| Abstract:
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In Section 1 I present basic facts on binary relations and their algebras.
This is followed by an introduction to abstract relation algebras.
Expressiveness and powers of definability of the calculus of binary relations
will be explored in Section 4. As a gentle introduction to relation algebras
occurring in reasoning about time and space, I will recall Allen's interval
algebra and the algebra of closed circles in the Euclidean plane.
Contact relations and some small relation algebras generated by them are
introduced in Section 6. The smallest relation algebras on an atomless Boolean
algebra generated by a contact relation whose associated order is the Boolean
order will be presented in Section 7. In the next Section, I will introduce
the Region Connection Calculus (RCC), and will explore which relations must
be present in any model of the RCC, in particular, in any standard topological
model whose base consists of regular open sets.
I will also interpret some of these relations topologically in the Euclidean
plane. Section 9 presents a sound and complete proof system for relation
algebras generated by a contact relation, and, finally, I will propose a
frame for reasoning about regions with imperfect information, which is
based on the data model of rough sets.
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