Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex