Abstract
We show how to combine the standard tableau system for the basic description logic ALC and Wolper’s tableau calculus for proposi- tional temporal logic PTL (with the temporal operators ‘next-time’ and ‘until’) in order to design a terminating sound and complete tableau- based satisfiability-checking algorithm for the temporal description logic PTL ALC of [20] interpreted in models with constant domains. We use the method of quasimodels [18,16] to represent models with in finite domains, and the technique of minimal types [11] to maintain these domains constant. The combination is flexible and can be extended to more expressive description logics or even to decidable fragments of first-order temporal logics.
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Lutz, C., Sturm, H., Wolter, F., Zakharyaschev, M. (2001). Tableaux for Temporal Description Logic with Constant Domains. In: Goré, R., Leitsch, A., Nipkow, T. (eds) Automated Reasoning. IJCAR 2001. Lecture Notes in Computer Science, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45744-5_10
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DOI: https://doi.org/10.1007/3-540-45744-5_10
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