A van Benthem Theorem for Fuzzy Modal Logic

2018/02/01 by Wild, Paul, Schröder, Lutz, Pattinson, Dirk +1 · 2 citations
#03B45 #03B52 #03B70 #F.4.1 #FOS: Computer and information sciences #I.2.4 #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.1802.00478

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.

Cited by

• Non-Expansive Fuzzy Coalgebraic Logic
• Locality in Residuated-Lattice Structures

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