Completeness of many-sorted equational logic

The rules of deduction which are usually used for many-sorted equational logic in computer science, for example in the study of abstract data types, are not sound. Correcting these rules by introducing explicit quantifiers yields a system which, although it is sound, is not complete; some new rules are needed for the addition and deletion of quantifiers. This note is intended as an informal, but precise, introduction to the main issues and results. It gives an example showing the unsoundness of the usual rules; it also gives a completeness theorem for our new rules, and gives necessary and sufficient conditions for the old rules to agree with the new.