On Tool Support for Duration Calculus on the Basis of Presburger Arithmetic

Interval Logics are often very expressive logics for which decision and model-checking algorithms are hard or even impossible to achieve, and this also applies for Duration Calculus, which adds the notion of accumulated duration to the Interval Temporal Logic introduced by Moszkowski et al. In this ongoing work, we report on our experiences with implementing the model-checking algorithm in [12], which reduces model checking to checking formulas of Presburger arithmetic.

The model-checking algorithm generates Presburger formulas that may have sizes being exponential in the chop depth of the Duration Calculus formulas, so it is not clear whether this is a feasible approach. The decision procedure is partitioned into a frontend with reductions including ”cheap”, equation-based quantifier eliminations, and a general quantifier-elimination procedure, where we have experimented with an implementation based on Cooper’s algorithm and with the SMT solver Z3.

The formula reductions are facilitated using a new ’guarded normal form’. Applying the frontend before a general quantifier elimination procedure gave significant improvements for most of the experiments.