Revising Z: semantics and logic
Abstract:
Note to editor/referees: We provide full details of proofs in this draft. Naturally we would envisage most of this being removed from a published version. However, even with all proofs removed, the paper is around 30 pages long (in the jounal style). With a sensible amount of proof detail it is 34 pages long. We appreciate that the nominal upper bound for papers is currently 20 pages. One possible solution would be to reform this draft into two papers of 17 pages: roughly breaking the material at the end of the current section 5. Your advice would be appreciated. Abstract. We introduce a simple specification logic ZC comprising a logic and semantics (in ZF set theory). We then provide an interpretation for (a rational reconstruction of) the specification language Z within ZC. As a result we obtain a sound logic for Z, including the schema calculus. A consequence of our formalisation is a critique of a number of concepts used in Z. We demonstrate that the complications and confusions which these concepts introduce can be avoided without compromising expressibility.
