Casl Specifications of Qualitative Calculi [chapter]

Stefan Wölfl, Till Mossakowski
2005 Lecture Notes in Computer Science  
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
more » ... 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. A.G. Cohn and D.M. Mark (Eds.): COSIT 2005, LNCS 3693, pp. 200-217, 2005. c Springer-Verlag Berlin Heidelberg 2005 I J before J meets J overlaps J during J starts J finishes J equals J before J meets J overlaps J during J starts J finishes Fig. 1. Allen's interval relations
doi:10.1007/11556114_13 fatcat:7xuhplmsfbftbf7cxrcj6td6qe