English

A van Benthem Theorem for Fuzzy Modal Logic

Logic in Computer Science 2018-02-06 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1802.00478,
  title  = {A van Benthem Theorem for Fuzzy Modal Logic},
  author = {Paul Wild and Lutz Schröder and Dirk Pattinson and Barbara König},
  journal= {arXiv preprint arXiv:1802.00478},
  year   = {2018}
}
R2 v1 2026-06-23T00:08:06.615Z