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Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 242 (20 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
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 77 (32 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
Stable Models and Circumscription
, 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 (includ ..."
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Cited by 71 (37 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 John McCarthy’s definition of circumscription.
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 23 (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.
Nonmonotonic Inheritance, Argumentation and Logic Programming
 In Proc. LPNMR95
, 1995
"... . We study the conceptual relationship between the semantics of nonmonotonic inheritance reasoning and argumentation. We show that the credulous semantics of nonmonotonic inheritance network can be captured by the stable semantics of argumentation. We present a transformation of nonmonotonic inherit ..."
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Cited by 12 (3 self)
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. We study the conceptual relationship between the semantics of nonmonotonic inheritance reasoning and argumentation. We show that the credulous semantics of nonmonotonic inheritance network can be captured by the stable semantics of argumentation. We present a transformation of nonmonotonic inheritance networks into equivalent extended logic programs. 1 Introduction Argumentbased approaches to nonmonotonic reasoning have been intensively studied and became prominent in AI and Logic Programming [6, 21, 24, 1, 20] just recently. But reasoning based on arguments represented as paths, has been studied in nonmonotonic inheritance reasoning, a specific field of nonmonotonic reasoning, from the very first day [30] and then in [13, 15, 27, 28, 29, 26, 25, 8]. Pathbased reasoning approaches to nonmonotonic inheritance networks are widely accepted because they are intuitive and easy to implement. The interesting and surprising problem here is that the argumentbased semantics of nonmonotonic...
FirstOrder Loop Formulas for Normal Logic Programs ∗ Abstract
"... In this paper we extend Lin and Zhao’s notions of loops and loop formulas to normal logic programs that may contain variables. Under our definition, a loop formula of such a logic program is a firstorder sentence. We show that together with Clark’s completion, our notion of firstorder loop formula ..."
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Cited by 12 (5 self)
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In this paper we extend Lin and Zhao’s notions of loops and loop formulas to normal logic programs that may contain variables. Under our definition, a loop formula of such a logic program is a firstorder sentence. We show that together with Clark’s completion, our notion of firstorder loop formulas captures the answer set semantics on the instantiationbasis: for any finite set F of ground facts about the extensional relations of a program P, the answer sets of the ground program obtained by instantiating P using F are exactly the models of the propositional theory obtained by instantiating using F the first order theory consisting of the loop formulas of P and Clark’s completion of the union of P and F. We also prove a theorem about how to check whether a normal logic program with variables has only a finite number of nonequivalent firstorder loops.
A Default Interpretation of Defeasible Network
 In Proc. IJCAI'97
, 1997
"... This paper studies the semantics for the class of all defeasible (inheritance) networks, including cyclic and inconsistent networks using a transformation approach. First we show that defeasible networks can be translated, tractably, to default theories while preserving Horty's offpath credul ..."
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Cited by 8 (1 self)
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This paper studies the semantics for the class of all defeasible (inheritance) networks, including cyclic and inconsistent networks using a transformation approach. First we show that defeasible networks can be translated, tractably, to default theories while preserving Horty's offpath credulous semantics for all consistent networks. Using the existing methods in dealing with the semantics of default logic, we are able to provide a tractable skeptical semantics, the wellfounded semantics, and a new credulous semantics, the regular semantics, both of which are defined for any defeasible network. Furthermore, we show that these semantics are based on the same principle of specificity used by Horty in defining his credulous semantics of defeasible networks. 1 Introduction Two fundamental problems are to be addressed in this paper. First, the semantics of defeasible networks has previously been studied mainly under the assumption that such a network is acyclic and consistent. There is...
From Functional Specifications to Logic Programs
 IN PROCEEDINGS OF THE INTERNATIONAL LOGIC PROGRAMMING SYMPOSIUM (ILPS’97
, 1997
"... The paper investigates a methodology for representing knowledge in logic programming using functional specifications. The methodology is illustrated by an example formalizing several forms of inheritance reasoning. We also introduce and study a new specification constructor which corresponds to remo ..."
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Cited by 7 (5 self)
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The paper investigates a methodology for representing knowledge in logic programming using functional specifications. The methodology is illustrated by an example formalizing several forms of inheritance reasoning. We also introduce and study a new specification constructor which corresponds to removal of the closed world assumption from input predicates of functional specifications.
An Argumentationtheoretic Approach to Reasoning with Specificity
 In KR96
, 1996
"... We present a new argumentationtheoretic approach to default reasoning with specificity. The new approach differs from other approaches in the way priority between defaults is handled. Here, it is context sensitive rather than context independent as in other approaches. We start by showing that any ..."
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Cited by 6 (0 self)
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We present a new argumentationtheoretic approach to default reasoning with specificity. The new approach differs from other approaches in the way priority between defaults is handled. Here, it is context sensitive rather than context independent as in other approaches. We start by showing that any context independent handling of priorities between defaults as advocated in the literature until now is not sufficient to capture general defeasible inheritance reasoning. This motivates the introduction of an argumentation framework for default reasoning with specificity where the context sensitive priorities between defaults are captured by the attacksrelation between the arguments. We present several new and novel results. First we show that our framework subsumes the semantics of defeasible inheritance networks. We then show that the new semantics satisfies core properties of default reasoning such as the conditioning, deduction, reduction, and cumulative propositions 1 . To give a pr...
Characterising equilibrium logic and nested logic programs: Reductions and complexity
, 2009
"... Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kind ..."
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Cited by 6 (2 self)
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Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of secondorder logic, and its formulas are usually referred to as quantified Boolean formulas (QBFs). We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some QBF such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are the consistency problem, brave reasoning, and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions