Residuated relational systems

Bonzio S.

Primo

;Chajda I.

2018-01-01

---

Abstract

The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated. In particular, we modify the definition of adjointness in such a way that the ordering relation can be harmlessly replaced by a binary relation. By enriching such binary relation with additional properties, we get interesting properties of residuated relational systems which are analogical to those of residuated posets and lattices.