Abstract
In this contribution, we introduce the class of protonegational logics as a natural extension of the class of protoalgebraic logics, a typical example of a protonegational logic which is not protoalgebraic being the f^;_; g fragment of intuitionistic logic. For logics which satisfy a mild condition called the maximal consistency property, protonegationality may be characterized by a variety of equivalent conditions, in a manner reminiscent of the several equivalent denitions of protoalgebraicity.
In addition to having some intrinsic interest, it turns out that protonegational logics form the appropriate framework for the study of so-called inconsistency lemmas, initiated recently by Raftery , a topic picked up in the sequel to this contribution.