What kind of proof system have Zalta used in "Basic Concepts in Modal Logic"? I have read that text and I'm so interested in the proof theoretic style (as also claimed by Zalta that it is used in modern approaches to modal logic) in it: That is both more mathematically rigorous than the traditional approaches (at least I think so), and also applicable for non-axiomatizable logics. Very nice I think!
Please let me know what is it called and where I can find more about it?
Thanks.

Maybe you are interested into the "algebraic" approach to logic ...
See Abstract algebraic logic and Propositional Consequence Relations and Algebraic Logic with bibliography.
You can see also :


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*H.Andréka, J.D.Monk, I.Németi (eds.), Algebraic logic (1991)

*Dov M.Gabbay & F.Guenthner (editors), Handbook of Philosophical Logic : 2nd ed. Vol.2 (2013), Hajnal Andréka, Istvan Németi and Ildiko Sain, Algebraic Logic, page 133-on.
