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Dualities between Alternative Semantics for Logic Programming and Nonmonotonic Reasoning
 Journal of Automated Reasoning
, 1998
"... The GelfondLifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around whic ..."
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Cited by 93 (9 self)
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The GelfondLifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around which the GelfondLifschitz [GL88] operator "bounces around". The same phenomenon occurs with default logic when Reiter's operator \Gamma \Delta is considered. Based on this, a "stable class" semantics and "extension class" semantics was proposed in [BS90]. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's \Gamma \Delta operator. In this paper, our primary aim is to prove that there is a very interesting duality between stable class theory and the well founded semantics for logic programming. In the stable class semantics, class...
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 49 (26 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.
Modal nonmonotonic logics: ranges, characterization, computation
 INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING
, 1991
"... In the paper, we investigate the way in which nonmonotonic modal logics depend on their underlying monotonic modal logics. Most notably, we study when diﬀerent monotonic modal logics deﬁne the same nonmonotonic system. In particular, we show that for an important class of the so called stratified th ..."
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Cited by 45 (2 self)
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In the paper, we investigate the way in which nonmonotonic modal logics depend on their underlying monotonic modal logics. Most notably, we study when diﬀerent monotonic modal logics deﬁne the same nonmonotonic system. In particular, we show that for an important class of the so called stratified theories all nonmonotonic logics considered in the paper, with the exception of S5, coincide.
It turns out that in some cases, nonstandard
(that is, nonnormal) logics have interesting nonmonotonic counterparts. Two such systems are investigated in the paper in detail.
For the case of ﬁnite theories, all nonmonotonic logics considered are shown to be decidable and an appropriate algorithm is presented.
Moral Dilemmas and Nonmonotonic Logic
, 1994
"... this paper is to establish some formal connections between deontic and nonmonotonic logics, and to suggest some ways in which the techniques developed in the study of nonmonotonic reasoning and the issues confronted there might help to illuminate deontic ideas. These two subjects have evolved within ..."
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Cited by 44 (9 self)
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this paper is to establish some formal connections between deontic and nonmonotonic logics, and to suggest some ways in which the techniques developed in the study of nonmonotonic reasoning and the issues confronted there might help to illuminate deontic ideas. These two subjects have evolved within different disciplines. The field of deontic logic was developed by philosophers and legal theorists as a high level framework for describing valid patterns of normative reasoning. The study of nonmonotonic logic was initiated, much more recently, by researchers in artificial intelligence who felt that ordinary logical techniques could not be applied properly to a number of practical problems arising within that areamost notably, problems involving planning and action, such as the frame problem. Even though the two subjects come from different disciplines, however, it is not really surprising that there should be close connections between them. Both are concerned, very broadly, with formalizing certain aspects of commonsense reasoning. Both recognize that many of the rules governing our commonsense reasoning are prima facie, or defeasible. And both must deal, in particular, with clashes among these defeasible rules. Although I believe that the relations between deontic and nonmonotonic logic may be extensive, I focus here, narrowly, only on two particular theories. The first is the account of obligation sketched by Bas van Fraassen [26], which differs from standard deontic logic in allowing for moral conflicts; the second is Raymond Reiter's default logic [20], one of the first nonmonotonic formalisms, and one of the most widely applied. These two theories are reviewed in Sections 2 and 3. In Section 4, I show that van Fraassen's account of simple (categorical) oughts can ...
Epistemic semantics for fixedpoint nonmonotonic logics
 In Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge (TARK90
, 1990
"... Default Logic and Autoepistemic Logic are the two bestknown fixedpoints nonmonotonic logics. Despite the fact that they are known to be closely related and that the epistemic nature of Autoepistemic Logic is obvious, the only semantics that have been offered for Default Logic to date are complex ..."
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Cited by 42 (0 self)
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Default Logic and Autoepistemic Logic are the two bestknown fixedpoints nonmonotonic logics. Despite the fact that they are known to be closely related and that the epistemic nature of Autoepistemic Logic is obvious, the only semantics that have been offered for Default Logic to date are complex and have little to do with epistemic notions [Etherington 1987]. In this paper we provide simple uniform epistemic semantics for the two logics. We do so by translating them both into a new logic, called GK, of Grounded Knowledge, which embodies a modification of preference semantics [Shoham 1987]. Beside their simplicity and uniformity, the semantics have two other advantages: They allow easy proofs of the connections between Default Logic and Autoepistemic Logic, and suggest a general class of logics of which the two logics are special cases. 1
WellFounded and Stationary Models of Logic Programs
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 1994
"... ..."
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
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 28 (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...
Default Reasoning Using Classical Logic
 Artificial Intelligence
, 1996
"... In this paper we show how propositional default theories can be characterized by classical propositional theories: for each finite default theory, we show a classical propositional theory such that there is a onetoone correspondence between models for the latter and extensions of the former. T ..."
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Cited by 25 (2 self)
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In this paper we show how propositional default theories can be characterized by classical propositional theories: for each finite default theory, we show a classical propositional theory such that there is a onetoone correspondence between models for the latter and extensions of the former. This means that computing extensions and answering queries about coherence, setmembership and setentailment are reducible to propositional satisfiability. The general transformation is exponential but tractable for a subset which we call 2DT  a superset of network default theories and disjunctionfree default theories. Consequently, coherence and setmembership for the class 2DT is NPcomplete and setentailment is coNPcomplete. This work paves the way for the application of decades of research on efficient algorithms for the satisfiability problem to default reasoning. For example, since propositional satisfiability can be regarded as a constraint satisfaction problem (CSP...
Approximations, Stable Operators, WellFounded Fixpoints And Applications In Nonmonotonic Reasoning
, 2000
"... In this paper we develop an algebraic framework for studying semantics of nonmonotonic logics. Our approach is formulated in the language of lattices, bilattices, operators and fixpoints. The goal is to describe fixpoints of an operator O defined on a lattice. The key intuition is that of an approxi ..."
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Cited by 23 (9 self)
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In this paper we develop an algebraic framework for studying semantics of nonmonotonic logics. Our approach is formulated in the language of lattices, bilattices, operators and fixpoints. The goal is to describe fixpoints of an operator O defined on a lattice. The key intuition is that of an approximation, a pair (x, y) of lattice elements which can be viewed as an approximation to each lattice element z such that x z y. The key notion is that of an approximating operator, a monotone operator on the bilattice of approximations whose fixpoints approximate the fixpoints of the operator O. The main contribution of the paper is an algebraic construction which assigns a certain operator, called the stable operator, to every approximating operator on a bilattice of approximations. This construction leads to an abstract version of the wellfounded semantics. In the paper we show that our theory offers a unified framework for semantic studies of logic programming, default logic and autoepistemic logic.