A sequent calculus wG5 is introduced for the variety of partition topological quasi-Boolean algebras. The sequent calculus wG5 has the cut elimination property, i.e., every sequent derivable in wG5 has a cut-free derivation. Furthermore, a sequent calculus wG4_t is introduced for the variety of topological quasi-Boolean algebras with tense operators, and it is a conservative extension of a sequent calculus wG4 for the variety of topological quasi-Boolean algebras.
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