Abstract
Commutative, integral and bounded G B L -algebras form a subvariety of residuated lattices which provides the algebraic semantics of an interesting common fragment of intuitionistic logic and of several fuzzy logics. It is known that both the equational theory and the quasiequational theory of commutative G B L -algebras are decidable (in contrast to the noncommutative case), but their complexity has not been studied yet. In this paper, we prove that both theories are in PSPACE , and that the quasiequational theory is PSPACE -hard.
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