Spatial Cognition and Computation 1: 261–290, 1999.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
The cognitive adequacy of Allen’s interval calculus for
qualitative spatial representation and reasoning
University of Freiburg, Center for Cognitive Science, Friedrichstr. 50, D-79098 Freiburg,
Abstract. Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plau-
sible than conventional numerical approaches to spatial reasoning, because it copes with the
indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge.
The paper reports experimental results concerning the cognitive adequacy of an important
approach used in QSR, namely the spatial interpretation of the interval calculus introduced by
Allen (1983). Knauff, Rauh and Schlieder (1995) distinguished between the conceptual and
inferential cognitive adequacy of Allen’s interval calculus. The former refers to the thirteen
base relations as a representational system and the latter to the compositions of these relations
as a tool for reasoning. The results of two memory experiments on conceptual adequacy show
that people use ordinal information similar to the interval relations when representing and
remembering spatial arrangements. Furthermore, symmetry transformations on the interval
relations were found to be responsible for most of the errors, whereas conceptual neigh-
borhood theory did not appear to correspond to cognitively relevant concepts. Inferential
adequacy was investigated by two reasoning experiments and the results show that in inference
tasks where the number of possible interval relations for the composition is more than one,
subjects ignore numerous possibilities and interindividually prefer the same relations. Reori-
entations and transpositions operating on the relations seem to be important for reasoning
performance as well, whereas conceptual neighborhood did not appear to affect the difﬁculty
of reasoning tasks based on the interval relations.
Key words: cognitive adequacy, conceptual neighborhood, interval relations, spatial knowl-
edge, spatial memory, spatial reasoning, symmetry transformation
Reasoning based on the qualitative representation of spatial knowledge is an
active research area of AI and has found growing interest from two quite
different perspectives: from an engineering point of view and from a cognitive
science perspective. From an engineer’s standpoint, qualitative representa-
tions of spatial relationships together with appropriate reasoning mechanisms
are a promising way to enable computers to make predictions, diagnoses,
planing etc. in a qualitative manner, even if detailed quantitative knowledge
is not available or inferences based on such knowledge are computationally
intractable (Cohn 1997).
The cognitive science motivation for working on
QSR is that it possibly allows us to gain insight into the way human beings