS, DLV, CMODELS, and ASSAT. In this paper, our goal is to study the computational properties of such systems both from a theoretical and an experimental point of view. ..."
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Cited by 13 (0 self)
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Answer Set Programming (ASP) is a declarative paradigm for solving search problems. Stateoftheart systems for ASP include SMODELS, DLV, CMODELS, and ASSAT. In this paper, our goal is to study the computational properties of such systems both from a theoretical and an experimental point of view. From the theoretical point of view, we start our analysis with CMODELS and SMODELS. We show that though these two systems are apparently different, they are equivalent on a significant class of programs, called tight. By equivalent, we mean that they explore search trees with the same branching nodes, (assuming, of course, a same branching heuristic). Given our result and that the CMODELS search engine is based on the Davis Logemann Loveland procedure (DLL) for propositional satisfiability (SAT), we are able to establish that many of the properties holding for DLL also hold for CMODELS and thus for SMODELS. On the other hand, we also show that there exist classes of nontight programs which are exponentially hard for CMODELS, but “easy” for SMODELS. We also discuss how our results extend to other
Temporal Phylogenetic Networks and Logic Programming
"... The concept of a temporal phylogenetic network is a mathematical model of evolution of a family of natural languages. It takes into account the fact that languages can trade their characteristics with each other when linguistic communities are in contact, and also that a contact is only possible whe ..."
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Cited by 11 (3 self)
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The concept of a temporal phylogenetic network is a mathematical model of evolution of a family of natural languages. It takes into account the fact that languages can trade their characteristics with each other when linguistic communities are in contact, and also that a contact is only possible when the languages are spoken at the same time. We show how computational methods of answer set programming and constraint logic programming can be used to generate plausible conjectures about contacts between prehistoric linguistic communities, and illustrate our approach by applying it to the evolutionary history of IndoEuropean languages. 1