Naïve Comprehension and Contracting Implications

Abstract

In his paper [6], Greg Restall conjectured that a logic supports a naive comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall's conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naive comprehension.