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JUXTAPOSITION: A NEW WAY TO COMBINE LOGICS

Published online by Cambridge University Press:  12 October 2011

JOSHUA SCHECHTER
JOSHUA SCHECHTER*
Affiliation:
Department of Philosophy, Brown University
*
*DEPARTMENT OF PHILOSOPHY, BROWN UNIVERSITY, BOX 1918, PROVIDENCE, RI 02912. E-mail: [email protected]
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Abstract

This paper develops a new framework for combining propositional logics, called “juxtaposition.” Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is paid to the phenomenon of collapse. It is shown that there are logics with two stocks of classical or intuitionist connectives that do not collapse. Finally, the paper briefly investigates the question of which rules, when added to these logics, lead to collapse.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 4 , December 2011 , pp. 560 - 606
Copyright
Copyright © Association for Symbolic Logic 2011

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