Inproceedings,
CASL Specifications of Qualitative Calculi
Conference on Spatial Information Theory, volume 3693 of Lecture Notes in Computer Science, page 200-217. Springer; Berlin, (2005)
Abstract
In AI a large number of calculi for efficient reasoning about
spatial and temporal entities have been developed. The most
prominent temporal calculi are the point algebra of linear time and
Allen's interval calculus. Examples of spatial calculi include
mereotopological calculi, Frank's cardinal direction calculus,
Freksa's double cross calculus, Egenhofer and Franzosa's
intersection calculi, and Randell, Cui, and Cohn's region connection
calculi.
These calculi are designed for modeling specific aspects of space or
time, respectively, to the effect that the class of intended models
may vary widely with the calculus at hand. But from a formal point
of view these calculi are often closely related to each other.
For example, the spatial region connection calculus RCC5 may be
considered a coarsening of Allen's (temporal) interval calculus. And
vice versa, intervals can be used to represent spatial objects that
feature an internal direction.
The central question of this paper is how these calculi as well as
their mutual dependencies can be axiomatized by algebraic
specifications. This question will be investigated within the
framework of the Common Algebraic Specification Language
(CASL), a specification language developed by the Common
Framework Initiative for algebraic specification and development
(CoFI). We explain scope and expressiveness of CASL by discussing
the specifications of some of the calculi mentioned before.
