Abstract
Starting from the observation that rational closure has the undesirable property of being an “all or nothing” mechanism, we here consider a multipreferential semantics, which enriches the preferential semantics underlying rational closure in order to separately deal with the inheritance of different properties in an ontology with exceptions. We show that the MP-closure of an \(\mathcal {ALC}\) knowledge base is a construction which is sound with respect to minimal entailment in the multipreference semantics for \(\mathcal {ALC}\).
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Notes
- 1.
Indeed, it is easy to see that, for a satisfiable \(K_i\), in the minimal ranked models \(\mathcal {M}_i\) of \(K_i\), which are the models of the rational closure of \(K_i\), two elements \(x,y \in \varDelta \) either have rank 0, and satisfy all the conditionals \(\mathbf{T}(C) \sqsubseteq A_i\) in \( K_i\), or have rank 1, and falsify at least some conditional \(\mathbf{T}(C) \sqsubseteq A_i\) in \( K_i\).
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This research is partially supported by INDAM-GNCS Project 2018 “Metodi di prova orientati al ragionamento automatico per logiche non-classiche”.
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Giordano, L., Gliozzi, V. (2019). Reasoning About Exceptions in Ontologies: An Approximation of the Multipreference Semantics. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_18
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