Co-rotation constructions of residuated semigroups

A construction method, called connected co-rotation, is introduced in this paper. The precursor of its disconnected version has been introduced by R.K. Meyer. Both co-rotation constructions result in residuated semigroups, among them non-positive rank involutive FLeFLe-algebras. These constructions can be considered as ‘skew-dual’ to their rotation counterparts (those without the co-syllable). The classes of residuated semigroups, for which the connected co-rotation construction results in associative operations, are characterized. Since the constructions are suitable to construct non-positive rank involutive FLeFLe-algebras, co-rotations provide a better insight into the algebraic semantic of the substructural logic IUL.