Partial-State Progression for Stream Reasoning with Metric Temporal Logic.

The formula progression procedure for Metric Temporal Logic (MTL), originally proposed by Bacchus and Kabanza, makes use of syntactic formula rewritings to incrementally evaluate MTL 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 robot applications. Our main contribution is an extension of the progression procedure to handle partial state information. For each missing truth value, we efficiently consider all consistent hypotheses by branching progression for each such hypothesis. The resulting procedure is flexible, allowing a trade-off between faster but approximate and slower but precise partial-state progression.