Extending Metacompleteness to Systems with Classical Formulae

Abstract

In honour of Bob Meyer, the paper extends the use of his concept of metacompleteness to include various classical systems, as much as we are able. To do this for the classical sentential calculus, we add extra axioms so as to treat the variables like constants. Further, we use a one-sorted and a two-sorted approach to add classical sentential constants to the logic DJ of my book, Universal Logic. It is appropriate to use rejection to represent classicality in the one-sorted case. We then extend these methods to the quantified logics, but we use a finite domain of individual constants to do this.