caa a22 4500 605539197 CHVBK 20210128100905.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10992-014-9329-3 doi (NATIONALLICENCE)springer-10.1007/s10992-014-9329-3 On the Decidability Status of Fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ with General Concept Inclusions [Elektronische Daten] [Franz Baader, Stefan Borgwardt, Rafael Peñaloza] The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. It has turned out, however, that in the presence of general concept inclusion axioms (GCIs) this extension is less straightforward than thought. In fact, a number of tableau algorithms claimed to deal correctly with fuzzy DLs with GCIs have recently been shown to be incorrect. In this paper, we concentrate on fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ , the fuzzy extension of the well-known DL A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ . We present a terminating, sound, and complete tableau algorithm for fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ with arbitrary continuous t-norms. Unfortunately, in the presence of GCIs, this algorithm does not yield a decision procedure for consistency of fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ ontologies since it uses as a sub-procedure a solvability test for a finitely represented, but possibly infinite, system of inequations over the real interval [0,1], which are built using the t-norm. In general, it is not clear whether this solvability problem is decidable for such infinite systems of inequations. This may depend on the specific t-norm used. In fact, we also show in this paper that consistency of fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ ontologies with GCIs is undecidable for the product t-norm. This implies, of course, that for the infinite systems of inequations produced by the tableau algorithm for fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ with product t-norm, solvability is in general undecidable. We also give a brief overview of recently obtained (un)decidability results for fuzzy A ℒ C $\mathcal {A}\mathcal {L}\mathcal {C}$ w.r.t. other t-norms. Springer Science+Business Media Dordrecht, 2014 Fuzzy description logics nationallicence Decidability nationallicence Baader Franz Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany aut Borgwardt Stefan Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany aut Peñaloza Rafael Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany aut Journal of Philosophical Logic Springer Netherlands 44/2(2015-04-01), 117-146 0022-3611 44:2<117 2015 44 10992 https://doi.org/10.1007/s10992-014-9329-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10992-014-9329-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baader Franz Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany aut NATIONALLICENCE 700 1- Borgwardt Stefan Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany aut NATIONALLICENCE 700 1- Peñaloza Rafael Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany aut NATIONALLICENCE 773 0- Journal of Philosophical Logic Springer Netherlands 44/2(2015-04-01), 117-146 0022-3611 44:2<117 2015 44 10992