Affiliation:
1. University of Niš, Pedagogical Faculty in Vranje, Vranje, Serbia
2. University of Niš, Faculty of Sciences and Mathematics, Niš, Serbia
Abstract
In the present paper, we study fuzzy multimodal logics over complete Heyting
algebras and Kripke models for these logics. We introduce two types of
simulations (forward and backward) and five types of bisimulations (forward,
backward, forward-backward, backward-forward and regular) between Kripke
models, as well as the corresponding presimulations and prebisimulations,
which are simulations and bisimulations with relaxed conditions. For each
type of simulations and bisimulations an efficient algorithm has been
provided that works as follows: it computes the greatest
presimulation/prebisimulation of that type, and then checks whether it meets
the additional condition: if it does, then it is also the greatest
simulation/ bisimulation of that type, otherwise, there is not any
simulation/bisimulation of that type. The algorithms are inspired by
algorithms for checking the existence and computing the greatest simulations
and bisimulations between fuzzy automata. We also demonstrate the application
of these algorithms in the state reduction of Kripke models. We show that
forward bisimulation fuzzy equivalences on the Kripke model provide reduced
models equivalent to the original model concerning plus-formulas, backward
bisimulation fuzzy equivalences provide reduced models equivalent concerning
minus-formulas, while regular bisimulation fuzzy equivalences provide
reduced models equivalent concerning all modal formulas.
Publisher
National Library of Serbia
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