A robust interpretation of duration calculus

We transfer the concept of robust interpretation from arithmetic first-order theories to metric-time temporal logics. The idea is that the interpretation of a formula is robust iff its truth value does not change under small variation of the constants in the formula. Exemplifying this on Duration Calculus (DC), our findings are that the robust interpretation of DC is equivalent to a multi-valued interpretation that uses the real numbers as semantic domain and assigns Lipschitz-continuous interpretations to all operators of DC.

Furthermore, this continuity permits approximation between discrete and dense time, thus allowing exploitation of discrete-time (semi-)decision procedures on dense-time properties.