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Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 224 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
Fixpoint semantics for logic programming  a survey
, 2000
"... The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close para ..."
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Cited by 106 (0 self)
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The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
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...
Stratified and Threevalued Logic Programming Semantics
, 1988
"... The familiar fixed point semantics for Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratified logic programs, producing a semantics we call weak stratified, that is compatible with but not the same as the c ..."
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Cited by 17 (2 self)
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The familiar fixed point semantics for Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratified logic programs, producing a semantics we call weak stratified, that is compatible with but not the same as the conventional stratified semantics. And we show weak stratified semantics coincides with one based on three valued logic, a semantics that is generally applicable, and that does not require stratification assumptions. 1 Introduction A beautiful fixed point semantics for Horn clause logic programming has been developed, based on classical logic ([16], [2]). But it can not deal adequately with negations when they are allowed in clause bodies. Two kinds of generalizations have been proposed to deal with this problem. The best known is stratification [1], [17]. Here the kind of logic programs one is allowed to write is restricted; recursions through negations are forbidden. For such programs...
Probabilistic and TruthFunctional ManyValued Logic Programming
 IN PROCEEDINGS OF THE 29TH IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC
, 1998
"... We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that a ..."
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Cited by 14 (9 self)
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We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are Pcomplete for classical logic programs are shown to be coNPcomplete for probabilistic manyvalued logic programs. We then focus on manyvalued logic programming in Pr ? n as an approximation of probabilistic manyvalued logic programming. Surprisingly, manyvalued logic programs in Pr ? n have both a probabilistic semantics in probabilities over a set of possible worlds and a truthfunctional semantics in the finitevalued Łukasiewicz logics Łn . Moreover, manyvalued logic programming in Pr ? n has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming. We especially introduce the proof...
ManyValued FirstOrder Logics with Probabilistic Semantics
 In Proceedings of the Annual Conference of the European Association for Computer Science Logic, 1998, volume 1584 of LNCS
, 1998
"... . We present nvalued firstorder logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of nvalued firstorder logics that lies between the purely probabilistic semantics and the truthfunctional semantics of the nvalued / Lukasiewicz logics / Ln . Within t ..."
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Cited by 8 (6 self)
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. We present nvalued firstorder logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of nvalued firstorder logics that lies between the purely probabilistic semantics and the truthfunctional semantics of the nvalued / Lukasiewicz logics / Ln . Within this semantics, closed formulas of classical firstorder logics that are logically equivalent in the classical sense also have the same truth value under all nvalued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, nvalued logical consequence in disjunctive logic programs with nvalued disjunctive facts can be reduced to classical logical consequence in n \Gamma 1 layers of classical disjunctive logic programs. Moreover, we show that nvalued logic programs have a model and a fixpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in nvalued logic ...
A General Theory of Confluent Rewriting Systems for Logic Programming and its Applications
, 2001
"... Recently, Brass and Dix showed (Journal of Automated Reasoning 20(1), 1998) that the wellfounded semantics WFS can be defined as a conuent calculus of transformation rules. This lead not only to a simple extension to disjunctive programs (Journal of Logic Programming 38(3), 1999), but also to a new ..."
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Cited by 7 (4 self)
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Recently, Brass and Dix showed (Journal of Automated Reasoning 20(1), 1998) that the wellfounded semantics WFS can be defined as a conuent calculus of transformation rules. This lead not only to a simple extension to disjunctive programs (Journal of Logic Programming 38(3), 1999), but also to a new computation of the wellfounded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LPSystems CS. Such a system CS is a rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: (1) most of the wellknown semantics are induced by confluent LPsystems, (2) there are many more transformation rules that lead to confluent LPsystems, (3) semantics induced by such systems can be used to model aggregation, (4) the new systems can be ...
Negation as Partial Failure
 in Proceedings of the Second International Workshop on Logic Programming and Nonmonotonic Reasoning
, 1993
"... We present a logic programming language which uses a fourvalued bilattice as the underlying framework for semantics of programs. The two orderings of the bilattice reflect the concepts of truth and knowledge. The space of truth values includes not only true and false, but also other truth values wh ..."
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Cited by 3 (3 self)
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We present a logic programming language which uses a fourvalued bilattice as the underlying framework for semantics of programs. The two orderings of the bilattice reflect the concepts of truth and knowledge. The space of truth values includes not only true and false, but also other truth values which represent no information or conflicting information. Programs are interpreted according to their knowledge content, resulting in a monotonic semantic operator . We present a novel procedural semantics similar to resolution which can retrieve both negative and positive information about a particular goal in a uniform setting. We extend the bilatticebased fixpoint and procedural semantics to incorporate a version of Closed World Assumption. We give soundness and completeness results, with and without the presence of Closed World Assumption. These results are general and are not restricted to ground atomic goals. We further develop the concept of substitution unification and study some of its properties as related to the proposed procedural semantics. Some of these properties may be of independent interest, particularly in the implementation of parallel logic programs.
Tableaus for Logic Programming
, 1993
"... We present a logic programming language, which we call Proflog, with an operational semantics based on tableaus, and a denotational semantics based on supervaluations. We show the two agree. Negation is wellbehaved, and semantic noncomputability issues do not arise. This is accomplished essenti ..."
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We present a logic programming language, which we call Proflog, with an operational semantics based on tableaus, and a denotational semantics based on supervaluations. We show the two agree. Negation is wellbehaved, and semantic noncomputability issues do not arise. This is accomplished essentially by dropping a domain closure requirement. The cost is that intuitions developed through the use of classical logic may need modification, though the system is still classical at a level once removed. Implementation problems are discussed very briefly  the thrust of the paper is primarily theoretical. 1 Introduction Life would be almost perfect if we had a logic programming language that was e#cient, treated negation naturally, and had a semantics that exactly fit its computational mechanism. As we all know, life is not almost perfect. But in the spirit of honest compromise, we propose a logic programming language that goes part way towards meeting these ideal goals. Over the ye...
Model States Revisited
"... Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the logic progra ..."
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Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the logic program. Replacing logic programs by the more general disjunctive logic programs where we admit disjunctions in the head of rules we have the following situation. However, a disjunctive fact has several different minimal Herbrand models. Hence, disjunctive logic programs posess in general a set of minimal Herbrand models, the minimal model semantics. To obtain an analoguous fixpoint characterization one has to collect the Herbrand structures into one object. Therefore Lobo, Minker, Rajasekar (cf.[5]) have introduced the notion of a model state of a disjunctive logic program where disjunctions of ground goals replace the ground goals.  However, a small counterexample shows that their d...