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31
Answer Sets for Propositional Theories
 In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR
, 2005
"... Abstract. Equilibrium logic, introduced by David Pearce, extends the concept of an answer set from logic programs to arbitrary sets of formulas. Logic programs correspond to the special case in which every formula is a “rule ” — an implication that has no implications in the antecedent (body) and c ..."
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Cited by 70 (8 self)
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Abstract. Equilibrium logic, introduced by David Pearce, extends the concept of an answer set from logic programs to arbitrary sets of formulas. Logic programs correspond to the special case in which every formula is a “rule ” — an implication that has no implications in the antecedent (body) and consequent (head). The semantics of equilibrium logic looks very different from the usual definitions of an answer set in logic programming, as it is based on Kripke models. In this paper we propose a new definition of equilibrium logic which uses the concept of a reduct, as in the standard definition of an answer set. Second, we apply the generalized concept of an answer set to the problem of defining the semantics of aggregates in answer set programming. We propose, in particular, a semantics for weight constraints that covers the problematic case of negative weights. Our semantics of aggregates is an extension of the approach due to Faber, Leone, and Pfeifer to a language with choice rules and, more generally, arbitrary rules with nested expressions. 1
Abduction in Logic Programming: A New Definition and an Abductive Procedure Based on Rewriting
 Artificial Intelligence
, 2002
"... We propose a new definition of abduction in logic programming, and contrast it with that of Kakas and Mancarella's. We then introduce a rewriting system for answering queries and generating explanations, and show that it is both sound and complete under the partial stable model semantics a ..."
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Cited by 20 (5 self)
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We propose a new definition of abduction in logic programming, and contrast it with that of Kakas and Mancarella's. We then introduce a rewriting system for answering queries and generating explanations, and show that it is both sound and complete under the partial stable model semantics and sound and complete under the answer set semantics when the underlying program is socalled oddloop free. We discuss an application of the work to a problem in reasoning about actions and provide some experimental results. 1 Abduction in logic programming In general, given a background theory T , and an observation q to explain, an abduction of q w.r.t. T is a theory \Pi such that \Pi [ T j= q. Normally, we want to put some additional conditions on \Pi, such as that it is consistent with T and contains only those propositions called abducibles. For instance, in propositional logic, given a background theory T , a set A of assumptions or abducibles, and a proposition q, an explanation S...
USASmart: Improving the Quality of Plans in Answer Set Planning
 IN PADL’04, LECTURE NOTES IN ARTIFICIAL INTELLIGENCE (LNCS
, 2004
"... In this paper we show how CRProlog, a recent extension of AProlog, was used in the successor of USAAdvisor (USASmart) in order to improve the quality of the plans returned. The general problem that we address is that of improving the quality of plans by taking in consideration statements that ..."
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Cited by 13 (4 self)
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In this paper we show how CRProlog, a recent extension of AProlog, was used in the successor of USAAdvisor (USASmart) in order to improve the quality of the plans returned. The general problem that we address is that of improving the quality of plans by taking in consideration statements that describe "most desirable" plans. We believe that USASmart proves that CRProlog provides a simple, elegant, and flexible solution to this problem, and can be easily applied to any planning domain. We also discuss how alternative extensions of AProlog can be used to obtain similar results.
What's in a Model? Epistemological analysis of Logic Programming
 CeurWS
, 2003
"... The paper is an epistemological analysis of logic programming and shows an epistemological ambiguity. Many different logic programming formalisms and semantics have been proposed. Hence, logic programming can be seen as a family of formal logics, each induced by a pair of a syntax and a semantics ..."
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Cited by 8 (3 self)
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The paper is an epistemological analysis of logic programming and shows an epistemological ambiguity. Many different logic programming formalisms and semantics have been proposed. Hence, logic programming can be seen as a family of formal logics, each induced by a pair of a syntax and a semantics, and each having a different declarative reading. However, we may expect that (a) if a program belongs to different logics of this family and has the same formal semantics in these logics, then the declarative meaning attributed to this program in the different logics is equivalent, and (b) that one and the same logic in this family has not been associated with distinct declarative readings.
Twoliteral logic programs and satisfiability representation of stable models: A comparison
 In Proc. 15th Canadian Conference on AI, LNCS
, 2002
"... Logic programming with the stable model semantics has been proposed as a constraint programming paradigm for solving constraint satisfaction and other combinatorial problems. In such a language one writes functionfree logic programs with negation. Such a program is instantiated to a ground program ..."
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Cited by 7 (3 self)
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Logic programming with the stable model semantics has been proposed as a constraint programming paradigm for solving constraint satisfaction and other combinatorial problems. In such a language one writes functionfree logic programs with negation. Such a program is instantiated to a ground program from which the stable models are computed. In this paper, we identify a class of logic programs for which the current techniques in solving SAT problems can be adopted for the computation of stable models efficiently. These logic programs are called 2literal programs where each rule or constraint consists of at most two literals. Many logic programming encodings of graphtheoretic, combinatorial problems given in the literature fall into the class of 2literal programs. We show that a 2literal program can be translated to a SAT instance without using extra variables. We report and compare experimental results on solving a number of benchmarks by a stable model generator and by a SAT solver. 1
Splitting an operator: An algebraic modularity result and its application to autoepistemic logic
 In Proceedings of International Workshop on NonMonotonic Reasoning
, 2004
"... It is well known that it is possible to split certain autoepistemic theories under the semantics of expansions, i.e. to divide such a theory into a number of different “levels”, such that the models of the entire theory can be constructed by incrementally constructing models for each level. Similar ..."
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Cited by 6 (3 self)
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It is well known that it is possible to split certain autoepistemic theories under the semantics of expansions, i.e. to divide such a theory into a number of different “levels”, such that the models of the entire theory can be constructed by incrementally constructing models for each level. Similar results exist for other nonmonotonic formalisms, such as logic programming and default logic. In this work, we present a general, algebraic theory of splitting under a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of this approach, by applying our results to autoepistemic logic.
Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
 ACM Transactions on computational logic (TOCL
, 2005
"... Abstract. It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for ea ..."
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Cited by 4 (4 self)
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Abstract. It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other nonmonotonic formalisms, such as autoepistemic logic and default logic. In this work, we present a general, algebraic splitting theory for logics with a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of these results, by generalizing existing results for logic programming, autoepistemic logic and default logic. 1
Logic Programs with Propositional Connectives and Aggregates
, 2008
"... Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory semantics of aggregates turned out to be a difficult problem, and i ..."
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Cited by 3 (0 self)
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Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory semantics of aggregates turned out to be a difficult problem, and in this paper we propose a new approach, based on an analogy between aggregates and propositional connectives. First, we extend the definition of an answer set/stable model to cover arbitrary propositional theories; then we define aggregates on top of them both as primitive constructs and as abbreviations for formulas. Our definition of an aggregate combines expressiveness and simplicity, and it inherits many theorems about programs with nested expressions, such as theorems about strong equivalence and splitting. 1
Relativized Hyperequivalence of Logic Programs for Modular Programming
"... Abstract. A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, indep ..."
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Cited by 3 (2 self)
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Abstract. A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, independently of each other, the head and body alphabets in context programs. We study relativized hyperequivalence for the three semantics of logic programs given by stable, supported and supported minimal models. For each semantics, we identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyperequivalence relative to contexts where the head and body alphabets are specified directly has been studied before. In this paper, we establish the complexity of deciding relativized hyperequivalence wrt the three other types of context programs. 1