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Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 245 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
Reasoning about Termination of Pure Prolog Programs
 Information and Computation
, 1993
"... We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of ..."
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Cited by 124 (14 self)
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We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of left terminating positive programs by means of the notion of an acceptable program that provides us with a practical method of proving termination. The method is illustrated by giving a simple proof of termination of the quicksort program for the desired class of goals. Then we extend this approach to the class of general logic programs by modifying the concept of acceptability. We prove that acceptable general programs are left terminating. The converse implication does not hold but we show that under the assumption of nonfloundering from ground goals every left terminating general program is acceptable. Finally, we prove that various ways of defining semantics coincide for acceptable gen...
Logic Programs and Connectionist Networks
 Journal of Applied Logic
, 2004
"... One facet of the question of integration of Logic and Connectionist Systems, and how these can complement each other, concerns the points of contact, in terms of semantics, between neural networks and logic programs. In this paper, we show that certain semantic operators for propositional logic p ..."
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Cited by 43 (16 self)
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One facet of the question of integration of Logic and Connectionist Systems, and how these can complement each other, concerns the points of contact, in terms of semantics, between neural networks and logic programs. In this paper, we show that certain semantic operators for propositional logic programs can be computed by feedforward connectionist networks, and that the same semantic operators for firstorder normal logic programs can be approximated by feedforward connectionist networks. Turning the networks into recurrent ones allows one also to approximate the models associated with the semantic operators. Our methods depend on a wellknown theorem of Funahashi, and necessitate the study of when Funahasi's theorem can be applied, and also the study of what means of approximation are appropriate and significant.
Characterizations of Classes of Programs by ThreeValued Operators
, 1999
"... . Several important classes of normal logic programs, including the classes of acyclic, acceptable, and locally hierarchical programs, have the property that every program in the class has a unique twovalued supported model. In this paper, we call such classes unique supported model classes. We ..."
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Cited by 22 (21 self)
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. Several important classes of normal logic programs, including the classes of acyclic, acceptable, and locally hierarchical programs, have the property that every program in the class has a unique twovalued supported model. In this paper, we call such classes unique supported model classes. We analyse and characterize these classes by means of operators on threevalued logics. Our studies will motivate the definition of a larger unique supported model class which we call the class of \Phi accessible programs. Finally, we show that the class of \Phi accessible programs is computationally adequate in that every partial recursive function can be implemented by such a program. Proceedings of the 5th International Conference on Logic Programmingand NonMonotonic Reasoning (LPNMR'99), El Paso, Texas, December, 1999. Springer Lecture Notes in Artificial Intelligence Vol. 1730, 1999, pp. 357371. 1 Introduction A good deal of recent research in logic programming has been put in...
The FixedPoint Theorems of PriessCrampe and Ribenboim in Logic Programming
 Proceedings of the International Conference and Workshop on Valuation Theory, University of Saskatchewan in
, 1999
"... Sibylla PriessCrampe and Paulo Ribenboim recently established a general fixedpoint theorem for multivalued mappings defined on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of ..."
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Cited by 18 (10 self)
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Sibylla PriessCrampe and Paulo Ribenboim recently established a general fixedpoint theorem for multivalued mappings defined on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to ScottErshov domains, familiar in programming language semantics, and to the generalized metrics of Khamsi, Kreinovich and Misane which have been applied, by these latter authors, to logic programming. Amongst other things, we will also show that a unified treatment of the fixedpoint theory of wide classes of programs can be given by means of the theorems of PriessCrampe and Ribenboim.
Programming by Combining General Logic Programs
 Journal of logic and computation
, 1997
"... The program composition approach can be fruitfully applied to combine general logic programs, that is, logic programs possibly containing negative premises. We show how the introduction of a basic set of (metalevel) composition operations over general programs increases the knowledge representation ..."
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Cited by 15 (2 self)
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The program composition approach can be fruitfully applied to combine general logic programs, that is, logic programs possibly containing negative premises. We show how the introduction of a basic set of (metalevel) composition operations over general programs increases the knowledge representation capabilities of logic programming for nonmonotonic reasoning. Examples of modular programming, hierarchical reasoning, constraints and rules with exceptions will be illustrated. The semantics of programs and program compositions is dened in terms of threevalued logic by extending the threevalued semantics for logic programs proposed by Fitting [16]. A computational interpretation of program compositions is formalised by means of an equivalence preserving syntactic transformation of arbitrary program compositions into standard general programs. 1 Introduction It is becoming more and more evident that the activity of building software is moving from writing lines of code in some program...
Acceptable Programs Revisited
 Proceedings of the Workshop on Verification in Logic Programming, Sixteenth International Conference on Logic Programming (ICLPâ€™99), Las Cruces
, 1999
"... Acceptable logic programs have been studied extensively in the context of proving termination of Prolog programs. It is difficult, however, to establish acceptability from the definition since this depends on finding a suitable model, which need not be a Herbrand model in general, together with a ..."
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Cited by 10 (10 self)
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Acceptable logic programs have been studied extensively in the context of proving termination of Prolog programs. It is difficult, however, to establish acceptability from the definition since this depends on finding a suitable model, which need not be a Herbrand model in general, together with a suitable level mapping that one can use to check the conditions which characterize acceptability. In this paper, we will see that when working over a fixed but arbitrary preinterpretation, a method can be provided for obtaining both a suitable model and a canonical level mapping which are sufficient for this purpose. Furthermore, the canonical model and level mapping obtained will turn out to be sufficient for discussing termination of nonground queries. 1 Introduction Acceptable programs were first studied in detail in [AP93] where they were shown to coincide, if floundering is ignored, with the programs which are leftterminating. They have been much examined in the literature, fo...
Some Issues Concerning Fixed Points in Computational Logic: QuasiMetrics, Multivalued Mappings and the KnasterTarski Theorem
, 2000
"... Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the KnasterTarski theorem and of ..."
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Cited by 8 (7 self)
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Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the KnasterTarski theorem and of the Banach contraction mapping theorem, and formulate a version of the classical fixedpoint theorem (sometimes attributed to Kleene) which is new. All these results have applications to the semantics of disjunctive logic programs, and we will describe a class of programs to which the new theorem can be applied. We also show that a unification of the latter two theorems is possible, using quasimetrics, which parallels the wellknown unification of Rutten and Smyth in the case of conventional programming language semantics.
The Use of Renaming in Composing General Programs
 Proc. of the 8th International Workshop on Logic Programming Synthesis and Transformation (LOPSTR'98
, 1999
"... . Most modern computing systems consist of large numbers of software components that interact with each other. Correspondingly, the capability of reusing and composing existing software components is of primary importance in this scenario. In this paper we analyse the role of renaming as a key ..."
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Cited by 4 (0 self)
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. Most modern computing systems consist of large numbers of software components that interact with each other. Correspondingly, the capability of reusing and composing existing software components is of primary importance in this scenario. In this paper we analyse the role of renaming as a key ingredient of componentbased programming. More precisely, a metalevel renaming operation is introduced in the context of a logicbased program composition setting which features a number of other composition operations over general logic programs, that is, logic programs possibly containing negative premises. Several examples are presented to illustrate the increased knowledge representation capabilities of logic programming for nonmonotonic reasoning. The semantics of programs and program compositions is dened in terms of threevalued logic by extending the threevalued semantics for logic programs proposed by Fitting [10]. A computational interpretation of program composition...