# Connection between algebraic logic and computational complexity of logics?

I'm learning a bit about algebraic logic and I was wondering how knowing the algebraic semantics of a given logic might help the study of the logic itself from a computational point of view.

In particular, is there any example of a complexity (or decidability) result for the satisfiability problem for some logics that was obtained by reasoning about its algebraic semantics?

For example, the semantics of propositional logic can be given in terms of boolean algebras. Is there any connection between them and the fact that SAT is decidable and $NP$-complete?

• Removing excluded middle turns SAT from NP to PSPACE complete, but it's still expressible with Boolean Algebra, with one less rule. – jmite Feb 3 '18 at 22:11
• As I said, I’m learning those things, so I thought you need Heyting algebras to give semantics to intuitionistic logic. What am I missing? – gigabytes Feb 4 '18 at 2:59
• Now cross-posted to mathoverflow.net/questions/292183/… . – Emil Jeřábek Feb 5 '18 at 8:53