Proof Theory of a Multi-Lane Spatial Logic

Linker, Sven and Hilscher, Martin (2013) Proof Theory of a Multi-Lane Spatial Logic. In: Theoretical Aspects of Computing – ICTAC 2013 : Proceedings of the 10th International Colloquium on Theoretical Aspects of Computing -- ICTAC 2013. Lecture Notes in Computer Science . Springer, Berlin, pp. 231-248. ISBN 9783642397172

Abstract

We extend the Multi-lane Spatial Logic MLSL, introduced in previous work for proving the safety (collision freedom) of traffic maneuvers on a multi-lane highway, by length measurement and dynamic modalities. We investigate the proof theory of this extension, called EMLSL. To this end, we prove the undecidability of EMLSL but nevertheless present a sound proof system which allows for reasoning about the safety of traffic situations. We illustrate the latter by giving a formal proof for a lemma we could only prove informally before.