Abstract
We develop a novel description logic (DL) for representing and reasoning with contextual knowledge. Our approach descends from McCarthy’s tradition of treating contexts as formal objects over which one can quantify and express first-order properties. As a foundation we consider several common product-like combinations of DLs with multimodal logics and adopt the prominent \((\mathbf{K}_n)_\mathcal{ALC}\). We then extend it with a second sort of vocabulary for describing contexts, i.e., objects of the second dimension. In this way, we obtain a two-sorted, two-dimensional combination of a pair of DLs \(\mathcal{ALC}\), called \({\mathcal{ALC}_\mathcal{ALC}}\). As our main technical result, we show that the satisfiability problem in this logic, as well as in its proper fragment \((\mathbf{K}_n)_\mathcal{ALC}\) with global TBoxes and local roles, is 2ExpTime-complete. Hence, the surprising conclusion is that the significant increase in the expressiveness of \({\mathcal{ALC}_\mathcal{ALC}}\) due to adding the vocabulary comes for no substantial price in terms of its worst-case complexity.
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Klarman, S., Gutiérrez-Basulto, V. (2010). \({\mathcal{ALC}_\mathcal{ALC}}\): A Context Description Logic. In: Janhunen, T., Niemelä, I. (eds) Logics in Artificial Intelligence. JELIA 2010. Lecture Notes in Computer Science(), vol 6341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15675-5_19
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DOI: https://doi.org/10.1007/978-3-642-15675-5_19
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