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27
Nested expressions in logic programs
 Annals of Mathematics and Artificial Intelligence
, 1999
"... We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are in ..."
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Cited by 114 (13 self)
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We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are introduced as abbreviations. The study of equivalent transformations of programs with nested expressions shows that any such program is equivalent to a set of disjunctive rules, possibly with negation as failure in the heads. The generalized answer set semantics is related to the LloydTopor generalization of Clark's completion and to the logic of minimal belief and negation as failure.
Logic Programming and Knowledge Representation  the AProlog perspective
 Artificial Intelligence
, 2002
"... In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer ..."
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Cited by 87 (0 self)
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In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on wellfounded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.
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 68 (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
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
Reasoning with Prioritized Defaults
 Third International Workshop on Logic Programming and Knowledge Representation, volume 1471 of Lecture Notes in Computer Science
, 1998
"... The purpose of this paper is to investigate the methodology of reasoning with prioritized defaults in the language of logic programs under the answer set semantics. We present a domain independent system of axioms, written as an extended logic program, which defines reasoning with prioritized defaul ..."
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Cited by 48 (4 self)
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The purpose of this paper is to investigate the methodology of reasoning with prioritized defaults in the language of logic programs under the answer set semantics. We present a domain independent system of axioms, written as an extended logic program, which defines reasoning with prioritized defaults. These axioms are used in conjunction with a description of a particular domain encoded in a simple language allowing representation of defaults and their priorities. Such domain descriptions are of course domain dependent and should be specified by the users. We give sufficient conditions for consistency of domain descriptions and illustrate the use of our system by formalizing various examples from the literature. Unlike many other approaches to formalizing reasoning with priorities ours does not require development of the new semantics of the language. Instead, the meaning of statements in the domain description is given by the system of (domain independent) axioms. We believe that in ...
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
Strong Equivalence for Logic Programs and Default Theories (Made Easy)
 In Proc. LPNMR01, LNCS 2173
, 2001
"... Logic programs P and Q are strongly equivalent if, given any logic 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 wit ..."
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Cited by 25 (2 self)
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Logic programs P and Q are strongly equivalent if, given any logic 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. Recently, Lifshitz, Pearce and Valverde showed that Heyting's logic of hereandthere can be used to characterize strong equivalence of logic programs. This paper introduces a more direct characterization, and extends it to default logic. In their paper, Lifschitz, Pearce and Valverde study a very general form of logic programs, called "nested" programs. For the study of strong equivalence of default theories, it is convenient to introduce a corresponding "nested" version of default logic, which generalizes Reiter's default logic.
Characterization of Strongly Equivalent Logic Programs in Intermediate Logics
 in Intermediate Logics. Theory and Practice of Logic Programming
, 2001
"... The nonclassical, nonmonotonic inference relation associated with the stable model semantics for logic programs gives rise to a relationship of strong equivalence between logical programs that can be veri ed in the 3valued Godel logic, G3, the strongest nonclassical intermediate proposition ..."
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Cited by 23 (0 self)
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The nonclassical, nonmonotonic inference relation associated with the stable model semantics for logic programs gives rise to a relationship of strong equivalence between logical programs that can be veri ed in the 3valued Godel logic, G3, the strongest nonclassical intermediate propositional logic (see [10]). In this paper we will show that KC (the logic of :p _ ::p), is the weakest intermediate logic for which strongly equivalent logic programs in a language allowing negations are logically equivalent.
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
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.