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25
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...
Analysis of inconsistency in graphbased viewpoints
 In ASE
, 2003
"... Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpointsbased approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, ..."
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Cited by 27 (11 self)
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Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpointsbased approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, we propose a categorytheoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. We illustrate an application of the framework through a casestudy showing how fuzzy viewpoints can serve as a requirements elicitation tool in reactive systems. 1
Kleene’s threevalued logics and their children
 Fundamenta Informaticae
, 1994
"... Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetri ..."
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Cited by 25 (4 self)
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Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences. 1
Coherent Integration of Databases by Abductive Logic Programming
 Journal of Artificial Intelligence Research
, 2004
"... We introduce an abductive method for a coherent integration of independent datasources. ..."
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Cited by 11 (4 self)
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We introduce an abductive method for a coherent integration of independent datasources.
Anyworld assumptions in logic programming
, 2005
"... Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the C ..."
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Cited by 8 (1 self)
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Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the Closed World Assumption (CWA), which asserts that by default the truth of an atom is false. There is a second wellknown assumption, called Open World Assumption (OWA), which asserts that the truth of the atoms is supposed to be unknown by default. However, the CWA, the OWA and the combination of them are extremal, though important, assumptions over a large variety of possible assumptions on the truth of the atoms, whenever the truth is taken from an arbitrary truth space. The topic of this paper is to allow any assignment (i.e. interpretation), over a truth space, to be a default assumption. Our main result is that our extension is conservative in the sense that under the “everywhere false ” default assumption (CWA) the usual stable model semantics is captured. Due to the generality and the purely algebraic nature of our approach, it abstracts from the particular formalism of choice and the results may be applied in other contexts as well.
A categorytheoretic approach to syntactic software merging
 In ICSM ’05: Proceedings of the 21st IEEE International Conference on Software Maintenance (ICSM’05
, 2005
"... Software merging is a common and essential activity during the lifespan of largescale software systems. Traditional textual merge techniques are inadequate for detecting syntactic merge conflicts. In this paper, we propose a domainindependent approach for syntactic software merging that exploits t ..."
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Cited by 7 (3 self)
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Software merging is a common and essential activity during the lifespan of largescale software systems. Traditional textual merge techniques are inadequate for detecting syntactic merge conflicts. In this paper, we propose a domainindependent approach for syntactic software merging that exploits the graphbased structure(s) of programs. We use morphisms between fuzzy graphs to capture the relationships between the structural elements of the programs to be merged, and apply a truth ordering lattice to express inconsistencies and evolutionary properties as we compute the merge. We demonstrate the approach with a threeway consolidation merge in a commercial software system; in particular, we show how analyzing merged call structures can help developers gain a better understanding and control of software evolution. 1
A FormulaPreferential Base for Paraconsistent and Plausible Reasoning Systems
 In Proceedings of the Workshop on Inconsistency in Data and Knowledge (KRR4) Int. Joint Conf. on AI (Ijcai 2001
, 2001
"... We provide a general framework for constructing natural consequence relations for paraconsistent and plausible nonmonotonic reasoning. The framework is based on preferential systems whose preferences are based on the satisfaction of formulas in models. We show that these natural preferential s ..."
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Cited by 6 (0 self)
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We provide a general framework for constructing natural consequence relations for paraconsistent and plausible nonmonotonic reasoning. The framework is based on preferential systems whose preferences are based on the satisfaction of formulas in models. We show that these natural preferential systems that were originally designed for paraconsistent reasoning fulfill a key condition (stopperedness or smoothness) from the theoretical research of nonmonotonic reasoning. Consequently, the nonmonotonic consequence relations that they induce fulfill the desired conditions of plausible consequence relations. Hence our frameword encompasses different types of preferential systems that were developed from different motivations of paraconsistent reasoning and nonmonotonic reasoning, and reveals an important link between them.
On The Expressive Power of ThreeValued and FourValued Languages
 Journal of Logic and Computation
, 1999
"... We investigate the expressive power relative to threevalued and fourvalued logics of various subsets of the set of connectives which are used in the bilatticesbased logics. Our study of a language is done in two stages. In the first stage the ability of the language to characterize sets of tuples ..."
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Cited by 6 (3 self)
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We investigate the expressive power relative to threevalued and fourvalued logics of various subsets of the set of connectives which are used in the bilatticesbased logics. Our study of a language is done in two stages. In the first stage the ability of the language to characterize sets of tuples of truthvalues is determined. In the second stage the results of the first are used to determine its power to represent operations. Special attention is given to the role of monotonicity, closure and freedom properties in classifying languages, as well as to maximality properties (for example: we prove that by adding any nonmonotonic connective to the set of fourvalued monotonic connectives, we get a functionally complete set). 1 Introduction In [Be77a, Be77b] Belnap introduced a logic intended to deal in a useful way with inconsistent and incomplete information. This logic is based on four truth values: the classical ones, denoted here by t and f , and two new ones: ?, that intuitively d...
Classical Gentzentype Methods in Propositional ManyValued Logics
 In Fitting, M., & Orlowska, E. (Eds.), Theory and Applications in MultipleValued Logics
, 2002
"... A classical Gentzentype system is one which employs twosided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzentype system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula p ..."
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Cited by 5 (2 self)
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A classical Gentzentype system is one which employs twosided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzentype system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property. In this tutorial we explain the main difficulty in developing classical Gentzentype systems with these properties for manyvalued logics. We then illustrate with numerous examples the various possible ways of overcoming this difficulty. Our examples include practically all 3valued logics, the most important class of 4valued logics, as well as central infinitevalued logics (like GodelDummett logic, S5 and some substructural logics). 1