A van Benthem Theorem for Fuzzy Modal Logic

Barbara K\"onig; Dirk Pattinson; Lutz Schr\"oder; Paul Wild

A van Benthem Theorem for Fuzzy Modal Logic

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arxiv 1802.00478 v2 pith:CTODIOWI submitted 2018-02-01 cs.LO

Paul Wild , Lutz Schröder , Dirk Pattinson , Barbara König This is my paper · ORCID

classification cs.LO

keywords fuzzylogicmodalfirst-orderbenthemformulasfragmenttheorem

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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.

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Hausdorff coalgebras
math.CT 2019-08 conditional novelty 6.0 of 10

On quantale-enriched categories the Hausdorff functor has no terminal coalgebra, but on enriched compact Hausdorff spaces it preserves codirected limits, making categories of Hausdorff polynomial coalgebras complete.

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