The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes, to relations of contact and connectedness, to the concepts of surface, point, neighbourhood, and so on. The basis of the theory is mereology, the formal theory of part and whole, a theory which is shown to have a number of advantages, for ontological purposes, over standard treatments of topology in set-theoretic terms. One (...) central goal of the paper is to provide a rigorous formulation of Brentano's thesis to the effect that a boundary can exist as a matter of necessity only as part of a whole of higher dimension which it is the boundary of. It concludes with a brief survey of current applications of mereotopology in areas such as natural-language analysis, geographic information systems, machine vision, naive physics, and database and knowledge engineering. (shrink)

Whitehead, in his famous book "Process and Reality", proposed a definition of point assuming the concepts of “region” and “connection relation” as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.

This paper describes the topological aspect of a logic-based, artificial intelligence approach to formalising the qualitative description of spatial properties and relations, and reasoning about those properties and relations. This approach, known as RCC theory, has been under development for several years at the University of Leeds. The main rationale for this project is that qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human thinking about the world: even where quantitative spatial data (...) are most important, they must be attached to the components of a perceived spatial structure if we are to make use of them. RCC theory covers other qualitative aspects of spatial description and reasoning, but the topological properties and relations of spatially extended entities are fundamental to our work. The topological formalisms used by mathematicians are, in general, not well suited to the task of formalising the kinds of ‘common-sense’ or ‘everyday’ qualitative spatial description and reasoning which are our primary interest. Nevertheless, we must come to grips with the concepts of topology as practised by mathematicians if we are not to risk constantly ‘reinventing wheels’. (shrink)