Montanari, Angelo and Puppis, Gabriele and Sala, Pietro - A decidable weakening of Compass Logic based on cone-shaped cardinal directions

lmcs:1608 - Logical Methods in Computer Science, December 10, 2015, Volume 11, Issue 4
A decidable weakening of Compass Logic based on cone-shaped cardinal directions

Authors: Montanari, Angelo and Puppis, Gabriele and Sala, Pietro

We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening of Venema's Compass Logic. We prove that, unlike Compass Logic and other projection-based spatial logics, its satisfiability problem is decidable (precisely, PSPACE-complete). We also show that it is expressive enough to capture meaningful interval temporal logics - in particular, the interval temporal logic of Allen's relations "Begins", "During", and "Later", and their transposes.


Source : oai:arXiv.org:1510.03319
DOI : 10.2168/LMCS-11(4:7)2015
Volume: Volume 11, Issue 4
Published on: December 10, 2015
Submitted on: December 16, 2014
Keywords: Computer Science - Logic in Computer Science


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