Digitizing Interval Duration Logic

Interval Duration Logic, (IDL), is a dense time logic for specifying properties of real-time systems. Its validity is undecidable. A corresponding discrete-time logic QDDC has decidable validity. In this paper, we consider a reduction of IDL validity question to QDDC validity using notions of digitization. A new notion of Strong Closure under Inverse Digitization, SCID, is proposed. It is shown that for all SCID formulae, the dense and the discrete-time validity coincide. Moreover, SCID has good algebraic properties which allows us to conveniently prove that many interesting IDL formulae are in fact SCID. We also give some approximation techniques to strengthen/weaken formulae to SCID form. We illustrate the use of this approach by an example where a densetime IDL formula is digitized and then verified using the QDDC validity checker, DCVALID.