Results 1  10
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37
A new perspective on stable models
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (includi ..."
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Cited by 66 (31 self)
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The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar from the definition of circumscription. 1
Strong Equivalence Made Easy: Nested Expressions and Weight Constraints
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... Logic programs P and Q are strongly equivalent if, given any program R, programs P + R and Q + R are equivalent (that is, have the same answer sets). Strong equivalence is convenient for the study of equivalent transformations of logic programs: one can prove that a local change is correct without c ..."
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Cited by 62 (1 self)
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Logic programs P and Q are strongly equivalent if, given any program R, programs P + R and Q + R are equivalent (that is, have the same answer sets). Strong equivalence is convenient for the study of equivalent transformations of logic programs: one can prove that a local change is correct without considering the whole program. Lifschitz, Pearce and Valverde showed that Heyting's logic of hereandthere can be used to characterize strong equivalence for logic programs with nested expressions (which subsume the betterknown extended disjunctive programs). This note considers a simpler, more direct characterization of strong equivalence for such programs, and shows that it can also be applied without modication to the weight constraint programs of Niemel?a and Simons. Thus, this characterization of strong equivalence is convenient for the study of equivalent transformations of logic programs written in the input languages of answer set programming systems dlv and smodels. The note concludes with a brief discussion of results that can be used to automate reasoning about strong equivalence, including a novel encoding that reduces the problem of deciding the strong equivalence of a pair of weight constraint programs to that of deciding the inconsistency of a weight constraint program.
Uniform Equivalence of Logic Programs under the Stable Model Semantics
, 2003
"... In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to sta ..."
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Cited by 50 (13 self)
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In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to stable models (which is the particular case for R = ;), and has an application in program optimization. In this paper, we consider the more liberal notion of uniform equivalence, in which R ranges only over the sets of facts rather than all sets of rules. This notion, which is wellknown, is particularly useful for assessing whether programs P and Q are equivalent as components in a logic program which is modularly structured. We provide semantical characterizations of uniform equivalence for disjunctive logic programs and some restricted classes, and analyze the computational cost of uniform equivalence in the propositional (ground) case. Our results, which naturally extend to answer set semantics, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for inputbased problem solving.
Stable models and circumscription
 Artificial Intelligence
"... The concept of a stable model provided a declarative semantics for Prolog programs with negation as failure and became a starting point for the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programmin ..."
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Cited by 48 (34 self)
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The concept of a stable model provided a declarative semantics for Prolog programs with negation as failure and became a starting point for the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming and, unlike the original definition, refers neither to grounding nor to fixpoints. It is based on a syntactic transformation similar to parallel circumscription. 1
Simplifying logic programs under uniform and strong equivalence
 In LPNMR’04
, 2004
"... Abstract. We consider the simplification of logic programs under the stablemodel semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 198 ..."
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Cited by 37 (22 self)
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Abstract. We consider the simplification of logic programs under the stablemodel semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 1980s, though) and provide semantic foundations for optimizing programs with input. Extending previous work, we investigate syntactic and semantic rules for program transformation, based on proper notions of consequence. We furthermore provide encodings of these notions in answerset programming, and give characterizations of programs which are semantically equivalent to positive and Horn programs, respectively. Finally, we investigate the complexity of program simplification and determining semantical equivalence, showing that the problems range between coNP and Π P 2 complexity, and we present some tractable cases. 1
Semantical Characterizations and Complexity of Equivalences in Answer Set Programming
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2007
"... In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answe ..."
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Cited by 28 (12 self)
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In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answer sets (which is the particular case for R =∅), and has its applications in program optimization, verification, and modular logic programming. In this article, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence where R is a set of facts, rather than a set of rules. This notion, which is wellknown in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong
A generalization of the linzhao theorem
 Annals of Mathematics and Artificial Intelligence
, 2006
"... The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program’s stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definiti ..."
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Cited by 21 (7 self)
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The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program’s stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program’s completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more. 1
Discovering Classes of Strongly Equivalent Logic Programs
 In: Proc. of the Intl. Joint Conf. on Artificial Intelligence (IJCAI’05
, 2005
"... In this paper we apply computeraided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that pre ..."
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Cited by 20 (5 self)
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In this paper we apply computeraided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules. 1.
Twelve Definitions of a Stable Model
"... This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A n ..."
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Cited by 18 (1 self)
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This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas.
Semantic Forgetting in Answer Set Programming
, 2008
"... The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In t ..."
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Cited by 17 (5 self)
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The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.