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We develop the first bisimulation-based method of concept learning, called BBCL, for knowledge bases in description logics (DLs). Our method is formulated for a large class of useful DLs, with well-known DLs like ALC, SHIQ, SHOIQ, SROIQ. As bisimulation is the notion for characterizing indiscernibility of objects in DLs, our method is natural and very promising.

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 extensions of DLs can be used for such domains when data and knowledge about them are vague and imprecise. 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 DLs and their fuzzy extensions, such equivalence relations can be used for concept learning. In this paper, we define and study fuzzy bisimulation and bisimilarity for fuzzy DLs under the Gödel semantics, as well as crisp bisimulation and strong bisimilarity for such logics extended with involutive negation. The considered logics are fuzzy extensions of the DL ALC reg (a variant of PDL) with additional features among inverse roles, nominals, (qualified or unqualified) number restrictions, the universal role, local reflexivity of a role and involutive negation. We formulate and prove results on invariance of concepts under fuzzy (resp. crisp) bisimulation, conditional invariance of fuzzy TBoxex/ABoxes under bisimilarity (resp. strong bisimilarity), and the Hennessy-Milner property of fuzzy (resp. crisp) bisimulation for fuzzy DLs without (resp. with) involutive negation under the Gödel semantics. Apart from these fundamental results, we also provide results on using fuzzy bisimulation to separate the expressive powers of fuzzy DLs, as well as results on using strong bisimilarity to minimize fuzzy interpretations. * This is a revised and corrected version of the publication "Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics", Fuzzy Sets and Systems 388: 146-178 (2020)

In description logic-based information systems, objects are described not only by attributes but also by binary relations between them. This work studies concept learning in such information systems. It extends the bisimulationbased concept learning method of Nguyen and Szałas (Rough sets and intelligent systems. Springer, Berlin, pp 517-543, 2013). We take attributes as basic elements of the language. Each attribute may be discrete or numeric. A Boolean attribute is treated as a concept name. This approach is more general and suitable for practical information systems based on description logic than the one of Nguyen and Szałas (Rough sets and intelligent systems. Springer, Berlin, pp 517-543, 2013). As further extensions, we also allow data roles and the concept constructors "functionality" and "unqualified number restrictions". We formulate and prove an important theorem on basic selectors. We also present a domain partitioning method based on information gain that has been used for our implementation of the method. Apart from basic selectors and simple selectors, we introduce a new kind of selectors, called extended selectors. The evaluation

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