No need knowing numerous neighbours towards a realizable interpretation of MLSL

Abstract

The Multi-Lane Spatial Logic MLSL introduced by Hilscher et al. in [4] is a two-dimensional spatial logic geared towards modelling and analysis of traffic situations, where the two dimensions are interpreted as the lanes of a road and the distance travelled down that road, respectively. The intended use of MLSL is for capturing (and reasoning about) guards and invariants in decision-making schemes for highly automated driving [12]. Unfortunately, the logic turns out to be undecidable [7,8,11], rendering implementability and thus the actual use of such guard conditions in real-time decision making questionable in general. We here show that under a reasonable model of technical observation of the traffic situation, the actual decidability and implementability issues take a much more pleasing form: given that an actual autonomous car can only sample state information of a finite set of environmental cars in real-time, we show that it is decidable whether truth of an arbitrary MLSL formula can be safely determined on a given sample size. For such feasible formulas, we furthermore state a procedure for determining their truth values based on such a sample.