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A non-monotonic Description Logic for reasoning about typicality

Abstract : In this paper we propose a non-monotonic extension of the Description Logic ALC for reasoning about prototypical properties and inheritance with exceptions. The resulting logic, called ALC + T-min, is built upon a previously introduced (monotonic) logic ALC + T that is obtained by adding a typicality operator T to ALC. The operator T is intended to select the "most normal" or "most typical" instances of a concept, so that knowledge bases may contain subsumption relations of the form T(C) subset of D ("T(C) is subsumed by D"), expressing that typical C-members are instances of concept D. From a knowledge representation point of view, the monotonic logic ALC + T is too weak to perform inheritance reasoning. In ALC + T-min, in order to perform non-monotonic inferences, we define a "minimal model" semantics over ALC + T. The intuition is that preferred or minimal models are those that maximize typical instances of concepts. By means of ALC + T-min we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding ALC + T-min entailment that allows to give a complexity upper bound for the logic, namely that query entailment is in co-NExp(NP)
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Submitted on : Tuesday, February 28, 2017 - 8:38:57 PM
Last modification on : Friday, March 11, 2022 - 5:53:22 PM

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Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Pozzato. A non-monotonic Description Logic for reasoning about typicality. Artificial Intelligence, Elsevier, 2013, 195, pp.165-202. ⟨10.1016/j.artint.2012.10.004⟩. ⟨hal-01479546⟩

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