Naslov (srp)

Approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras

Autor

Stanković, Marko
Ćirić, Miroslav
Stanimirović, Stefan
Stakić, Đorđe

Opis (eng)

Abstract In this paper, we study two types of L-approximate simulations and five types of L-approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras. The value L is an element from a Heyting algebra, which serves to relax the conditions in the definitions of simulations and bisimulations. Additionally, L represents the degree of modal equivalence between two worlds from distinct Kripke models, considering the given non-empty set of modal formulae. Further, we develop an efficient algorithm for computing the greatest L-approximate simulation and bisimulation for every type. We also demonstrate the application of these algorithms in the state reduction of Kripke models in such a way that the reduced model preserves the same semantic properties to the extent determined by the scalar L. We also present the algorithm that partitions the interval of the degrees of modal equivalence into subintervals with the same minimal corresponding factor fuzzy Kripke model.

Opis (eng)

The first three authors acknowledge the support of the Science Fund of the Republic of Serbia, Grant No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications – QUAM. The authors are also supported by the Ministry of Science, Technological Development and Innovation, Republic of Serbia. The first author acknowledges support under Contract No. 451-03-66/2024-03/200139, while the second and third authors were supported under Contract No. 451-03-65/2024-03/200124. The fourth author acknowledges support under Contract No. 451-03-65/2024-03/20097.

Jezik

engleski

Datum

2025

Licenca

© All rights reserved

Predmet

Keywords: Fuzzy Kripke model, Approximate bisimulation, Fuzzy bisimulation,Modal logic

Deo kolekcije (1)

o:28218

Ekonomski fakultet