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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 1038 (74 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
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 343 (10 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 &quot;default&quot;:
The Alternating Fixpoint of Logic Programs with Negation
, 1995
"... The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative ..."
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Cited by 242 (2 self)
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The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative conclusions, the positive conclusions follow (without deriving any further negative ones), by traditional Horn clause semantics. The union of positive and negative conclusions is called the alternating xpoint partial model. The name "alternating" was chosen because the transformation runs in two passes; the first pass transforms an underestimate of the set of negative conclusions into an (intermediate) overestimate; the second pass transforms the overestimate into a new underestimate; the composition of the two passes is monotonic. The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the wellfounded partial model, and (2) that alternating xpoint logic is at least as expressive as xpoint logic on all structures. Also, on finite structures, fixpoint logic is as expressive as alternating fixpoint logic.
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 238 (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.
Impediments to Universal PreferenceBased Default Theories
 Artificial Intelligence
, 1989
"... Research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences. The theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference, in which the reasoner selects maximally preferr ..."
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Cited by 72 (13 self)
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Research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences. The theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference, in which the reasoner selects maximally preferred states of belief. Though researchers have noted some cases of apparent conflict between the preferences supported by different theories, it has been hoped that these special theories of reasoning may be combined into a universal logic of nonmonotonic reasoning. We show that the different categories of preferences conflict more than has been realized, and adapt formal results from social choice theory to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning. Our results can be interpreted as demonstrating that, within the preferential framework, we cannot expect much improvement on the rigid lexicographic priority mechanisms that have been proposed for conflict resolution.
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 a ..."
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Cited by 35 (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...
Artificial Intelligence, Logic And Formalizing Common Sense
 Philosophical Logic and Artificial Intelligence
, 1990
"... This article discusses the problems and difficulties, the results so far, and some improvements in logic and logical languages that may be required to formalize common sense. Fundamental conceptual advances are almost certainly required. The object of the paper is to get more help for AI from philos ..."
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Cited by 33 (5 self)
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This article discusses the problems and difficulties, the results so far, and some improvements in logic and logical languages that may be required to formalize common sense. Fundamental conceptual advances are almost certainly required. The object of the paper is to get more help for AI from philosophical logicians. Some of the requested help will be mostly philosophical and some will be logical. Likewise the concrete AI approach may fertilize philosophical logic as physics has repeatedly fertilized mathematics.
Non Monotonic Reasoning
, 1997
"... These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series ..."
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Cited by 33 (1 self)
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These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series
Logicbased Knowledge Representation
 Artificial Intelligence Today, Recent Trends and Developments, number 1600 in Lecture Notes in Computer Science
, 1996
"... . After a short analysis of the requirements that a knowledge representation language must satisfy, we introduce Description Logics, Modal Logics, and Nonmonotonic Logics as formalisms for representing terminological knowledge, timedependent or subjective knowledge, and incomplete knowledge res ..."
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Cited by 31 (0 self)
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. After a short analysis of the requirements that a knowledge representation language must satisfy, we introduce Description Logics, Modal Logics, and Nonmonotonic Logics as formalisms for representing terminological knowledge, timedependent or subjective knowledge, and incomplete knowledge respectively. At the end of each section, we briefly comment on the connection to Logic Programming. 1 Introduction This section is concerned with the question under which conditions one may rightfully claim to have represented knowledge about an application domain, and not just stored data occurring in this domain. 1 In the early days of Artificial Intelligence and Knowledge Representation, there was a heated discussion on whether logic can at all be used as a formalism for Knowledge Representation (see e.g. [135, 91, 92]). One aspect of the requirements on knowledge representation formalisms that can be derived from the considerations in this section is very well satisfied by logical for...