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88
On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and nperson games
 Artificial Intelligence
, 1995
"... The purpose of this paper is to study the fundamental mechanism humans use in argumentation and its role in different major approaches to commonsense reasoning in AI and logic programming. We present three novel results: We develop a theory for argumentation in which the acceptability of arguments i ..."
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Cited by 789 (11 self)
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The purpose of this paper is to study the fundamental mechanism humans use in argumentation and its role in different major approaches to commonsense reasoning in AI and logic programming. We present three novel results: We develop a theory for argumentation in which the acceptability of arguments is precisely defined. We show that logic programming and nonmonotonic reasoning in AI are different forms of argumentation. We show that argumentation can be viewed as a special form of logic programming with negation as failure. This result introduces a general method for generating metainterpreters for argumentation systems. 1.
Representing Action and Change by Logic Programs
 Journal of Logic Programming
, 1993
"... We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics ..."
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Cited by 380 (26 self)
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We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics of action based on states and transition functions. 1 Introduction This paper extends the work of Eshghi and Kowalski [6], Evans [7] and Apt and Bezem [1] on representing properties of actions in logic programming languages with negation as failure. Our goal is to overcome some of the limitations of the earlier work. The existing formalizations of action in logic programming are adequate for only the simplest kind of temporal reasoning"temporal projection." In a temporal projection problem, we are given a description of the initial state of the world, and use properties of actions to determine what the world will look like after a series of actions is performed. Moreover, the existing ...
Splitting a Logic Program
 Principles of Knowledge Representation
, 1994
"... In many cases, a logic program can be divided into two parts, so that one of them, the \bottom " part, does not refer to the predicates de ned in the \top " part. The \bottom " rules can be used then for the evaluation of the predicates that they de ne, and the computed va ..."
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Cited by 260 (15 self)
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In many cases, a logic program can be divided into two parts, so that one of them, the \bottom &quot; part, does not refer to the predicates de ned in the \top &quot; part. The \bottom &quot; rules can be used then for the evaluation of the predicates that they de ne, and the computed values can be used to simplify the \top &quot; de nitions. We discuss this idea of splitting a program in the context of the answer set semantics. The main theorem shows how computing the answer sets for a program can be simpli ed when the program is split into parts. The programs covered by the theorem may use both negation as failure and classical negation, and their rules may have disjunctive heads. The usefulness of the concept of splitting for the investigation of answer sets is illustrated by several applications. First, we show that a conservative extension theorem by Gelfond and Przymusinska and a theorem on the closed world assumption by Gelfond and Lifschitz are easy consequences of the splitting theorem. Second, (locally) strati ed programs are shown to have a simple characterization in terms of splitting. The existence and uniqueness of an answer set for such a program can be easily derived from this characterization. Third, we relate the idea of splitting to the notion of orderconsistency. 1
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 227 (21 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.
Consistency of Clark's Completion and Existence of Stable Models
, 1994
"... The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the wellsupported Herbrand models of the program, and a new fixed point semantics that formalizes the bottomup truth mainten ..."
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Cited by 145 (3 self)
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The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the wellsupported Herbrand models of the program, and a new fixed point semantics that formalizes the bottomup truth maintenance procedure of [4] is based on that characterization. Here we focus our attention on the abstract notion of wellsupportedness in order to derive sufficient conditions for the existence of stable models. We show that if a logic program \Pi is positiveorderconsistent (i.e. there is no infinite decreasing chain w.r.t. the positive dependencies in the atom dependency graph of \Pi) then the Herbrand models of comp(\Pi) coincide with the stable models of \Pi. From this result and the ones of [10] [17] [2] on the consistency of Clark's completion, we obtain sufficient conditions for the existence of stable models for positiveorderconsistent programs. Then we show that a negative cycle free ...
Negation and Constraint Logic Programming
, 1995
"... Almost all constraint logic programming systems include negation, yet nowhere has a sound operational model for negation in CLP been discussed. The SLDNF approach of only allowing ground negative subgoals to execute is very restrictive in constraint logic programming where most variables appearing i ..."
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Cited by 121 (2 self)
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Almost all constraint logic programming systems include negation, yet nowhere has a sound operational model for negation in CLP been discussed. The SLDNF approach of only allowing ground negative subgoals to execute is very restrictive in constraint logic programming where most variables appearing in a derivation never become ground. By describing a scheme for constructive negation in constraint logic programming we give a sound and complete operational model for negation in these languages. Constructive negation was first formulated for logic programming in the Herbrand Universe and involves introducing disequality constraints. Constraint logic programming thus provides a much more natural framework for describing constructive negation. In this paper we describe a framework for constructive negation for constraint logic programming over arbitrary structures which is sound and complete with respect to the threevalued consequences of the completion of a program. Through this descriptio...
Fixpoint semantics for logic programming  a survey
, 2000
"... The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close para ..."
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Cited by 105 (0 self)
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The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
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 u ..."
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Cited by 85 (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.
Representing Knowledge in AProlog
"... In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of AProlog, can be used to represent various types of knowledge about the world. By way of example ..."
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Cited by 60 (1 self)
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In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of AProlog, can be used to represent various types of knowledge about the world. By way of example we demonstrate how the corresponding representations together with inference mechanisms associated with AProlog can be used to solve various programming tasks.
What is Failure? An Approach to Constructive Negation
, 1994
"... A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction of failed ..."
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Cited by 54 (4 self)
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A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction of failed trees for some instances of a negated query. For this purpose a generalization of the standard notion of a failed tree is needed. We show that a straightforward generalization leads to unsoundness and present a correct one. The method is applicable to arbitrary normal programs. If finitely failed trees are concerned then its semantics is given by Clark completion in 3valued logic (and our approach is a proper extension of SLDNFresolution). If infinite failed trees are allowed then we obtain a method for the wellfounded semantics. In both cases soundness and completeness are proved.