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14
Resolutionbased approximate reasoning for OWL DL
 PROC. ISWC2005
, 2005
"... We propose a new technique for approximate ABox reasoning with OWL DL ontologies. Essentially, we obtain substantially improved reasoning performance by disregarding nonHorn features of OWL DL. Our approach comes as a sideproduct of recent research results concerning a new transformation of OWL D ..."
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Cited by 27 (5 self)
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We propose a new technique for approximate ABox reasoning with OWL DL ontologies. Essentially, we obtain substantially improved reasoning performance by disregarding nonHorn features of OWL DL. Our approach comes as a sideproduct of recent research results concerning a new transformation of OWL DL ontologies into negationfree disjunctive datalog [1,2,3,4], and rests on the idea of performing standard resolution over disjunctive rules by treating them as if they were nondisjunctive ones. We analyse our reasoning approach by means of nonmonotonic reasoning techniques, and present an implementation, called Screech.
Answer sets for logic programs with arbitrary abstract constraint atoms
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 2007
"... In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (catoms). These approaches generalize the fixpointbased and the level mapping based answer set semantics of normal logic programs to the case of logic p ..."
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Cited by 20 (2 self)
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In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (catoms). These approaches generalize the fixpointbased and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of catoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpointbased semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negationasfailure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of catoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly wellsupported models, are generalizations of the notion of wellsupported models of normal logic programs to the case of programs with catoms. As for the case of fixpointbased semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) wellsupported models of a program, thus generalizing the theorem on the correspondence between stable models and wellsupported models of a normal logic program to the class of programs with catoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone catoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with catoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature.
Logic Programs, Iterated Function Systems, and Recurrent Radial Basis Function Networks
 Journal of Applied Logic
, 2004
"... Graphs of the singlestep operator for firstorder logic programs  displayed in the real plane  exhibit selfsimilar structures known from topological dynamics, i.e. they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be ..."
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Cited by 14 (11 self)
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Graphs of the singlestep operator for firstorder logic programs  displayed in the real plane  exhibit selfsimilar structures known from topological dynamics, i.e. they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which approximate logic programs in the presence of function symbols.
A Coherent Wellfounded Model for Hybrid MKNF Knowledge Bases
"... Abstract. With the advent of the Semantic Web, the question becomes important how to best combine openworld based ontology languages, like OWL, with closedworld rules paradigms. One of the most mature proposals for this combination is known as Hybrid MKNF knowledge bases [11], which is based on an ..."
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Cited by 14 (5 self)
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Abstract. With the advent of the Semantic Web, the question becomes important how to best combine openworld based ontology languages, like OWL, with closedworld rules paradigms. One of the most mature proposals for this combination is known as Hybrid MKNF knowledge bases [11], which is based on an adaptation of the stable model semantics to knowledge bases consisting of ontology axioms and rules. In this paper, we propose a wellfounded semantics for such knowledge bases which promises to provide better efficiency of reasoning, which is compatible both with the OWLbased semantics and the traditional wellfounded semantics for logic programs, and which surpasses previous proposals for such a wellfounded semantics by avoiding some issues related to inconsistency handling. 1
Local Closed World Reasoning with Description Logics under the WellFounded Semantics
, 2011
"... An important question for the upcoming Semantic Web is how to best combine open world ontology languages, such as the OWLbased ones, with closed world rulebased languages. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases [52], and it is based on an adap ..."
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Cited by 13 (7 self)
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An important question for the upcoming Semantic Web is how to best combine open world ontology languages, such as the OWLbased ones, with closed world rulebased languages. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases [52], and it is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. In this paper we propose a wellfounded semantics for nondisjunctive hybrid MKNF knowledge bases that promises to provide better efficiency of reasoning, and that is compatible with both the OWLbased semantics and the traditional WellFounded Semantics for logic programs. Moreover, our proposal allows for the detection of inconsistencies, possibly occurring in tightly integrated ontology axioms and rules, with only little additional effort. We also identify tractable fragments of the resulting language.
The well supported semantics for multidimensional dynamic logic programs
 LPNMR 2005, LNCS 3662
, 2005
"... Multidimensional dynamic logic programs are a paradigm which allows to express (partially) hierarchically ordered evolving knowledge bases through (partially) ordered multi sets of logic programs. They solve contradictions among rules in different programs by allowing rules in more important progr ..."
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Cited by 8 (0 self)
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Multidimensional dynamic logic programs are a paradigm which allows to express (partially) hierarchically ordered evolving knowledge bases through (partially) ordered multi sets of logic programs. They solve contradictions among rules in different programs by allowing rules in more important programs to reject rules in less important ones. This class of programs extends the class of dynamic logic program that provides meaning to sequences of logic programs. Recently the refined stable model semantics has fixed some counterintuitive behaviour of previously existing semantics for dynamic logic programs. However, it is not possible to directly extend the definitions and concepts of the refined semantics to the multidimensional case and hence more sophisticated principles and techniques are in order. In this paper we face the problem of defining a proper semantics for multidimensional dynamic logic programs by extending the idea of well supported model to this class of programs and by showing that this concept alone is enough for univocally characterizing a proper semantics. We then show how the newly defined semantics coincides with the refined one when applied to sequences of programs.
Layer supported models of logic programs
 IN PROCS. 10TH LPNMR
"... For practical applications, the use of topdown querydriven proofprocedures is essential for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a topdown search method. A 2valued semantics for Normal Lo ..."
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Cited by 6 (5 self)
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For practical applications, the use of topdown querydriven proofprocedures is essential for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a topdown search method. A 2valued semantics for Normal Logic Programs (NLPs) allowing for topdown querysolving is thus highly desirable. The current standard 2valued semantics for NLPs, the Stable Models (SMs) semantics, does not allow for topdown querysolving because it does not enjoy the relevance property — and moreover, it does not guarantee the existence of a model for every NLP. To overcome these current limitations we introduce here a new 2valued semantics for NLPs — the Layer Supported Models semantics — which conservatively extends the SMs, enjoys relevance and cumulativity, guarantees model existence, and respects the WellFounded Model. We also show how our semantics can be easily extended to deal with Disjunctive Logic Programs and Extended Logic Programs (including explicit negation), thus providing a practical, comprehensive and advantageous alternative to SMsbased Answer
Level mapping characterizations of selector generated models for logic programs
 of Ulmer InformatikBerichte., Universität Ulm
, 2005
"... Abstract. Assigning semantics to logic programs via selector generated models (Schwarz 2002/2003) extends several semantics, like the stable, the inflationary, and the stable generated semantics, to programs with arbitrary formulae in rule heads and bodies. We study this approach by means of a unify ..."
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Cited by 4 (2 self)
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Abstract. Assigning semantics to logic programs via selector generated models (Schwarz 2002/2003) extends several semantics, like the stable, the inflationary, and the stable generated semantics, to programs with arbitrary formulae in rule heads and bodies. We study this approach by means of a unifying framework for characterizing different logic programming semantics using level mappings (Hitzler and Wendt 200x, Hitzler 2003), thereby supporting the claim that this framework is very flexible and applicable to very diversely defined semantics. 1
Level Mapping Characterizations for Quantitative and Disjunctive Logic Programs
"... Several di#erent approaches of logic programming semantics have been proposed during the last two decades. These semantics varied in many aspects and it was di# cult to find the exact relationships between them. Hitzler and Wendt proposed a new method, based on level mappings, which allows to pr ..."
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Cited by 3 (2 self)
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Several di#erent approaches of logic programming semantics have been proposed during the last two decades. These semantics varied in many aspects and it was di# cult to find the exact relationships between them. Hitzler and Wendt proposed a new method, based on level mappings, which allows to provide uniform characterizations of di#erent semantics for logic programs. They gave new characterizations of di#erent semantics, like the wellfounded semantics or the Fitting semantics. We will apply this method to other classes of logic programs, namely quantitative logic programs and disjunctive logic programs. There are also di#erent approaches of semantics for both classes and we will provide characterizations for some of them. In fact, we will consider a quantitative semantics due to van Emden and a specialization of a semantics due to Mateis where real numbers, respectively intervals of real numbers, are used as measures of uncertainty. Furthermore, we will provide a level mapping characterization of the minimal model semantics for disjunctive logic programs and a characterization for the combination of these two classes, i.e. quantitative disjunctive logic programs.
Decidability Under the WellFounded Semantics ⋆
"... Abstract. The wellfounded semantics (WFS) for logic programs is one of the few major paradigms for closedworld reasoning. With the advent of the Semantic Web, it is being used as part of rule systems for ontology reasoning, and also investigated as to its usefulness as a semantics for hybrid syste ..."
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Cited by 2 (1 self)
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Abstract. The wellfounded semantics (WFS) for logic programs is one of the few major paradigms for closedworld reasoning. With the advent of the Semantic Web, it is being used as part of rule systems for ontology reasoning, and also investigated as to its usefulness as a semantics for hybrid systems featuring combined open and closedworld reasoning. Even in its most basic form, however, the WFS is undecidable. In fact, it is not even semidecidable, which means that it is a theoretical impossibility that sound and complete reasoners for the WFS exist. Surprisingly, however, this matter has received next to no attention in research, although it has already been shown in 1995 by John Schlipf [1]. In this paper, we present several conditions under which queryanswering under the wellfounded semantics is decidable or semidecidable. To the best of our knowledge, these are the very first results on such conditions. 1