Relations Algebras in Qualitative Spatial Reasoning

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.