Modal logics for mereotopological relations

We present a complete axiomatization of a logic denoted by MTML (Mereo-Topological Modal Logic) based on the following set of mereotopological relations: part-of, overlap, underlap, contact, dual contact and interior part-of. We prove completeness theorems for MTML with respect to several classes of models including the standard topological models over the set of regular-closed subsets of arbitrary topological spaces. We show that MTML possesses fmp with respect to a class of non-standard models, which implies its decidability. In this way we propose also a solution of the main open problem, formulated in [17] to find a decidable modal logic for topological relations.

• Type: Conference
• Year: 2008
• Where: AIML
• Authors: Yavor Nenov, Dimiter Vakarelov
• Keywords: AIML 2008, Logical Reasoning, Mereo-Topological Modal Logic, Modal Logic, Standard Topological Models