Two notes on propositional primal logic
Propositional primal logic, as defined by Gurevich and Neeman, has two kinds of quotations: p said φ, and p implied φ. Note 1. The derivation problem for propositional primal logic with one kind of quotations is solvable linear time. Note 2. In the Hilbertian calculus for propositional primal logic, the shortest derivation of a formula φ from hypotheses H may be exponential in the length of (H,φ).