A necessary relation algebra for mereotopology

Studia Logica 69 (3):381 - 409 (2001)
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Abstract

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T 0 topological space with an additional "contact relation" C defined by xCy x ØA (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane.

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Michael J. Winter
University of St. Thomas, Minnesota

Citations of this work

New Work for Carnap’s Quasi-Analysis.Thomas Mormann - 2009 - Journal of Philosophical Logic 38 (3):249-282.
Generalized Region Connection Calculus.Sanjiang Li & Mingsheng Ying - 2004 - Artificial Intelligence 160 (1-2):1-34.
A proof system for contact relation algebras.Ivo Düntsch & Ewa Orłowska - 2000 - Journal of Philosophical Logic 29 (3):241-262.
On the Homogeneous Countable Boolean Contact Algebra.Ivo Düntsch & Sanjiang Li - 2013 - Logic and Logical Philosophy 22 (2):213-251.

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References found in this work

On the calculus of relations.Alfred Tarski - 1941 - Journal of Symbolic Logic 6 (3):73-89.
A calculus of individuals based on "connection".Bowman L. Clarke - 1981 - Notre Dame Journal of Formal Logic 22 (3):204-218.
Connection structures.Loredana Biacino & Giangiacomo Gerla - 1991 - Notre Dame Journal of Formal Logic 32 (2):242-247.

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