Depth-Bounded Fuzzy Bisimulation for Fuzzy Modal Logic

Abstract

We introduce depth-bounded fuzzy bisimulation between fuzzy Kripke models. Roughly speaking, a depth-bounded fuzzy bisimulation is a decreasing sequence of fuzzy binary relations whose infimum is a fuzzy bisimulation. We provide logical characterizations of depth-bounded fuzzy bisimulations between fuzzy Kripke models w.r.t. a fuzzy multimodal logic over complete residuated lattices, including fuzzy invariance of formulas of with a modal depth bounded by under the th component of a depth-bounded fuzzy bisimulation, as well as the Hennessy-Milner property of depth-bounded fuzzy bisimulations. We also provide a polynomial-time algorithm for computing the th component of the greatest depth-bounded fuzzy bisimulation between two finite fuzzy Kripke models when the underlying complete residuated lattice is linear.