Authors: Angelo Montanari ; Gabriele Puppis ; Pietro Sala

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.

• 03B25 - Decidability of theories and sets of sentences
• 03B44 - Temporal logic
• 03B45 - Modal logic (including the logic of norms)
• 03B70 - Logic in computer science
• 03D15 - Complexity of computation (including implicit computational complexity)