On Sampling Abstraction of Continuous Time Logic with Durations

Abstract

Duration Calculus (DC) is a real-time logic with measurement of duration of propositions in observation intervals. It is a highly expressive logic with continuous time behaviours (also called signals) as its models. Validity checking of DC is undecidable.We propose a method for validity checking of Duration Calculus by reduction to a sampled time version of this logic called Well Sampled Interval Duration Logic (WSIDL). This reduction relies on representing a continuous time behaviour by a well-sampled behaviour with 1-oversampling. We provide weak and strong reductions (abstractions) of logic DC to logic WSIDL which respectively preserve the validity and the counter models. By combining these reductions with previous work on deciding IDL, we have implemented a tool for validity checking of Duration Calculus. This provides a partial but practical method for validity checking of Duration Calculus. We present some preliminary experimental results to measure the success of this approach.