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...

We describe an envisionment-based simulation program. The program bears some design similarities to Kuipers' QSIM algorithm, but differs in the underlying ontology and in the implemented theory in the envisioning process. The program implements part of an axiomatic, first order theory that has been developed to represent and reason about space and time. Topological information is extracted from the modelled domain and is expressed in the theory as sets of distinct topological relations holding betwen sets of objects. These form the qualitative states in the underlying theory and simulation. Processes in the theory are represented in the envisionment as paths in the envisionment tree. We show the feasability of this particular ontology in the implementation of a simulation program derived from a logic-based formal theory. A description of the algorithm is given and the whole is illustrated with an example of a simulation of the processes phagocytosis and exocytosis - two pro...

Qualitative spatial reasoning is important for many spatial information systems, including GISs. It is based on the manipulation of qualitative spatial relationships and is used to infer spatial relationships which are not stored explicitly in the Geographic DataBase (GDB), to answer spatial queries given partial spatial knowledge and to maintain the consistency of the GDB. This paper compares the basic approaches developed for expressing qualitative topological, orientation and direction relationships. An extension of one of the classified approaches is then used for the representation of directional relationships (north, south, east, etc.) between objects of arbitrary shapes and for the representation of flow direction relationships (topological relationships between objects carrying flow, e.g. road segments, utility networks, etc.) as required within a GIS.

. The paper describes spatial indexes, a 2D array structure which can be used for the representation of spatial information. A spatial index preserves only a set of spatial relations of interest, called the modelling space, and discards visual information (such as shape, size etc.) and information about irrelevant spatial relations. Every relation in the modelling space can be defined using a set of special points, called the representative points. By filling the index array cells with representative points we can gain adequate expressive power to answer queries regarding the spatial relations of the modelling space without the need to access the initial image or an object database. 1 Introduction Several representational structures have been proposed for the representation of spatial knowledge in different areas. Depending on the particular viewpoint the goals have been explanatory and predictive power, in the case of psychological models of Vision and Imagery, expressive power and i...

We describe an envisionment-based simulation program. The program bears some design similarities to Kuipers ' QSIM algorithm, but di ers in the underlying ontology and in the implemented theory in the envisioning process. The program implements part of an axiomatic, rst order theory that has been developed to represent and reason about space and time. Topological information is extracted from the modelled domain and is expressed in the theory as sets of distinct topological relations holding betwen sets of objects. These form the qualitative states in the underlying theory and simulation. Processes in the theory are represented in the envisionment as paths in the envisionment tree. We show the feasability of this particular ontology in the implementation of a simulation program derived from a logic-based formal theory. A description of the algorithm is given and the whole is illustrated with an example of a simulation of the processes phagocytosis and exocytosis- two processes used by unicellular organisms for garnering food and expelling waste material respectively. Finally we show how the program can be viewed as a specialized theorem prover by mapping program transformations to logical inferences in the modelling theory. 1