Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics
| Autor: | Thi Hong Khanh Nguyen, Thanh-Luong Tran, Quang-Thuy Ha, Ngoc Thanh Nguyen, Linh Anh Nguyen |
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| Rok vydání: | 2020 |
| Předmět: |
Bisimulation
Computer Science - Logic in Computer Science 0209 industrial biotechnology Logic Binary relation Inverse 02 engineering and technology Fuzzy logic Algebra 020901 industrial engineering & automation Description logic Negation Artificial Intelligence 0202 electrical engineering electronic engineering information engineering Gödel Equivalence relation 020201 artificial intelligence & image processing computer computer.programming_language Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 388:146-178 |
| ISSN: | 0165-0114 |
| Popis: | 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 G\"odel 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 $\mathcal{ALC}_{reg}$ (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 G\"odel 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. Comment: This is a revised and corrected version of the publication "Bisimulation and bisimilarity for fuzzy description logics under the G\"odel semantics", Fuzzy Sets and Systems 388: 146-178 (2020) |
| Databáze: | OpenAIRE |
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