We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its useful expressiveness. An axiomatisation of the new theory and a comparison with the two original theories is given.

In this paper, we present a spatial logic which can be used to reason about topological and spatial relationships among objects in spatial databases. The main advantages of such a formalism are its rigorousness, clear semantics and sound inference mechanism. We also show how the formalism can be extended to include orientation and metrical information. Comparisons with other formalisms are discussed.

. In this paper we review previous work on non modal spatial logics and explore a corresponding modal spatial logic. Furthermore we present an initial classification of kinds of spatially indexed propositions. 1 Introduction Although the use of interval temporal logics has been an active research area in AI for some time, the analogous development of ontologies for space and spatial logics based on regions has only relatively recently started to become a serious research activity (eg Pribbenow and Schlieder 1992, Narayan 1992). Various approaches have been promulgated; for example one can simply use Allen's (1983) temporal relations on each of the cartesian axes to specify the qualitative relationship between two regions (eg Hernandez 1990, Mukerjee and Joe 1990), but this has the disadvantage of either requiring knowledge about the absolute orientation of the two regions or their orientation relative to a fixed viewpoint. For many applications one might only have local information a...