Axiomatizing distance logics.
Oliver Kutz, Holger Sturm, Nobu-Yuki Suzuki, Frank Wolter, and Michael Zakharyaschev
In "Logics of Metric Spaces" (TOCL 2003) we introduced a family of `modal' languages intended for talking about distances. These languages are interpreted in `distance spaces' which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to axiomatize the modal fragments of the semantically defined distance logics and give a new proof of their decidability.