A Meta-Logic of Inference Rules: Syntax

This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the presence of the rule of reverse substitution, requires certain change the definition of structurality

Rejection and Truth-Value Gaps

A theorem due to Shoesmith and Smiley that axiomatizes two-valued multiple-conclusion logics is extended to partial logics