A van Benthem Theorem for Fuzzy Modal Logic [article]

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2018 arXiv   pre-print
We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic. Specifically, we consider a first-order fuzzy predicate logic along with its modal fragment, and show that the fuzzy first-order formulas that are non-expansive w.r.t. the natural notion of bisimulation distance are exactly those that can be approximated by fuzzy modal formulas.
arXiv:1802.00478v2 fatcat:nypcw2p4kvefxefmrpv7vorsp4