Quantifiers on L-algebras

Abstract

Abstract In this paper, we introduce the notion of monadic L-algebras and we study properties of these new structures. We define and investigate the monadic ideals of a monadic L-algebra, and we characterize the monadic ideal generated by a subset of a monadic L-algebra. We define the existential and universal quantifiers on semiregular L-algebras with negation, and we investigate certain properties of these structures. In this sense, we prove that there exists a one to one correspondence between existential and universal quantifiers. We show that any pair of strict quantifiers on a semiregular L-algebra with negation is a monadic operator.