Abstract
In this paper we introduce a combination of Answer Set Programming (ASP) and Description Logics (DL) (in particular, \(\mathcal{ALC}\)) on top of a modal temporal basis using connectives from Linear-time Temporal Logic (LTL). On the one hand, for the temporal extension of \(\mathcal{ALC}\), we depart from Baader et al.’s proposal \(\mathcal{ALC}\)-LTL that restricts the use of temporal operators to occur only in front of DL axioms. On the other hand, for the temporal extension of ASP we use its formalization in terms of Temporal (Quantified) Equilibrium Logic (TEL). This choice is convenient since (non-temporal) Equilibrium Logic has been already used to capture the semantics of hybrid theories, that is, combinations of ASP programs with DL axioms. Our proposal, called \(\mathcal{ALC}\)-TEL, actually interprets \(\mathcal{ALC}\) axioms in terms of their translation into first order sentences, so that the semantics of TEL is eventually used in the background. The resulting formalism conservatively extends TEL, hybrid theories and \(\mathcal{ALC}\)-LTL as particular cases.
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