Towards a Duration Calculus Proof Assistant in PVS

The Duration Calculus (DC) is an interval temporal logic for reasoning about real-time systems. This paper describes a tool for constructing DC speciications and checking DC proofs. The proof assistant is implemented by encoding the semantics of DC within the higher-order logic of a general-purpose speciication and veriication environment called PVS. We develop a Gentzen style sequent proof system for DC which we show to be sound with respect to the semantic encoding. We exploit the similarity between the sequent calculus of PVS and the sequent calculus of DC to obtain a DC proof system where the proofs are carried out in PVS at the semantic level, but appear as proofs in the DC proof system. The resulting system, called PC/DC, retains the speciication and veriication capabilities of PVS within the framework of the Duration Calculus. We present an example of a DC proof whose PC/DC presentation closely follows the lines of the corresponding pencil-and-paper DC arguments. Our approach can be applied to speciication logics other than DC.