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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 56 (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...
Disjunctive Semantics based upon Partial and BottomUp Evaluation
 Proceedings of the 12th Int. Conf. on Logic Programming
, 1995
"... We present a new and general approach of defining semantics for disjunctive logic programs. Our framework consists of two parts: (1) a semantical , where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (2) a procedural, namely a bottomup queryeva ..."
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Cited by 45 (12 self)
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We present a new and general approach of defining semantics for disjunctive logic programs. Our framework consists of two parts: (1) a semantical , where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (2) a procedural, namely a bottomup queryevaluation method based on operators working on conditional facts (introduced independently by Bry and Dung/Kanchansut for nondisjunctive programs). As to (1), we concentrate in this paper on a particular set of abstract properties (the most important being the unfolding or partial evaluation property GPPE) and define a new semantics DWFS. Our semantics coincides for normal programs with the wellfounded semantics WFS. For positive disjunctive programs DWFS coincides with the generalized closed world semantics GCWA. As a byproduct, we get new characterizations of WFS and GCWA. DWFS is strongly related to Przymusinski's STATIC semantics: we conjecture that they coincide w.r.t. to the derivati...
Characterizations of the Disjunctive Wellfounded Semantics: Confluent Calculi and Iterated GCWA
 Journal of Automated Reasoning
, 1997
"... . Recently Brass and Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a non ..."
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Cited by 32 (10 self)
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. Recently Brass and Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a nontrivial bottomup construction using least fixpoints of two monotonic operators. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent and terminating. This means that all the transformations can be applied in any order: we always arrive at an irreducible program (no more transformation is applicable) and this program is already uniquely determined. Moreover, it coincides with the normalform res(\Phi) of the program we started with. The semantics DWFS can be read off from res(\Phi) immediately. No proper subset of the calculus has these properties  only when we restrict to certain subclasse...
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
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...
Characterizations of the Stable Semantics by Partial Evaluation
 Logic Programming and NonMonotonic Reasoning, Proceedings of the Third International Conference, LNCS 928
, 1995
"... . There are three most prominent semantics defined for certain subclasses of disjunctive logic programs: GCWA (for positive programs), PERFECT (for stratified programs) and STABLE (defined for the whole class of all disjunctive programs). While there are various competitors based on 3valued models, ..."
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Cited by 18 (7 self)
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. There are three most prominent semantics defined for certain subclasses of disjunctive logic programs: GCWA (for positive programs), PERFECT (for stratified programs) and STABLE (defined for the whole class of all disjunctive programs). While there are various competitors based on 3valued models, notably WFS and its disjunctive counterparts, there are no other semantics consisting of 2valued models. We argue that the reason for this is the Partial Evaluationproperty (also called Unfolding or Partial Deduction) wellknown from Logic Programming. In fact, we prove characterizations of these semantics and show that if a semantics SEM satisfies Partial Evaluation and Elimination of Tautologies then (1) SEM is based on 2valued minimal models for positive programs, and (2) if SEM satisfies in addition Elimination of Contradictions, it is based on stable models. We also show that if we require Isomorphy and Relevance then STABLE is completely determined on the class of all stratified...
Characterizing DWFS: Confluence and Iterated GCWA
 Logics in Artificial Intelligence (JELIA '96), LNCS 1126
, 1996
"... . Quite recently Brass/Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program. We sho ..."
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Cited by 11 (8 self)
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. Quite recently Brass/Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent . This means that all the transformations can be applied in any order: if we arrive at an irreducible program (no more transformation is applicable) then this is already the unique normalform. No proper subset of the calculus has this property. We also give an equivalent characterization of DWFS in terms of iterated minimal model reasoning. This construction is a generalization of a description of the wellfounded semantics: we introduce a very simple and neat construction of a sequence D i that eventually stops and represents the set of derivable...
Analysis and Transformation of Proof Procedures
, 1994
"... Automated theorem proving has made great progress during the last few decades. Proofs of more and more difficult theorems are being found faster and faster. However, the exponential increase in the size of the search space remains for many theorem proving problems. Logic program analysis and transfo ..."
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Cited by 8 (2 self)
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Automated theorem proving has made great progress during the last few decades. Proofs of more and more difficult theorems are being found faster and faster. However, the exponential increase in the size of the search space remains for many theorem proving problems. Logic program analysis and transformation techniques have also made progress during the last few years and automated theorem proving can benefit from these techniques if they can be made applicable to general theorem proving problems. In this thesis we investigate the applicability of logic program analysis and transformation techniques to automated theorem proving. Our aim is to speed up theorem provers by avoiding useless search. This is done by detecting and deleting parts of the theorem prover and theory under consideration that are not needed for proving a given formula. The analysis and transformation techniques developed for logic programs can be applied in automated theorem proving via a programming technique called ...
Optimization of Bound Disjunctive Queries with Constraints. Theory and Practice of Logic Programming
, 2002
"... This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the wellknown MagicSet technique and is wellsuited for being integrated in current bottomup (stable) model inference engines. More ..."
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Cited by 8 (2 self)
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This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the wellknown MagicSet technique and is wellsuited for being integrated in current bottomup (stable) model inference engines. More specifically, it is based on the exploitation of binding propagation techniques which reduce the size of the data relevant to answer the query and, consequently, reduces both the complexity of computing a single model and the number of models to be considered. The motivation of this work stems from the observation that traditional binding propagation optimization techniques for bottomup model generator systems, simulating the goal driven evaluation of topdown engines, are only suitable for positive (disjunctive) queries, while hard problems are expressed using unstratified negation. The main contribution of the paper consists in the extension of a previous technique, defined for positive disjunctive queries, to queries containing both disjunctive heads and constraints (a simple and expressive form of unstratified negation). As the usual way of expressing declaratively hard problems is based on the guessandcheck technique, where the guess part is expressed by means of disjunctive rules and the check part is expressed by means of constraints, the technique proposed here is highly relevant for the optimization of queries expressing hard problems. The value of the technique has been proved by several experiments. 1