Abstract
A sequent calculus S for the variety tqBa of all topological quasi-Boolean algebras is established. Using a construction of syntactic finite algebraic model, the finite model property of S is shown, and thus the decidability of S is obtained. We also introduce two non-distributive variants of topological quasi-Boolean algebras. For the variety TDM 5 of all topological De Morgan lattices with the axiom 5, we establish a sequent calculus S 5 and prove that the cut elimination holds for it. Consequently the decidability of S 5 is established. Furthermore, this proof-theoretic method is applied to some subvarieties of TDM 5 .
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