We deal with monotone structural deductive systems in an unspecified propositional language $${\mathcal{L}}$$L . These systems fall into several overlapping classes, forming a hierarchy. Along with well-known classes of deductive systems such as those of implicative, Fregean and equivalential systems, we consider new classes of unital and weakly implicative systems. The latter class is auxiliary, while the former is central in our discussion. Our analysis of unital systems leads to the concept of Lindenbaum–Tarski algebra which, under some natural conditions, is a free algebra in a variety closely related to the deductive system in focus.

Unital deductive systems, a new class of deductive systems, are central to our discussion and lead to the concept of the Lindenbaum-Tarski algebra.

Beyond Rasiowan Systems: Unital Deductive Systems

Key Takeaway: Unital deductive systems, a new class of deductive systems, are central to our discussion and lead to the concept of the Lindenbaum-Tarski algebra.