Abstract
Varieties of topological quasi-Boolean algebras in the vicinity of pre-rough algebras [28, 29] are expanded to residuated algebraic structures by introducing a new implication operation and its residual in these structures. Sequent calculi for some classes of residuated algebraic structures are established. These sequent calculi have the strong finite model property which yields the decidability of the word problem for corresponding classes of algebraic structures.
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