A Comparison of Inferences about Containers and Surfaces in
Small-Scale and Large-Scale Spaces
Andrea Rodríguez and
Max Egenhofer Journal of Visual Languages and Computing 11 (6): 639-662, 2000.
Abstract
Inference mechanisms about spatial relations constitute an
important aspect of spatial reasoning as they allow users to derive
unknown spatial information from a set of known spatial relations.
When formalized in the form of algebras, spatial-relation
inferences represent a mathematically sound definition of the
behavior of spatial relations, which can be used to specify
constraints in spatial query languages. Current spatial query
languages utilize spatial concepts that are derived primarily from
geometric principles, which do not necessarily match with the
concepts people use when they reason and communicate about spatial
relations. This paper presents an alternative approach to spatial
reasoning by starting with a small set of spatial operators that
are derived from concepts closely related to human cognition. This
cognitive foundation comes from the behavior of image schemata,
which are cognitive structures for organizing peopleÕs
experiences and comprehension. From the operations and spatial
relations of a small-scale space, a container-surface algebra is
defined with nine basic spatial operators -- inside, outside, on,
off, their respective converse relations -- contains, omits,
supports, separated, and the identity relation equal. The
container-surface algebra was applied to spaces of different sizes
-- large-scale space population with large-scale objects, and its
inferences were assessed through human-subject experiments.
Discrepancies between the container-surface algebra and the
human-subject testing appear for combinations of spatial relations
that result in more than one possible inference depending on the
relative size of objects. For configurations with small-scale and
large-scale objects larger discrepancies were found because people
use relations such as part of and at in lieu of in. Basic concepts
such as containers and surfaces seem to be a promising approach to
define and derive inferences among spatial relations that are close
to human reasoning.
Full article
Andrea Rodríguez and
Max Egenhofer