We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T 1 spaces.

We explore the relation--algebraic aspects of the region connection calculus (RCC) of Randell et al. (1992a). In particular, we present a refinement of the RCC8 table which shows that the axioms provide for more relations than are listed in the present table. We also show that each RCC model leads to a Boolean algebra. Finally, we prove that a refined version of the RCC5 table has as models all atomless Boolean algebras B with the natural ordering as the "part -- of" relation, and that the table is closed under first order definable relations iff B is homogeneous. 1 Introduction Qualitative reasoning (QR) has its origins in the exploration of properties of physical systems when numerical information is not sufficient -- or not present -- to explain the situation at hand (Weld and Kleer, 1990). Furthermore, it is a tool to represent the abstractions of researchers who are constructing numerical systems which model the physical world. Thus, it fills a gap in data modeling which often l...

We introduce Boolean proximity algebras as a generalization of Efremovi c proximities which are suitable in reasoning about discrete regions. Following Stone's representation theorem for Boolean algebras, it is shown that each such algebra is isomorphic to a substructure of a complete and atomic Boolean proximity algebra. Key words: Proximity algebras, discrete spaces, qualitative spatial reasoning 1

We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two non-empty regular closed sets are connected if they have a non-empty intersection. These are standard examples for structures used in qualitative reasoning, mereotopology, and proximity theory. We exhibit various methods how such algebras can be constructed and give several non-standard examples, the most striking one being a countable model of the Region Connection Calculus in which every proper region has infinitely many holes. 1

We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B/I is of Cantor-Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite Cantor-Bendixson rank.

this paper, we present various forms of set approximations via the unifying concept of modal--style operators. Two examples indicate the usefulness of the approach

This work explores the interconnections between a number of different perspectives on the formalisation of space. We begin with an informal discussion of the intuitions that motivate these formal representations.

In the present report, we study collections of contact relations on a fixed Boolean algebra and show that they can be provided with a rich lattice structure. This follows from a representation theorem which associates with each contact relation a closed graph on the ultrafilter space of the underlying Boolean algebra and vice versa. We also consider collections of special contact relations which have gained some importance in qualitative spatial reasoning. 1

Abstract. Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems. 1

Abstract. Contact relations on an algebra have been studied since the early part of the previous century, and have recently become a powerful tool in several areas of artificial intelligence, in particular, qualitative spatial reasoning and ontology building. In this paper we investigate the structure of the set of all contact relations on a Boolean algebra. 1