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ASSAT: Computing Answer Sets of a Logic Program by SAT Solvers
 Artificial Intelligence
, 2002
"... We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program’s completion, we obtain a onetoone corresp ..."
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Cited by 197 (6 self)
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We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program’s completion, we obtain a onetoone correspondence between the answer sets of the program and the models of the resulting propositional theory. In the worst case, there may be an exponential number of loops in a logic program. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based on these results, we implement a system called ASSAT(X), depending on the SAT solver X used, for computing one answer set of a normal logic program with constraints. We test the system on a variety of benchmarks including the graph coloring, the blocks world planning, and Hamiltonian Circuit domains. Our experimental results show that in these domains, for the task of generating one answer set of a normal logic program, our system has a clear edge over the stateofart answer set programming systems Smodels and DLV. 1 1
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 21 (13 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”.
178 Stable Model Semantics and FirstOrder Loop Formulas
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2005
"... Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship betwe ..."
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Cited by 3 (1 self)
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Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship between the firstorder stable model semantics and firstorder loop formulas, and study conditions under which the former can be represented by the latter. In order to facilitate the comparison, we extend the definition of a firstorder loop formula which was limited to a nondisjunctive program, to a disjunctive program and to an arbitrary firstorder theory. Based on the studied relationship we extend the syntax of a logic program with explicit quantifiers, which allows us to do reasoning involving nonHerbrand stable models using firstorder reasoners. Such programs can be viewed as a special class of firstorder theories under the stable model semantics, which yields more succinct loop formulas than the general language due to their restricted syntax. 1.
Causal Theories as Logic Programs
"... Abstract. We show how we can rewrite any causal theory — under the semantics of causal logic due to McCain and Turner — as a logic program in the answer set semantics. Using this translation the models of any causal theory can be computed using answer set solvers. 1 ..."
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Cited by 2 (2 self)
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Abstract. We show how we can rewrite any causal theory — under the semantics of causal logic due to McCain and Turner — as a logic program in the answer set semantics. Using this translation the models of any causal theory can be computed using answer set solvers. 1
Induction in Nonmonotonic Causal Theories for a Domestic Service Robot
"... Abstract. It is always possible to encounter an expected scenario which has not been covered by a certain theory for an action domain. This paper proposes an approach to treating this problem. We reduce this learning task into the problem of modifying a causal theory such that the interpretations co ..."
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Abstract. It is always possible to encounter an expected scenario which has not been covered by a certain theory for an action domain. This paper proposes an approach to treating this problem. We reduce this learning task into the problem of modifying a causal theory such that the interpretations corresponding to new scenarios become a model of the updated theory, while all the original models keep unchanged. We illustrate our approach through a case study based on a domestic service robot, KeJia. 1