Review of Symbolic Logic 4 (4):560-606 (2011)

Joshua Schechter
Brown University
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 briefy investigates the question of which rules, when added to these logics, lead to collapse.
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DOI 10.1017/s1755020311000219
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References found in this work BETA

Change in View.Gilbert Harman - 1986 - Behaviorism 16 (1):93-96.
Truth and the Absence of Fact.Hartry Field - 2001 - Oxford University Press.
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.

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Weakly Classical Theories of Identity.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):607-644.

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