Relations algebras in qualitative spatial reasoning

Authors:
Ivo Düntsch;Hui Wang;Stephen Mccloskey
Affiliations:
School of Information and Software Engineering, University of Ulster, Newtownabbey, BT37 OQB, N. Ireland. e-mail: I.Duentsch H.Wang S.McCloskey@ulst.ac.uk;School of Information and Software Engineering, University of Ulster, Newtownabbey, BT37 OQB, N. Ireland. e-mail: I.Duentsch H.Wang S.McCloskey@ulst.ac.uk;(Correspd.) School of Information and Software Engineering, University of Ulster, Newtownabbey, BT37 OQB, N. Ireland. e-mail: I.Duentsch H.Wang S.McCloskey@ulst.ac.uk
Venue:
Fundamenta Informaticae
Year:
1999

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Abstract

The formalization of the “part - of” relationship goes back to the mereology of S. Leśniewski, subsequently taken up by Leonard & Goodman (1940), and Clarke (1981). In this paper we investigate relation algebras obtained from different notions of “part-of”, respectively, “connectedness” in various domains. We obtain minimal models for the relational part of mereology in a general setting, and when the underlying set is an atomless Boolean algebra.