The Algebraic Structure of Sets of Regions. In Hirtle, S. C. and Frank, A. U., Eds. The provision of ontologies for spatial entities is an important topic in spatial information theory. This paper gives an introduction to these Heyting structures, and provides evidence of their importance as algebraic theories of sets of regions. The main evidence is a proof that elements of certain Heyting algebras provide models of the Region-Connection Calculus developed by Cohn et al.
Further evidence is provided by a new qualitative theory of regions with indeterminate boundaries.
This theory uses modal operators which are related to the algebraic operations present in a bi-Heyting algebra.