A complete axiom system for polygonal mereotopology of the real plane

This paper presents a calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities. A first order predicate language ℒ with a distinguished unary predicate c(x), function-symbols +, · and - and constants 0 and 1 is defined. An interpretation ℛ for ℒ is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as 'region x is connected' and the function-symbols and constants are given their meaning in terms of a Boolean algebra of polygons. We give an alternative interpretation script G sign based on the real closed plane which turns out to be isomorphic to ℛ. A set of axioms and a rule of inference are introduced. We prove the soundness and completeness of the calculus with respect to the given interpretation. © 1998 Kluwer Academic Publishers.