# Logical Characterizations of Fuzzy Bisimulations in Fuzzy Modal Logics over Residuated Lattices

There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models and fuzzy interpretations in description logics. Fuzzy bisimulations between fuzzy automata over a complete residuated lattice have been introduced by Ćirić et al. in 2012. Logical characterizations of fuzzy bisimulations between fuzzy Kripke models (respectively, fuzzy interpretations in description logics) over the residuated lattice [0,1] with the Gödel t-norm have been provided by Fan in 2015 (respectively, Nguyen et al. in 2020). There was the lack of logical characterizations of fuzzy bisimulations between fuzzy graph-based structures over a general residuated lattice, as well as over the residuated lattice [0,1] with the Łukasiewicz or product t-norm. In this article, we provide and prove logical characterizations of fuzzy bisimulations in fuzzy modal logics over residuated lattices. The considered logics are the fuzzy propositional dynamic logic and its fragments. Our logical characterizations concern invariance of formulas under fuzzy bisimulations and the Hennessy-Milner property of fuzzy bisimulations. They can be reformulated for other fuzzy structures such as fuzzy label transition systems and fuzzy interpretations in description logics.

## Authors

• 7 publications
09/06/2021

### Characterizing Crisp Simulations and Crisp Directed Simulations between Fuzzy Labeled Transition Systems by Using Fuzzy Modal Logics

We formulate and prove logical characterizations of crisp simulations an...
06/24/2021

### A fuzzy take on the logical issues of statistical hypothesis testing

Statistical Hypothesis Testing (SHT) is a class of inference methods whe...
07/18/2021

### Computing the Fuzzy Partition Corresponding to the Greatest Fuzzy Auto-Bisimulation of a Fuzzy Graph-Based Structure

Fuzzy graph-based structures such as fuzzy automata, fuzzy labeled trans...
08/06/2020

### Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics

Description logics (DLs) are a suitable formalism for representing knowl...
01/21/2022

### Scales and Hedges in a Logic with Analogous Semantics

Logics with analogous semantics, such as Fuzzy Logic, have a number of e...
10/27/2020

### Computing Crisp Bisimulations for Fuzzy Structures

Fuzzy structures such as fuzzy automata, fuzzy transition systems, weigh...
02/27/2013

### On Modal Logics for Qualitative Possibility in a Fuzzy Setting

Within the possibilistic approach to uncertainty modeling, the paper pre...
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