JUXTAPOSITION: A NEW WAY TO COMBINE LOGICS

JOSHUA SCHECHTER
2011 The Review of Symbolic Logic  
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
more » ... hilosophically 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.
doi:10.1017/s1755020311000219 fatcat:7ye3sh5n5naznlzkh5azkrsbzi