Computing Fuzzy Bisimulations for Fuzzy Structures Under the Gödel Semantics

Bisimulation is a well-known notion in modal logic and the theory of labeled transition systems. It is used for characterizing indiscernibility between states and has important applications in minimizing structures, separating expressive powers of modal and related logics, as well as concept learnin...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 29; no. 7; pp. 1715 - 1724
Main Authors: Nguyen, Linh Anh, Tran, Dat Xuan
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptation models
Algorithms
Automata
Complexity
Complexity theory
Computation
Computational modeling
Fans
Fuzzy automata
fuzzy bisimulation
fuzzy description logics
fuzzy labeled transition systems
Fuzzy logic
Semantics
Social networking (online)
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary:Bisimulation is a well-known notion in modal logic and the theory of labeled transition systems. It is used for characterizing indiscernibility between states and has important applications in minimizing structures, separating expressive powers of modal and related logics, as well as concept learning in description logics (DLs). Fuzzy bisimulation is a counterpart of bisimulation for dealing with fuzzy structures. In this article, we present an efficient algorithm with a complexity <inline-formula><tex-math notation="LaTeX">O((m+n)n)</tex-math></inline-formula> for computing the greatest fuzzy bisimulation between two finite fuzzy interpretations in the fuzzy DL <inline-formula><tex-math notation="LaTeX">\mathit {f}\!\mathcal {ALC}</tex-math></inline-formula> under the Gödel semantics, where <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> is the number of individuals and <inline-formula><tex-math notation="LaTeX">m</tex-math></inline-formula> is the number of nonzero instances of roles in the given fuzzy interpretations. We also adapt our algorithm for computing fuzzy bisimulations and simulations between fuzzy finite automata, as well as for dealing with other fuzzy DLs. The resulting algorithms are much more efficient than the previously known ones, as they reduce the complexity from <inline-formula><tex-math notation="LaTeX">O(n^5)</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">O((m+n)n)</tex-math></inline-formula>.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2020.2985000