Abstract
We study the fuzzy extension of the Description Logic \(\mathcal{F\!L}_0\) with semantics based on the Gödel t-norm. We show that subsumption w.r.t. a finite set of primitive definitions, using greatest fixed-point semantics, can be characterized by a relation on weighted automata. We use this result to provide tight complexity bounds for reasoning in this logic, showing that it is PSpace-complete. If the definitions do not contain cycles, subsumption becomes co-NP-complete.
Partially supported by the DFG under grant BA 1122/17-1, in the research training group 1763 (QuantLA), and the Cluster of Excellence ‘Center for Advancing Electronics Dresden’.
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Borgwardt, S., Leyva Galano, J.A., Peñaloza, R. (2014). The Fuzzy Description Logic \(\mathsf{G}\text{-}{\mathcal{F\!L}_0} \) with Greatest Fixed-Point Semantics. In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_5
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DOI: https://doi.org/10.1007/978-3-319-11558-0_5
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