Relation Algebras over Containers and Surfaces: An Ontological
Study of a Room Space
Max Egenhofer and Andrea Rodríguez Spatial Cognition and Computation 1 (2): 155-180, 1999.
Abstract
Recent research in geographic information systems has been
concerned with the construction of algebras to make inferences
about spatial relations by embedding spatial relations 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
TarskiÕs 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 surfaces).
Full article
Max Egenhofer and 
Andrea Rodríguez
