eprintid: 3551
rev_number: 11
eprint_status: archive
userid: 307
dir: disk0/00/00/35/51
datestamp: 2019-08-21 03:35:11
lastmod: 2019-08-21 03:35:11
status_changed: 2019-08-21 03:35:11
type: article
metadata_visibility: show
creators_name: Nguyen, Linh Anh
creators_name: Ha, Quang Thuy
creators_name: Nguyen, Ngoc Thanh
creators_name: Nguyen, Thi Hong Khanh
creators_name: Tran, Thanh Luong
creators_id: thuyhq@vnu.edu.vn
corp_creators: Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
corp_creators: aculty of Information Technology, VNU University of Engineering and Technology, 144 Xuan Thuy, Hanoi, Vietnam
corp_creators: Department of Information Systems, Faculty of Computer Science and Management, Wroclaw University of Science and Technology, Poland
corp_creators: Faculty of Information Technology, Nguyen Tat Thanh University, Ho Chi Minh City, Vietnam
corp_creators: Faculty of Information Technology, Electricity Power University, 235 Hoang Quoc Viet, Hanoi, Vietnam
corp_creators: Department of Information Technology, University of Sciences, Hue University, 77 Nguyen Hue, Hue city, Vietnam
title: Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics
ispublished: pub
subjects: IT
subjects: Scopus
subjects: isi
divisions: fac_fit
abstract: 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  (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 TBoxes/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.
date: 2019-08-12
date_type: published
publisher: Elsevier
official_url: https://www.journals.elsevier.com/fuzzy-sets-and-systems
id_number: https://doi.org/10.1016/j.fss.2019.08.004
full_text_status: none
publication: Fuzzy Sets and Systems
refereed: TRUE
issn: 0165-0114
related_url_url: https://www.sciencedirect.com/science/article/pii/S0165011419303367?via%3Dihub
citation:   Nguyen, Linh Anh and Ha, Quang Thuy and Nguyen, Ngoc Thanh and Nguyen, Thi Hong Khanh and Tran, Thanh Luong  (2019) Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics.  Fuzzy Sets and Systems .    ISSN 0165-0114