关于定性时空演算的分配子代数
On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi
摘要：
定性演算在定性时空知识的表示和推理中起着核心作用。本文研究了定性演算的分配子代数，即非空交上的（弱）合成分配子代数。对于RCC 5和RCC 8，已经证明分配子代数上的路径一致约束网络在定性意义上总是最小的且全局一致的（在强$n$-一致性的意义上）。众所周知的凸区间关系子类提供了一个这样的例子分配子代数。本文首先给出了分配子代数的一个刻划，即子代数中的一组$n\geq 3$关系的交非空当且仅当其中每两个关系的交非空.我们进一步计算并生成点代数、区间代数、RCC5和RCC8、基数关系代数和矩形代数的所有极大分配子代数。最后，我们建立了两个很好的性质，这将发挥重要作用，在有效的推理与约束网络涉及大量的变量。
英文摘要：
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.
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