Approximate Stream Reasoning with Metric Temporal Logic under Uncertainty

Stream reasoning can be defined as incremental reasoning over incrementally-available information. The formula progression procedure for Metric Temporal Logic (MTL) makes use of syntactic formula rewritings to incrementally evaluate formulas against incrementally-available states. Progression however assumes complete state information, which can be problematic when not all state information is available or can be observed, such as in qualitative spatial reasoning tasks or in robotics applications. In those cases, there may be uncertainty as to which state out of a set of possible states represents the 'true' state. The main contribution of this paper is therefore an extension of the progression procedure that efficiently keeps track of all consistent hypotheses. The resulting procedure is flexible, allowing a trade-off between faster but approximate and slower but precise progression under uncertainty. The proposed approach is empirically evaluated by considering the time and space requirements, as well as the impact of permitting varying degrees of uncertainty.