A Tableau-Based System for Spatial Reasoning about Directional Relations

Authors:
Davide Bresolin;Angelo Montanari;Pietro Sala;Guido Sciavicco
Affiliations:
Department of Computer Science, University of Verona, Verona, Italy;Department of Mathematics and Computer Science, University of Udine, Udine, Italy;Department of Mathematics and Computer Science, University of Udine, Udine, Italy;Department of Information, Engineering and Communications, University of Murcia, Murcia, Spain
Venue:
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Year:
2009

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Abstract

The management of qualitative spatial information is an important research area in computer science and AI. Modal logic provides a natural framework for the formalization and implementation of qualitative spatial reasoning. Unfortunately, when directional relations are considered, modal logic systems for spatial reasoning usually turn out to be undecidable (often even not recursively enumerable). In this paper, we give a first example of a decidable modal logic for spatial reasoning with directional relations, called Weak Spatial Propositional Neighborhood Logic (WSpPNL for short). WSpPNL features two modalities, respectively an east modality and a north modality, to deal with non-empty rectangles over *** ×***. We first show the NEXPTIME-completeness of WSpPNL, then we develop an optimal tableau method for it.