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Fuzzy Bisimulations in Fuzzy Description Logics Under the Gödel Semantics

Ha, Quang Thuy and Nguyen, Linh Anh and Nguyen, Thi Hong Khanh and Tran, Thanh Luong (2018) Fuzzy Bisimulations in Fuzzy Description Logics Under the Gödel Semantics. In: International Joint Conference on Rough Sets (IJCRS 2018). Lecture Notes in Computer Science (11103). Springer, pp. 559-571. ISBN ISBN 978-3-319-99367-6

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Description logics (DLs) are a suitable formalism for representing knowledge about domains in which objects are described not only by attributes but also by binary relations between objects. Fuzzy DLs can be used for such domains when data and knowledge about them are vague. One of the possible ways to specify classes of objects in such domains is to use concepts in fuzzy DLs. As DLs are variants of modal logics, indiscernibility in DLs is characterized by bisimilarity. The bisimilarity relation of an interpretation is the largest auto-bisimulation of that interpretation. In (fuzzy) DLs, it can be used for concept learning. In this paper, for the first time, we define fuzzy bisimulation and (crisp) bisimilarity for fuzzy DLs under the Gödel semantics. The considered logics are fuzzy extensions of the DL ALCreg with additional features among inverse roles, nominals, qualified number restrictions, the universal role and local reflexivity of a role. We give results on invariance of concepts as well as conditional invariance of TBoxes and ABoxes for bisimilarity in fuzzy DLs under the Gödel semantics. We also provide a theorem on the Hennessy-Milner property for fuzzy bisimulations in fuzzy DLs under the Gödel semantics.

Item Type: Book Section
Subjects: Information Technology (IT)
Divisions: Faculty of Information Technology (FIT)
Depositing User: Hà Quang Thụy
Date Deposited: 14 Nov 2018 04:30
Last Modified: 14 Nov 2018 04:30

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