In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept (...) of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator. (shrink)

Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used to define (...) point-free concept of connectedness that for the regular open regions of E coincides with the standard topological notion of connectedness, i.e., a region of the plane E is connected in the sense of topology if and only if it has no separable proper part. Moreover, it is shown that the contact relation algebra REL(O*E, C) and the relation algebra REL(O*E, NTPP) generated by the non-tangential proper parthood relation NTPP, coincide. This entails that the allegedly purely topological notion of connectedness can be defined in mereological terms. (shrink)