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Abstract:
Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible
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 Allens 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 neighborhood
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. Reorientations
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.
