Modal logics for mereotopological relations
Yavor Nenov, Dimiter Vakarelov · Advances in Modal Logic · 2008
We present a complete axiomatization of a logic denoted by MTML (Mereo-Topological Modal Logic) based on the followin g set of mereotopological relations: part-of, overlap, underlap, contact, dual con- tact and interior part-of. We prove completeness theorems for MTML with respect to several classes of models including the standard topological mod- els over the set of regular-closed subsets of arbitrary topo logical spaces. We show that MTML possesses fmp with respect to a class of non-st andard models, which implies its decidability. In this way we propose also a solu- tion of the main open problem, formulated in (17) to find a decidable modal logic for topological relations.