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

TL;DR

This paper develops logical characterizations for crisp simulations and directed simulations in fuzzy labeled transition systems using fuzzy modal logics with t-norm semantics, enhancing understanding of system behaviors.

Contribution

It introduces new logical characterizations of crisp simulations and directed simulations in fuzzy systems using a fragment of fuzzy propositional dynamic logic.

Findings

Logical characterizations of simulation preservation

Hennessy-Milner property established for these simulations

Framework applicable to fuzzy labeled transition systems

Abstract

We formulate and prove logical characterizations of crisp simulations and crisp directed simulations between fuzzy labeled transition systems with respect to fuzzy modal logics that use a general t-norm-based semantics. The considered logics are fragments of the fuzzy propositional dynamic logic with the Baaz projection operator. The logical characterizations concern preservation of positive existential (respectively, positive) modal formulas under crisp simulations (respectively, crisp directed simulations), as well as the Hennessy-Milner property of such simulations.