A Tableau-Based System for Spatial Reasoning about Directional Relations
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A decidable spatial logic with cone-shaped cardinal directions
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
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It is widely accepted that spatial reasoning plays a central role in artificial intelligence, for it has a wide variety of potential applications, e.g., in robotics, geographical information systems, and medical analysis and diagnosis. While spatial reasoning has been extensively studied at the algebraic level, modal logics for spatial reasoning have received less attention in the literature. In this paper we propose a new modal logic, called spatial propositional neighborhood logic (SpPNL for short) for spatial reasoning through directional relations. We study the expressive power of SpPNL, we show that it is able to express meaningful spatial statements, we prove a representation theorem for abstract spatial frames, and we devise a (non-terminating) sound and complete tableaux-based deduction system for it. Finally, we compare SpPNL with the well-known algebraic spatial reasoning system called rectangle algebra.