The validity of temporal properties of reactive programs is complete relative to pure assertional validity. That is, the authors prove that the validity of all temporal formulae expressing safety, response, and reactivity properties is reducible to the validity of assertional (that is, nontemporal) formulae. The value of this result is that whenever we might use assertional reasoning, we are free to use temporal reasoning, which is more expressive, confident that it is at least as well grounded as assertional reasoning.

The paper is exceptionally well written. The thread through the complex results is easy to follow, thanks to the authors’ explanations and examples; nonetheless, the paper is not verbose. I found only one place where the presentation was confusing. The authors define temporal formulae as constructed out of state formulae via Boolean operators for negation and disjunction and four basic temporal operators. If we took this literally, the temporal instantiation rule would allow us to infer from a state formula p that henceforth  not-p.  No doubt what the authors intended was to make sure temporal formulae are those with temporal operators as their main connectives and also Boolean combinations of these. The paper contains a few typos, but the corrections are easily inferred. The paper is well referenced, highly accessible, and self-contained. Unexplained references, such as to the Borel hierarchy, are not essential to understanding the paper.