This paper presents an axiomatic formalization of a theory of top-level relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the sub-universal relation among universals and the parthood relation among individuals, as well as cross-categorial relations such as instantiation and membership. We show that an adequate understanding of the formal properties of such relations - in particular their behavior with respect to time - is critical for geographic information processing. The axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer verified and the computational representation of the theory is available online.
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Qualitative spatio-temporal reasoning;
Document Type: Research Article
Department of Philosophy, State University of New York at Buffalo, Buffalo, NY, USA,New York State Center of Excellence in Bioinformatics and Life Sciences, State University of New York at Buffalo, Buffalo, NY, USA
Publication date: June 1, 2009
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