Spatial and Temporal Reasoning: Beyond Allen’s Calculus

Gérard Ligozat, Debasis Mitra, and Jean-François Condotta

Temporal knowledge representation and reasoning with qualitative temporal knowledge has now been around for several decades, as formalisms such as Allen’s calculus testify. Now a variety of qualitative calculi, both temporal and spatial, has been developed along similar lines to Allen’s calculus. The main object of this paper is to point to open questions which arise when, leaving the now well-chartered waters of Allen’s, we venture into rougher sea of these formalisms. What remains true among the properties of Allen’s calculus? Partial answers are indeed known, but numerous new problems also arise. We try to point to the main issues in this paper.

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