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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 233 (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.
A Classification Theory of Semantics of Normal Logic Programs: II. Weak Properties
 FUNDAMENTA INFORMATICAE
, 1995
"... Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a ..."
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Cited by 75 (0 self)
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Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical nonmonotonic entailment relation SEM scept . We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any wellbehaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any wellbehavedsemantics is an extension of the wellfounded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M supp P . We also...
On The Correctness Of Unfold/fold Transformation Of Normal And Extended Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1995
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On the Partial Semantics for Disjunctive Deductive Databases
, 1997
"... this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting subclasses of partial stable models, Mstable (Maximalstable) (also called regular models, preferred extension, and maximal ..."
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this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting subclasses of partial stable models, Mstable (Maximalstable) (also called regular models, preferred extension, and maximal stable classes) and Lstable (Least undefinedstable) models, are then extended from normal to disjunctive datalog programs. Lstable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict Mstable models, endowed with a nice modularity property, may be appealing from the programming and computational point of view. Mstable and Lstable models are also compared with the regular models for disjunctive datalog programs recently proposed in the literature. 1 Introduction Deductive dat
Expressive Power and Complexity of Partial Models for Disjunctive Deductive Databases
, 1999
"... This paper investigates the expressive power and complexity of partial model semantics for disjunctive deductive databases. In particular,... ..."
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Cited by 17 (7 self)
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This paper investigates the expressive power and complexity of partial model semantics for disjunctive deductive databases. In particular,...
The valid model semantics for logic programs
 In Proceedings of the ACM Symposium on Principles of Database Systems
, 1992
"... We present the valid model semantics, a new approach to providing semantics for logic programs with negation, setterms and grouping. The valid model semantics is a threevalued semantics, and is de ned in terms of a `normal form' computation. The valid model semantics also gives meaning to the g ..."
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We present the valid model semantics, a new approach to providing semantics for logic programs with negation, setterms and grouping. The valid model semantics is a threevalued semantics, and is de ned in terms of a `normal form' computation. The valid model semantics also gives meaning to the generation and use of nonground facts (i.e., facts with variables) in a computation. The formulation of the semantics in terms of a normal form computation o ers important insight not only into the valid model semantics, but also into other semantics proposed earlier. We show that the valid model semantics extends the wellfounded semantics in a natural manner, and has several advantages over it. The wellfounded semantics can also be understood using a variant of the normal form computations that we use; the normal form computations used for valid semantics seem more natural than those used for wellfounded semantics. We also show that the valid model semantics has several other desirable properties: it is founded ([SZ90]), it is contained in every regular model ([YY90]), and it is contained in every twovalued stable model. The work of Catriel Beeri was supported by the USAISRAEL Binational Science Foundation. Part of the work was done while visiting the University of Wisconsin. The
Contradiction in Argumentation Frameworks
 In Proceedings of the IPMU conference
, 1996
"... We present a theory of argumentation that can deal with contradiction within an argumentation framework, thus solving a problem posed in [1]. By representing logic programs as sets of interacting arguments, we can apply our results for general argumentation frameworks to logicprogramming seman ..."
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We present a theory of argumentation that can deal with contradiction within an argumentation framework, thus solving a problem posed in [1]. By representing logic programs as sets of interacting arguments, we can apply our results for general argumentation frameworks to logicprogramming semantics. This yields a new semantics for logic programs that properly extends traditional approaches such as stable [2] and wellfounded [3] models. Keywords: Argumentation framework, logic program, semantics 1 Introduction The challenge of understanding argumentation and its role in human reasoning has been addressed by many researchers in different fields including philosophy, logic and AI. A promising formal theory of argumentation has recently been proposed in a seminal article by Dung[1]. His theory is based on the idea that a statement (argument) is believable if it can be argued successfully against contesting arguments. Thus, the theory considers socalled argumentation frameworks ...
Autoepistemic Logic of First Order and Its Expressive Power
, 1994
"... . We study the expressive power of firstorder autoepistemic logic. We argue that full introspection of rational agents should be carried out by minimizing positive introspection and maximizing negative introspection. Based on full introspection, we propose the minimal wellfounded semantics that ch ..."
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. We study the expressive power of firstorder autoepistemic logic. We argue that full introspection of rational agents should be carried out by minimizing positive introspection and maximizing negative introspection. Based on full introspection, we propose the minimal wellfounded semantics that characterizes autoepistemic reasoning processes of rational agents, and show that breadth of the semantics covers all theories in autoepistemic logic of firstorder, Moore's AE logic, and Reiter's default logic. Our study demonstrates that the autoepistemic logic of firstorder is a very powerful framework for nonmonotonic reasoning, logic programming, deductive databases, and knowledge representation. Key words: nonmonotonic reasoning, autoepistemic logic, default logic, logic programming, knowledge representation. 1 Introduction An ideal rational agent has to decide which set of propositions to believe according to its knowledge. Moore's AE logic is a powerful framework for this kind of in...
Semantic Forcing in Disjunctive Logic Programs
 Computational Intelligence
, 2001
"... We propose a semantics for disjunctive logic programs, based on the single notion of forcing. We show that the semantics properly extends, in a natural way, previous approaches. A fixpoint characterization is also provided. We also take a closer look at the relationship between disjunctive logic ..."
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Cited by 4 (4 self)
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We propose a semantics for disjunctive logic programs, based on the single notion of forcing. We show that the semantics properly extends, in a natural way, previous approaches. A fixpoint characterization is also provided. We also take a closer look at the relationship between disjunctive logic programs and disjunctivefree logic programs. We present certain criteria under which a disjunctive program is semantically equivalent with its disjunctivefree (shifted) version.
Rstable Models for Logic Programs
 Logic in Databases (LID'96
"... . We propose a new semantics for general logic programs which stems from first principles of logicprogramming semantics. Our theory unifies previous approaches and is applicable to some useful programs which are not properly handled by existing semantics. Keywords: logic programming, semantics 1 In ..."
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. We propose a new semantics for general logic programs which stems from first principles of logicprogramming semantics. Our theory unifies previous approaches and is applicable to some useful programs which are not properly handled by existing semantics. Keywords: logic programming, semantics 1 Introduction The problem of defining semantics for general logic programs is a rapidly progressing area of research. Thus, there have recently emerged semantics such as the wellfounded semantics [2], stable semantics [1], stable partial models [9], acceptable semantics [6], threevalued stable models [8], and regular models [11]. Each of these approaches suggests ways of associating models to a program. The various approaches seem to differ slightly in their motivations, in that they have different expectations for models. In addition, there are some reasonable models of certain useful programs which are not delivered by some of the approaches. This paper derives a unifying logicprogramming...