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33
Classical Negation in Logic Programs and Disjunctive Databases
 New Generation Computing
, 1991
"... An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic progra ..."
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Cited by 853 (75 self)
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An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negationasfailure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...
Circumscription
, 1996
"... The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default": ..."
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Cited by 324 (13 self)
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The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default":
Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 245 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
Computing circumscription revisited: A reduction algorithm
 J. Automated Reasoning
, 1997
"... In recent years, a great deal of attention has been devoted to logics of "commonsense" reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but di cult to apply in practice. The major reason for this is ..."
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Cited by 44 (14 self)
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In recent years, a great deal of attention has been devoted to logics of "commonsense" reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but di cult to apply in practice. The major reason for this is the 2ndorder nature of circumscription axioms and the di culty in nding proper substitutions of predicate expressions for predicate variables. One solution to this problem is to compile, where possible, 2ndorder formulas into equivalent 1storder formulas. Although some progress has been made using this approach, the results are not as strong as one might desire and they are isolated in nature. In this article, we provide a general method which can be used in an algorithmic manner to reduce circumscription axioms to 1storder formulas. The algorithm takes as input an arbitrary 2ndorder formula and either returns as output an equivalent 1storder formula, or terminates with failure. The class of 2ndorder formulas, and analogously the class of circumscriptive theories which can be reduced, provably subsumes those covered by existing results. We demonstrate the generality of the algorithm using circumscriptive theories with mixed quanti ers (some involving Skolemization), variable constants, nonseparated formulas, and formulas with nary predicate variables. In addition, we analyze the strength of the algorithm and compare it with existing approaches providing formal subsumption results.
Prioritized Logic Programming and Its Application to Commonsense Reasoning
, 2000
"... Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite informa ..."
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Cited by 41 (1 self)
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Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce nondeterminism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation. Keywords: prioritized logic programs, abduction, default reasoning, prioritized circumscription 1 Introduction In commonsense reasoning a theory is usually assumed incomplete and may contain indefinite or conflicting knowledge. Under such circumstances, priority information is useful to select appropriate know...
On Open Defaults
, 1990
"... In Reiter's default logic, the parameters of a default are treated as metavariables for ground terms. We propose an alternative definition of an extension for a default theory, which handles parameters as genuine object variables. The new form of default logic may be preferable when the domain closu ..."
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Cited by 41 (5 self)
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In Reiter's default logic, the parameters of a default are treated as metavariables for ground terms. We propose an alternative definition of an extension for a default theory, which handles parameters as genuine object variables. The new form of default logic may be preferable when the domain closure assumption is not postulated. It stands in a particularly simple relation to circumscription. Like circumscription, it can be viewed as a syntactic transformation of formulas of higher order logic. 1 Introduction Default logic [Reiter, 1980] is one of the most expressive and most widely used nonmonotonic formalisms. In one respect, however, the main definition of default logic, that of an extension, is not entirely satisfactory. Recall that a default ff : fi 1 ; : : : ; fi m =fl (1) is open if it contains free variables, and closed otherwise. The concept of an extension is defined in two steps: It is first introduced, by means of a fixpoint construction, for default theories without op...
Representing Priorities in Logic Programs
, 1996
"... Reasoning with priorities is a central topic in knowledge representation. A number of techniques for prioritized reasoning have been developed in the field of AI, but existing logic programming lacks the mechanism of explicit representation of priorities in a program. In this paper, we introduce a f ..."
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Cited by 37 (3 self)
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Reasoning with priorities is a central topic in knowledge representation. A number of techniques for prioritized reasoning have been developed in the field of AI, but existing logic programming lacks the mechanism of explicit representation of priorities in a program. In this paper, we introduce a framework for representing priorities in logic programming. Prioritized logic programming represents preference knowledge more naturally than stratified programs, and is used to reduce nondeterminism in logic programming. Moreover, it can realize various forms of commonsense reasoning such as abduction, default reasoning, and prioritized circumscription. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation. 1 Introduction Recent extensions of logic programming provide mechanisms of handling incomplete knowledge in many ways as normal, disjunctive, abductive, and extended logic programs. In these extended framewo...
ThreeValued NonMonotonic Formalisms And Semantics of Logic Programs
 Artificial Intelligence
, 1991
"... We introduce 3valued extensions of major nonmonotonic formalisms and we prove that the recently proposed wellfounded semantics of logic programs is equivalent, for arbitrary logic programs, to 3valued forms of McCarthy's circumscription, Reiter's closed world assumption, Moore's autoepistemic lo ..."
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Cited by 34 (6 self)
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We introduce 3valued extensions of major nonmonotonic formalisms and we prove that the recently proposed wellfounded semantics of logic programs is equivalent, for arbitrary logic programs, to 3valued forms of McCarthy's circumscription, Reiter's closed world assumption, Moore's autoepistemic logic and Reiter's default theory. This result not only provides a further justification of the wellfounded semantics, as a natural extension of the perfect model semantics from the class of stratified programs to the class of all logic programs, but it also establishes the class of all logic programs as a large class of theories, for which natural forms of all four nonmonotonic formalisms coincide. It also paves the way for using efficient computation methods, developed for logic programming, as inference mechanisms for nonmonotonic reasoning. 1 Introduction A precise meaning or semantics must be associated with any logic program or a deductive database in order to provide its declarative...
Prolegomena to Logic Programming for NonMonotonic Reasoning
"... The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, b ..."
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Cited by 22 (16 self)
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The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, background history, important themes, bridges to other areas, and a common technical platform of the principal formalisms and approaches, augmented with examples. In the
Super Logic Programs
, 1996
"... Recently, considerable interest and research e#ort has been given to the problem of finding a suitable extension of the logic programming paradigm beyond the class of normal logic programs. In order to demonstrate that a class of programs can be justifiably called an extension of logic programs one ..."
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Cited by 21 (2 self)
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Recently, considerable interest and research e#ort has been given to the problem of finding a suitable extension of the logic programming paradigm beyond the class of normal logic programs. In order to demonstrate that a class of programs can be justifiably called an extension of logic programs one should be able to argue that: . the proposed syntax of such programs resembles the syntax of logic programs but it applies to a significantly broader class of programs; . the proposed semantics of such programs constitutes an intuitively natural extension of the semantics of normal logic programs; . there exists a reasonably simple procedural mechanism allowing, at least in principle, to compute the semantics; . the proposed class of programs and their semantics is a special case of a more general nonmonotonic formalism which clearly links it to other wellestablished nonmonotonic formalisms. In this paper we propose a specific class of extended logic programs which will be (modestly) called super logic programs or just superprograms. We will argue that the class of superprograms satisfies all of the above conditions, and, in addition, is su#ciently flexible to allow various applicationdependent extensions and modifications. We also provide a brief description of a Prolog implementation of a queryanswering interpreter for the class of superprograms which is available via FTP and WWW. Keywords: NonMonotonic Reasoning, Logics of Knowledge and Beliefs, Semantics of Logic Programs and Deductive Databases. # An extended abstract of this paper appeared in the Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (KR'96), Boston, Massachusetts, 1996, pp. 529541. + Partially supported by the National Science Fou...