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Reconciling description logics and rules
, 2010
"... Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and ru ..."
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Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNF + knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an openworld assumption, while the rules are based on a closedworld assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNF + knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds.
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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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.
P: Local Closed World Semantics: Grounded Circumscription for OWL
 In The Semantic Web  ISWC 2011, Volume 7031 of Lecture Notes in Computer Science
"... Abstract. We present a new approach to adding closed world reasoning to the Web Ontology Language OWL. It transcends previous work on circumscriptive description logics which had the drawback of yielding an undecidable logic unless severe restrictions were imposed. In particular, it was not possible ..."
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Abstract. We present a new approach to adding closed world reasoning to the Web Ontology Language OWL. It transcends previous work on circumscriptive description logics which had the drawback of yielding an undecidable logic unless severe restrictions were imposed. In particular, it was not possible, in general, to apply local closure to roles. In this paper, we provide a new approach, called grounded circumscription, which is applicable to SROIQ and other description logics around OWL without these restrictions. We show that the resulting language is decidable, and we derive an upper complexity bound. We also provide a decision procedure in the form of a tableaux algorithm. 1
U.: Defeasible inheritancebased description logics
 In: IJCAI11. (2011) 813–818
"... Defeasible inheritance networks are a nonmonotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to nonmonotonic reasoning. We will combine these two approaches and define a new nonmonotonic closur ..."
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Defeasible inheritance networks are a nonmonotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to nonmonotonic reasoning. We will combine these two approaches and define a new nonmonotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics wellsuited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on wellknown landmark test examples. 1.
Local Closed World Semantics: Keep it simple, stupid!
"... Abstract. A combination of open and closedworld reasoning (usually called local closed world reasoning) is a desirable capability of knowledge representation formalisms for Semantic Web applications. However, none of the proposals made to date for extending description logics with local closed worl ..."
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Abstract. A combination of open and closedworld reasoning (usually called local closed world reasoning) is a desirable capability of knowledge representation formalisms for Semantic Web applications. However, none of the proposals made to date for extending description logics with local closed world capabilities has had any significant impact on applications. We believe that one of the key reasons for this is that current proposals fail to provide approaches which are intuitively accessible for application developers and at the same time are applicable, as extensions, to expressive description logics such as SROIQ, which underlies the Web Ontology Language OWL. In this paper we propose a new approach which overcomes key limitations of other major proposals made to date. It is based on an adaptation of circumscriptive description logics which, in contrast to previously reported circumscription proposals, is applicable to SROIQ without rendering reasoning over the resulting language undecidable.
ModelTheoretic Inseparability and Modularity of Description Logic Ontologies
, 2013
"... The aim of this paper is to introduce and study modeltheoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called modeltheoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ ..."
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The aim of this paper is to introduce and study modeltheoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called modeltheoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ if they cannot be distinguished by the Σreducts of their models and thus can equivalently be replaced by one another in any application where only vocabulary items from Σ are relevant. We study indepth the complexity of deciding inseparability for the description logics EL and ALC and their extensions with inverse roles. We then discuss notions of modules of a TBox based on modeltheoretic inseparability and develop algorithms for extracting minimal modules from acyclic TBoxes. Finally, we provide an experimental evaluation of our module extraction algorithm based on the largescale medical TBox Snomed ct.
Reasoning about Explanations for Negative Query Answers in DLLite
"... In order to meet usability requirements, most logicbased applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the pre ..."
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In order to meet usability requirements, most logicbased applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DLLite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations. 1.
A tableau calculus for minimal modal model generation
"... Model generation and minimal model generation is useful for fault analysis, verification of systems and validation of data models. Whereas for classical propositional and firstorder logic several model minimization approaches have been developed and studied, for nonclassical logic the topic has be ..."
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Cited by 4 (4 self)
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Model generation and minimal model generation is useful for fault analysis, verification of systems and validation of data models. Whereas for classical propositional and firstorder logic several model minimization approaches have been developed and studied, for nonclassical logic the topic has been much less studied. In this paper we introduce a minimal model generation calculus for multimodal logic K(m) and extensions of K(m) with the axioms T and B. The calculus provides a method to generate all and only minimal modal Herbrand models, and each model is generated exactly once. A novelty of the calculus is a nonstandard complement splitting rule designed for minimal model generation. Experiments show the rule has the added benefit of reducing the search space.
THE COMPLEXITY OF EXPLAINING NEGATIVE QUERY ANSWERS IN DLLite
, 2012
"... In order to meet usability requirements, most logicbased applications provide explanation facilities for reasoning services. This holds also for DLs, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tupl ..."
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Cited by 4 (0 self)
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In order to meet usability requirements, most logicbased applications provide explanation facilities for reasoning services. This holds also for DLs, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for (conjunctive) query answering over DLLite ontologies, by adopting abductive reasoning, that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a certain assertion for an explanation. We characterize the computational complexity of these problems for subset minimal and cardinality minimal explanations.
Nonmonotonic Reasoning in Description Logics: Rational Closure for the ABox
"... Abstract. The introduction of defeasible reasoning in description logics has been a main research topic in the field in the last years. Despite the fact that various interesting formalizations of nonmonotonic reasoning for the TBox have been proposed, the application of such a kind of reasoning also ..."
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Abstract. The introduction of defeasible reasoning in description logics has been a main research topic in the field in the last years. Despite the fact that various interesting formalizations of nonmonotonic reasoning for the TBox have been proposed, the application of such a kind of reasoning also to ABoxes is more problematic. In what follows we are going to present the adaptation for the ABox of a classical nonmonotonic form of reasoning, namely Lehmann and Magidor’s Rational Closure. We present both a procedural and a semantical characterization, and we conclude the paper with a comparison between our and other analogous proposals. 1