Abstract

An extension of the Quantified Propositional Calculus1 obtained by the addition of two binary propositional functions is put forward as an inheritor of E. Schröder's “Algebra der Logik”. The formal system is itself not new, in fact it forms part of A. P. Morse's “A Theory of Sets”; although the latter is considered as a first-order system. Since the additional propositional functions are not invariant under the logical biconditional, this system–and many others naturally obtained from it–give us a collection of examples of non-standard, but mathematically meaningful, propositional systems.