Abstract
We introduce a tableau calculus for a nonmonotonic extension of low complexity Description Logic \(\mathcal{EL}^\bot\) that can be used to reason about typicality and defeasible properties. The calculus deals with Left Local knowledge bases in the logic \(\mathcal{EL}^{\bot} {\bf T}_{min}\) recently introduced in [8] . The calculus performs a two-phase computation to check whether a query is minimally entailed from the initial knowledge base. It is sound, complete and terminating. Furthermore, it is a decision procedure for Left Local \(\mathcal{EL}^{\bot} {\bf T}_{min}\) knowledge bases, whose complexity matches the known results for the logic, namely that entailment is in Πp 2.
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Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L. (2011). A Tableau Calculus for a Nonmonotonic Extension of \(\mathcal{EL}^\bot\) . In: Brünnler, K., Metcalfe, G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2011. Lecture Notes in Computer Science(), vol 6793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22119-4_15
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DOI: https://doi.org/10.1007/978-3-642-22119-4_15
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