Depth-Bounded Fuzzy Bisimulation for Fuzzy Modal Logic
Linh Anh Nguyen, Ivana Mičić, Ngoc Thanh Nguyên, Stefan Stanimirović
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 fK over complete residuated lattices, including fuzzy invariance of formulas of fK with a modal depth bounded by n under the nth 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 nth component of the greatest depth-bounded fuzzy bisimulation between two finite fuzzy Kripke models when the underlying complete residuated lattice is linear.