Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology

Abstract

Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the semantics of natural language expressions concerning locations and relative positions. While several authors have proposed axioms for these notions, no one with the exception of Tarski [18], who based his axiomatization of mereological notions on a Euclidean metric, has attempted to give them a semantics. We offer an alternative to Tarski, starting with mereotopological notions that have proved useful in the semantic analysis of spatial expressions. We also give a complete axiomatization of this account of mereotopological reasoning. 1 Introduction Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the Natural Language (NL) semantics of expressions concerning locations and relative positions. For example, reasoning about objects inside other objects or on them may involve complex...