Effectible residuated lattices and \(n\)-th roots
The author introduces ``effectible residuated lattices'' and ``effectible Girard algebras'' as generalizations of various structures considered by Höhle and others, which, in turn, are generalizations of many structures arising as the algebras of many-valued logics as well as the order-theoretic counterparts of classes of bounded linear operators in Hilbert space. The present paper gives sufficient conditions for a Girard algebra to be an effect algebra. Similar conditions are given for residuated lattices to coincide with a suitable generalization of effect algebras.
scientific article; zbMATH DE number 5762244