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Logic Journal of IGPL Advance Access originally published online on September 24, 2007
Logic Journal of IGPL 2007 15(5-6):689-706; doi:10.1093/jigpal/jzm044
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Logic of Classes

E. G. K. Lopez-Escobar

Mathematics Department, University of Maryland, College Park, USA. E-mail: egkle{at}math.umd.edu


  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 (of a rather non-standard type).

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.

Key Words: Boolean algebras • Propositional Logics • Protothetic • Set theory • Universal Logics.

1Also called: "Second Order Propositional Calculus", "Extended Propositional Calculus", "Protothetic" or "Elementary Protothetic"


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