On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is always minimal and globally consistent (in the sense of strong $n$-consistency) in a qualitative sense. The well-known subclass of convex interval relations provides one such an example of distributive subalgebras. This paper first gives a characterisation of distributive subalgebras, which states that the intersection of a set of $n\geq 3$ relations in the subalgebra is nonempty if and only if the intersection of every two of these relations is nonempty. We further compute and generate all maximal distributive subalgebras for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra, and Rectangle Algebra. Lastly, we establish two nice properties which will play an important role in efficient reasoning with constraint networks involving a large number of variables.Comment: Adding proof of Theorem 2 to appendi

Fuzzy vector structures for transient phenomenon representation

International audienceThis paper deals with data structures within GIS. Continuous phenomenons are usually represented by raster structures for simplicity reasons. With such structures spatial repartitions of the data is not easily interpretable. Moreover, in an overlapping clustering context these structures remove the links between the data and the algorithms. We propose a vector representation of such data based on non-regular multi-rings polygons. The structure requires multipart nested polygons and new set operations. We present the formalism based on belief theory and uncertainty reasoning. We also detail the implementation of the structures and the set operations. The structures and the set operations are illustrated in the context of forest classification having diffuse transitions