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Ultimate Wellfounded and Stable Semantics for Logic Programs With Aggregates (Extended Abstract)
 In Proceedings of ICLP01, LNCS 2237
, 2001
"... is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the sta ..."
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Cited by 45 (7 self)
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is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the standard wellfounded model of the program: # p. p. p is undefined while the associated TP operator is monotone and p is true in the ultimate wellfounded model. One disadvantage of using the ultimate semantics is that it has a higher computational cost even for programs without aggregates. The complexity goes one level higher in the polynomial hierarchy to # 2 for the wellfounded model and to 2 for a stable model which is also complete for this class [2]. Fortunately, by adding aggregates the complexity does not increase further. To give an example of a logic program with aggregates we consider the problem of computing the length of the shortest path between two nodes in a direc
Partial Stable Models for Logic Programs with Aggregates
 In: LPNMR7. LNCS 2923
, 2004
"... We introduce a family of partial stable model semantics for logic programs with arbitrary aggregate relations. The semantics are parametrized by the interpretation of aggregate relations in threevalued logic. Any semantics in this family satisfies two important properties: (i) it extends the pa ..."
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Cited by 16 (0 self)
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We introduce a family of partial stable model semantics for logic programs with arbitrary aggregate relations. The semantics are parametrized by the interpretation of aggregate relations in threevalued logic. Any semantics in this family satisfies two important properties: (i) it extends the partial stable semantics for normal logic programs and (ii) total stable models are always minimal. We also give a specific instance of the semantics and show that it has several attractive features.
Logical Constraints and Logic Programming
"... In this note we will investigate a form of logic programming with constraints. The constraints that we consider will not be restricted to statements on real numbers as in CLP(R), see [15]. Instead our constraints will be arbitrary global constraints. The basic idea is that the applicability of a giv ..."
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Cited by 16 (6 self)
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In this note we will investigate a form of logic programming with constraints. The constraints that we consider will not be restricted to statements on real numbers as in CLP(R), see [15]. Instead our constraints will be arbitrary global constraints. The basic idea is that the applicability of a given rule is not predicated on the fact that individual variables satisfy certain constraints, but rather on the fact that the least model of the set rules that are ultimately applicable satisfy the constraint of the rule. Thus the role of clauses will be slightly different than in the usual Logic Programming with constraints. In fact, the paradigm we present is closely related to stable model semantics of general logic programming [13]. We will define the notion of a constraint model of our constraint logic program and show that stable models of logic programs as well as the supported models of logic programs are just special cases of constraint models of constraint logic programs. Our definition of constraint logic programs and constraint models will be quite general. Indeed, in general definition, the constraint of a clause will not be restricted to be of a certain form or even to be expressible in the underlying language of the logic program. This feature is useful for certain applications in hybrid control systems and database applications that we have in mind. However for the most part in this paper, we focus on the properties of constraint programs and constraint models in the simplest case where the constraints are expressible in the
Managing uncertainty and vagueness in description logics, logic programs and description logic programs
, 2008
"... Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). ..."
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Cited by 16 (5 self)
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Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination).
Ultimate approximation and its application in nonmonotonic knowledge representation systems
, 2004
"... ..."
Translation of Aggregate Programs to Normal Logic Programs
 In ASP’03
, 2003
"... We define a translation of aggregate programs to normal logic programs which preserves the set of partial stable models. We then define the classes of definite and stratified aggregate programs and show that the translation of such programs are, respectively, definite and stratified logic progra ..."
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Cited by 11 (0 self)
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We define a translation of aggregate programs to normal logic programs which preserves the set of partial stable models. We then define the classes of definite and stratified aggregate programs and show that the translation of such programs are, respectively, definite and stratified logic programs. Consequently these two classes of programs have a single partial stable model which is twovalued and is also the wellfounded model. Our definition of stratification is more general than the existing one and covers a strictly larger class of programs.
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.
Logic programs with monotone cardinality atoms
 In Proc. LPNMR2004
, 2004
"... Abstract. We investigate mcaprograms, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a nonnegative integer and X is a finite set of propositional atoms. We develop a theory of mcaprograms. We demonstrate that the operational concept of the one ..."
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Cited by 7 (0 self)
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Abstract. We investigate mcaprograms, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a nonnegative integer and X is a finite set of propositional atoms. We develop a theory of mcaprograms. We demonstrate that the operational concept of the onestep provability operator generalizes to mcaprograms, but the generalization involves nondeterminism. Our main results show that the formalism of mcaprograms is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with cardinality atoms and with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possiblemodel semantics of Sakama and Inoue. 1
An epistemic foundation of stable model semantics
, 2003
"... The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goa ..."
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Cited by 5 (2 self)
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The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goal of this work is to present an alternative and epistemic based characterization of the stable model semantics, to the GelfondLifschitz transform. In particular, we show that the stable model semantics can be defined entirely as an extension of the KripkeKleene semantics and, thus, (i) does rely on the classical management of negation; and (ii) does not require any program transformation. Indeed, we show that the closed world assumption can be seen as an additional source for ‘falsehood ’ to be added cumulatively to the KripkeKleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.