Spatial Cognition and Computation 1: 155–180, 1999.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Relation algebras over containers and surfaces:
An ontological study of a room space
MAX J. EGENHOFER and M. ANDREA RODRÍGUEZ
Department of Spatial Information Science and Engineering, University of Maine, 5711
Boardman Hall, Orono, ME 04469-5711, USA
Abstract. Recent research in geographic information systems has been concerned with the
construction of algebras to make inferences about spatial relations by embedding spatial rela-
tions within a space in which decisions about compositions are derived geometrically. We
pursue an alternative approach by studying spatial relations and their inferences in a concrete
spatial scenario, a room space that contains such manipulable objects as a box, a ball, a table,
a sheet of paper, and a pen. We derive from the observed spatial properties an algebra related
to the fundamental spatial concepts of containers and surfaces and show that this container-
surface algebra holds all properties of Tarski’s relation algebra, except for the associativity.
The crispness of the compositions can be reﬁned by considering the relative size of the
objects) and their roles (i.e., whether it is explicitly known that the objects are containers or
Key words: image schemata, relation algebra, room space, spatial relations
We study the inference power of relation algebras related to the two basic
spatial concepts of containers and surfaces. Algebras over spatial relations
provide powerful mechanisms for spatial reasoning (Egenhofer and Sharma
1992; Frank 1992; Smith and Park 1992). Such inferences have become
increasingly important in geographic information systems where people
record ﬁeld observations (Futch et al. 1992; McGranaghan and Wester 1988)
and later analyze them to ﬁnd new information (Egenhofer and Sharma
1993). Unlike calculations that employ traditional computational geometry,
spatial-relation algebras rely on symbolic computations over small sets of
relations (de Kleer and Brown 1984). This method is very versatile since no
detailed information about the geometry of the objects, such as coordinates
of boundary points or shape parameters, is necessary to make inferences.
The domain for these algebras are qualitative spatial relations, which are
predicates that come close to what people use in everyday reasoning about