On Redundant Topological Constraints (Extended Abstract)

Redundancy checking is an important task in AI subfields such as knowledge representation and constraint solving. This paper considers redundant topological constraints, defined in the region connection calculus RCC8. We say a constraint in a set Γ of RCC8 constraints 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. While this problem is in general intractable, we show that, if S is a subalgebra of 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 by-product, we show that any path-consistent network over such a distributive subalgebra is minimal.