What kind of proof system have Zalta used in "Basic Concepts in Modal Logic"?

Question

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.

Answer 1

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 :

• 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.