Axiomatizing Distance Logics
In [STU 00, KUT 03] 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 of [KUT 03] and give a new proof of their decidability.