Authors: Sven Linker ; Martin Hilscher

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 the reservation lemma we could only prove informally before. Furthermore we prove a basic theorem showing that the length measurement is independent from the number of lanes on the highway.

• 03B35 - Mechanization of proofs and logical operations
• 03B40 - Combinatory logic and lambda calculus
• 03B70 - Logic in computer science
• 68Q42 - Grammars and rewriting systems