Undecidability Results for Multi-Lane Spatial Logic

We consider (un)decidability of Multi-Lane Spatial Logic (MLSL), a multi-dimensional modal logic introduced for reasoning about traffic manoeuvres. MLSL with length measurement has been shown to be undecidable. However, the proof relies on exact values. This raises the question whether the logic remains undecidable when we consider robust satisfiability, i.e. when values are known only approximately. Our main result is that robust satisfiability of MLSL is undecidable. Furthermore, we prove that even MLSL without length measurement is undecidable. In both cases we reduce the intersection emptiness of two context-free languages to the respective satisfiability problem. This is the full version of a paper with the same title published at the ICTAC 2015.