A TCSP-like decidable constraint language generalising existing cardinal direction relations

WORK EXACTLY AS REJECTED AT THE MAIN ECAI 2004 Abstract. We define a quantitative constraint language subsuming two calculi well-known in QSR: Frank’s cone-shaped and projection-based calculi of cardinal direction relations. The language is based on convex constraints of the form (α, β)(x, y), with α, β ∈ [0, 2π) and (β−α) ∈ [0, π): the meaning of such a constraint is that point x belongs to the (convex) cone-shaped area rooted at y, and bounded by angles α and β. The general form of a constraint is a disjunction of the form [(α1, β1) ∨ · · · ∨ (αn, βn)](x, y), with (αi, βi)(x, y), i = 1 . . . n, being a convex constraint as described above: the meaning of such a general constraint is that, for some i = 1 . . . n, (αi, βi)(x, y) holds. A conjunction of such general constraints is a TCSP-like CSP, which we will refer to as an SCSP (Spatial Constraint Satisfaction Problem). We describe how to compute converse, intersection and composition of SCSP constraints, allowing thus to achieve path consistency for an SCSP. We show how to translate a convex constraint into a conjunction of linear inequalities on variables consisting of the arguments’ coordinates. Our approach to effectively solving a general SCSP is then to adopt a solution search algorithm using (1) path consistency as the filtering method during the search, and (2) the Simplex algorithm, guaranteeing completeness, at the leaves of the search tree.