Ordering protoalgebraic logics

This article is a first step in the study of the order structure of the set of all protoalgebraic logics over a fixed (but arbitrary) language. In particular, it is shown herein that the set is a join-complete semilattice, that it has no minimum, and that is not a meet-semilattice. One of the key points in this study is the discovery of a large family of rather weak protoalgebraic logics, from whi...