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37
A Faithful Integration of Description Logics with Logic Programming
 In Proc. of the 20th Int. Joint Conf. on Artificial Intelligence (IJCAI 2007
"... Integrating description logics (DL) and logic programming (LP) would produce a very powerful and useful formalism. However, DLs and LP are based on quite different principles, so achieving a seamless integration is not trivial. In this paper, we introduce hybrid MKNF knowledge bases that faithfully ..."
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Cited by 91 (8 self)
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Integrating description logics (DL) and logic programming (LP) would produce a very powerful and useful formalism. However, DLs and LP are based on quite different principles, so achieving a seamless integration is not trivial. In this paper, we introduce hybrid MKNF knowledge bases that faithfully integrate DLs with LP using the logic of Minimal Knowledge and Negation as Failure (MKNF) [Lifschitz, 1991]. We also give reasoning algorithms and tight data complexity bounds for several interesting fragments of our logic. 1
Equilibria in Heterogeneous Nonmonotonic MultiContext Systems
 In 22nd AAAI Conference on Artificial Intelligence (AAAI2007
, 2007
"... We propose a general framework for multicontext reasoning which allows us to combine arbitrary monotonic and nonmonotonic logics. Nonmonotonic bridge rules are used to specify the information flow among contexts. We investigate several notions of equilibrium representing acceptable belief states f ..."
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Cited by 79 (17 self)
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We propose a general framework for multicontext reasoning which allows us to combine arbitrary monotonic and nonmonotonic logics. Nonmonotonic bridge rules are used to specify the information flow among contexts. We investigate several notions of equilibrium representing acceptable belief states for our multicontext systems. The approach generalizes the heterogeneous monotonic multicontext systems developed by F. Giunchiglia and colleagues as well as the homogeneous nonmonotonic multicontext systems of Brewka, Serafini and Roelofsen. Background and Motivation Interest in formalizations of contextual information and intercontextual information flow has steadily increased over the last years. Based on seminal papers by McCarthy (1987)
Rational closure for defeasible description logics.
 Logics in Artificial Intelligence  Proceedings of the12th European Conference (JELIA 2010). Volume 6341 of Lecture Notes in Computer Science (LNCS).,
, 2010
"... Abstract. In the field of nonmonotonic logics, the notion of rational closure is acknowledged as a landmark, and we are going to see that such a construction can be characterised by means of a simple method in the context of propositional logic. We then propose an application of our approach to ra ..."
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Cited by 26 (4 self)
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Abstract. In the field of nonmonotonic logics, the notion of rational closure is acknowledged as a landmark, and we are going to see that such a construction can be characterised by means of a simple method in the context of propositional logic. We then propose an application of our approach to rational closure in the field of Description Logics, an important knowledge representation formalism, and provide a simple decision procedure for this case.
Closing semantic web ontologies
, 2006
"... In this paper, we present a novel formalism of hybrid MKNF knowledge bases, which allows us to seamlessly integrate an arbitrary decidable description logic with logic programming rules. We thus obtain a powerful hybrid formalism that combines the best features of both description logics, such as th ..."
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Cited by 22 (2 self)
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In this paper, we present a novel formalism of hybrid MKNF knowledge bases, which allows us to seamlessly integrate an arbitrary decidable description logic with logic programming rules. We thus obtain a powerful hybrid formalism that combines the best features of both description logics, such as the ability to model taxonomic knowledge, and logic programming, such as the ability to perform nonmonotonic reasoning. Extending DLs with unrestricted rules makes reasoning undecidable. To obtain decidability, we apply the wellknown DLsafety restriction that makes the rules applicable only to explicitly named individuals, and thus trade some expressivity for decidability. We present several reasoning algorithms for different fragments of our logic, as well as the corresponding complexity results. Our results show that, in many cases, the data complexity of reasoning with hybrid MKNF knowledge bases is not higher than the data complexity of reasoning
PROBABILISTIC DESCRIPTION LOGICS FOR THE SEMANTIC WEB
, 2007
"... The work in this paper is directed towards sophisticated formalisms for reasoning under probabilistic uncertainty in ontologies in the Semantic Web. Ontologies play a central role in the development of the Semantic Web, since they provide a precise definition of shared terms in web resources. They ..."
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Cited by 20 (2 self)
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The work in this paper is directed towards sophisticated formalisms for reasoning under probabilistic uncertainty in ontologies in the Semantic Web. Ontologies play a central role in the development of the Semantic Web, since they provide a precise definition of shared terms in web resources. They are expressed in the standardized web ontology language OWL, which consists of the three increasingly expressive sublanguages OWL Lite, OWL DL, and OWL Full. The sublanguages OWL Lite and OWL DL have a formal semantics and a reasoning support through a mapping to the expressive description logics SHIF(D) and SHOIN(D), respectively. In this paper, we present the expressive probabilistic description logics PSHIF(D) and PSHOIN(D), which are probabilistic extensions of these description logics. They allow for expressing rich terminological probabilistic knowledge about concepts and roles as well as assertional probabilistic knowledge about instances of concepts and roles. They are semantically based on the notion of probabilistic lexicographic entailment from probabilistic default reasoning, which naturally interprets this terminological and assertional probabilistic knowledge as knowledge about random and concrete instances, respectively. As an important additional feature, they also allow for expressing terminological default knowledge, which is semantically interpreted as in Lehmann’s lexicographic
Next Steps for Description Logics of Minimal Knowledge and Negation as Failure
"... The more DLs are being used in applications such as the Semantic Web [2], biology, and the clinical sciences, the more certain expressive weaknesses are commented upon. A recurring set of these comments is due to the fact that only few DLs and even fewer DL reasoners support forms of defeasible reas ..."
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Cited by 15 (1 self)
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The more DLs are being used in applications such as the Semantic Web [2], biology, and the clinical sciences, the more certain expressive weaknesses are commented upon. A recurring set of these comments is due to the fact that only few DLs and even fewer DL reasoners support forms of defeasible reasoning. For
Preferential Description Logics
 In LPAR 2007. LNCS(LNAI
, 2007
"... Abstract. We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + T. The typicality operator is intended to select the “most normal ” or “most typical ” instance ..."
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Cited by 14 (7 self)
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Abstract. We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + T. The typicality operator is intended to select the “most normal ” or “most typical ” instances of a concept. In our framework, knowledge bases may then contain, in addition to ordinary ABoxes and TBoxes, subsumption relations of the form “T(C) is subsumed by P”, expressing that typical Cmembers have the property P. The semantics of a typicality operator is defined by a set of postulates that are strongly related to KrausLehmannMagidor axioms of preferential logic P. We first show that T enjoys a simple semantics provided by ordinary structures equipped by a preference relation. This allows us to obtain a modal interpretation of the typicality operator. Using such a modal interpretation, we present a tableau calculus for deciding satisfiability of ALC + T knowledge bases. Our calculus gives a nondeterministicexponential time decision procedure for satisfiability of ALC + T. We then extend ALC + T knowledge bases by a nonmonotonic completion that allows inferring defeasible properties of specific concept instances 1. 1
Adding Integrity Constraints to OWL
"... Abstract. Schema statements in OWL are interpreted quite differently from analogous statements in relational databases. If these statements are meant to be interpreted as integrity constraints (ICs), OWL’s interpretation may seem confusing and/or inappropriate. Therefore, we propose an extension of ..."
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Cited by 13 (0 self)
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Abstract. Schema statements in OWL are interpreted quite differently from analogous statements in relational databases. If these statements are meant to be interpreted as integrity constraints (ICs), OWL’s interpretation may seem confusing and/or inappropriate. Therefore, we propose an extension of OWL with ICs that captures the intuition behind ICs in relational databases. We show that, if the constraints are satisfied, we can disregard them while answering a broad range of positive queries. 1
G.L.: Reasoning about typicality in preferential Description Logics
 In: JELIA
, 2008
"... Abstract. Extensions of Description Logics (DLs) to reason about typicality and defeasible inheritance have been largely investigated. In this paper, we consider two such extensions, namely (i) the extension of DLs with a typicality operator T, having the properties of Preferential nonmonotonic enta ..."
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Cited by 13 (7 self)
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Abstract. Extensions of Description Logics (DLs) to reason about typicality and defeasible inheritance have been largely investigated. In this paper, we consider two such extensions, namely (i) the extension of DLs with a typicality operator T, having the properties of Preferential nonmonotonic entailment P, and (ii) its variant with a typicality operator having the properties of the stronger Rational entailment R. The first one has been proposed in [1, 2]. Here, we investigate the second one and we show, by a representation theorem, that it is equivalent to the approach to preferential subsumption proposed in [3]. We compare the two extensions, preferential and rational, and argue that the first one is more suitable than the second one to reason about typicality, as the latter leads to unintuitive inferences. 1