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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
Preferential Role Restrictions
"... Abstract. We extend ALC with preferential role restrictions as concept constructors, and argue that preferential universal restriction represents a defeasible version of standard universal restriction. The resulting DL is more expressive without adding to the complexity of TBox reasoning. We present ..."
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Abstract. We extend ALC with preferential role restrictions as concept constructors, and argue that preferential universal restriction represents a defeasible version of standard universal restriction. The resulting DL is more expressive without adding to the complexity of TBox reasoning. We present a tableau system to compute TBox entailment, show that this notion of entailment is not sufficient when adding ABoxes, and refine entailment to deal adequately with ABox reasoning. 1
Towards a Logic of Dilation
"... Abstract. We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a seman-tic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, a ..."
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Abstract. We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a seman-tic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, and a generalized no-tion of forgetting in propositional logic on the other hand. We place our work in the context of existing theories of approximation spaces and forgetting, and show that neighbourhoods obtained by combining collective and selective dilation pro-vide a suitable semantic framework within which to reason computationally with uncertainty in a classical setting.
