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74
The Family of Stable Models
, 1993
"... The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the well ..."
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Cited by 54 (4 self)
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The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the wellfounded model. There is also a dual largest stable model, S k P , which has not been considered before. There is another ordering based on degree of truth. Taking the meet and the join, in the truth ordering, of the two extreme stable models s k P and S k P just mentioned, yields the alternating fixed points of [29], denoted s t P and S t P here. From s t P and S t P in turn, s k P and S k P can be produced again, using the meet and join of the knowledge ordering. All stable models are bounded by these four valuations. Further, the methods of proof apply not just to logic programs considered classically, but to logic programs over any bilattice meeting certain co...
Uniform Semantic Treatment of Default and Autoepistemic Logics
 ARTIFICIAL INTELLIGENCE
, 2000
"... We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the latti ..."
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Cited by 41 (23 self)
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We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise onetoone correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.
Experimenting with Nonmonotonic Reasoning
 IN PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1995
"... In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic pr ..."
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Cited by 37 (6 self)
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In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic program or a default theory from its identifier. Hence, exchanging test cases requires only exchanging identifiers. TheoryBase can generate a large variety of examples of default theories and logic programs. We believe that its universal adoption may significantly advance experimental studies of nonmonotonic reasoning systems.
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 31 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at
WellFounded and Stationary Models of Logic Programs
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 1994
"... ..."
Antitonic Logic Programs
, 2001
"... In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, ..."
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Cited by 30 (10 self)
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In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3, 4]. However, none of these semantics define a form of nonmonotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Wellfounded Model alike semantics.
Towards Constraint Satisfaction through Logic Programs and the Stable Model Semantics
, 1997
"... Logic programs with the stable model semantics can be thought of as a new paradigm for constraint satisfaction, where the rules of a program are seen as constraints on the stable models. In this work the paradigm is realized by developing an efficient procedure for computing the stable models of gro ..."
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Cited by 27 (1 self)
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Logic programs with the stable model semantics can be thought of as a new paradigm for constraint satisfaction, where the rules of a program are seen as constraints on the stable models. In this work the paradigm is realized by developing an efficient procedure for computing the stable models of ground logic programs. A strong pruning technique based on two deductive closures is introduced. The technique is further strengthened by the introduction of backjumping, which is an improvement over chronological backtracking, and lookahead, a new pruning method. Moreover, a strong heuristic is derived. The two deductive closures are given lineartime implementations that provide a linearspace implementation method for the decision procedure. A high lower bound on the least upper bound on the complexity of the procedure is found. In order to generalize the procedure such that it can handle programs with variables, an algorithm for grounding a functionfree range restricted logic program that...
An Overview of Nonmonotonic Reasoning and Logic Programming
 Journal of Logic Programming, Special Issue
, 1993
"... The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the prehistory of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic ..."
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Cited by 27 (2 self)
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The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the prehistory of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...
Bottomup Evaluation and Query Optimization of WellFounded Models
 Theoretical Computer Science
, 1995
"... We present a bottomup operational procedure for computing wellfounded models of allowed programs with negation. This procedure provides a practical method of handling programs that involve unstratified negation in a manner that may be mixed with other evaluation approaches, such as seminaive eval ..."
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Cited by 26 (1 self)
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We present a bottomup operational procedure for computing wellfounded models of allowed programs with negation. This procedure provides a practical method of handling programs that involve unstratified negation in a manner that may be mixed with other evaluation approaches, such as seminaive evaluation and various program transformations. We define classes of programs and sideways information passing strategies (sips) for which the magic sets transformation preserves wellfounded models with respect to the query. The classes of programs and sips we consider strictly subsume those already considered in the literature, and include stratified programs (with any choice of sips), lefttoright modularly stratified programs (with leftto right sips) and arbitrary programs (with wellfounded sips). For these programs and sips, our procedure for computing wellfounded models is applicable to the rewritten programs, thus allowing increased efficiency by specializing a program for a query. Fi...
Stationary Default Extensions
 Fundamenta Informaticae
, 1992
"... this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \Delta has at least one stationar ..."
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Cited by 24 (0 self)
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this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \Delta has at least one stationary extension and among its extensions there always exists the least stationary extension E \Delta . The (cautious) stationary semantics S (\Delta) of a default theory \Delta, i.e., the theory consisting of sentences which are true in all stationary extensions of \Delta, is always welldefined, and, since it clearly coincides with the least stationary extension E \Delta of \Delta, it is itself a stationary extension of \Delta. The stationary semantics of default theories is always cumulatively monotonic and it can be computed by means of a natural iterative procedure. The complexity of its computation essentially coincides with the computational complexity of satisfiability tests on the underlying first order theory and therefore it does not involve any additional complexity caused by the nonmonotonicity of default logic. More precisely, for default theories consisting of