On redundant topological constraints

Abstract

The Region Connection Calculus (RCC) [41] is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC5 and RCC8 (two fragments of RCC) as well as other qualitative spatial/temporal calculi has been investigated in depth in the literature. Most of these works focus on the consistency of qualitative constraint networks. In this paper, we consider the important problem of redundant qualitative constraints. For a set Γ of qualitative constraints, we say a constraint (xRy) in Γ is redundant if it is entailed by the rest of Γ. A prime subnetwork of Γ is a subset of Γ which contains no redundant constraints and has the same solution set as Γ. It is natural to ask how to compute such a prime subnetwork, and when it is unique.In this paper, we show that this problem is in general intractable, but becomes tractable if Γ is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of RCC5 or RCC8 in which weak composition distributes over nonempty intersections, then Γ has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from Γ. As a byproduct, we show that any path-consistent network over such a distributive subalgebra is weakly globally consistent and minimal. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant con- * Corresponding Author

Qualitative Spatial Logics for Buffered Geometries

“…A similar property is defined by Li, Long, Liu, Duckham, and Both (2015) for RCC relations. The proofs for the last three calculation rules are provided in Appendix A, whilst others are more obvious.…”

“…The concept of DS(Σ + ) is similar to the concept of distributive subalgebra defined by Li et al (2015), as the composition operation distributes over non-empty intersections of intervals involved in DS(Σ + ) (Rule 16 in Lemma 16). However, in our work, the composition operation is defined for intervals rather than relations.…”

On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

“…As every globally consistent network is minimal, this shows that path consistent networks over C IA is also minimal. Later, Chandra and Pujari [5] defined a class of convex RCC8 relations (written D 8 41 in [15] and this paper) and proved that every path consistent network over D 8 41 is minimal. More recently, Amaneddine and Condotta [2] found another subclass of IA, written as S IA , and proved that C IA and S IA are the only maximal subalgebras of IA such that path consistent networks over which are globally consistent.…”

“…These problems have been investigated in depth in the past three decades for many qualitative calculi in the literature, see e.g. [1,2,3,5,15,18,21,23,26].…”

“…Although distributive subalgebra is a new concept proposed recently in [9,15], several examples of distributive subalgebras have been studied before. The first such a subalgebra, the subclass of convex IA relations C IA , was found in [17], where Ligozat also proved that path consistent networks over C IA is globally consistent.…”