Canonical Calculi: Invertibility, Axiom Expansion and (Non)-determinism.

We apply the semantic tool of non-deterministic matrices to characterize two important properties of canonical Gentzen-type calculi: invertibility of rules and axiom expansion. We show that in every canonical calculus G satisfying a natural condition, the following are equivalent: (i) the connectives of G admit axiom expansion, (ii) the rules of G are invertible, and (iii) G has a characteristic finite deterministic matrix. [ABSTRACT FROM AUTHOR]