Group representation for even and odd involutive commutative residuated chains

TL;DR

This paper presents a representation theorem for odd and even involutive, commutative residuated chains using direct systems of abelian o-groups, extending Dunn's work on finite Sugihara monoids.

Contribution

It generalizes Dunn's finite Sugihara monoid result to a broader class of residuated chains through a new representation theorem.

Findings

Representation theorem for involutive, commutative residuated chains.

Extension of Dunn's finite Sugihara monoids to infinite cases.

Framework using direct systems of abelian o-groups.

Abstract

For odd and for even involutive, commutative residuated chains a representation theorem is presented in this paper by means of direct systems of abelian o-groups equipped with further structure. This generalizes the corresponding result of J. M. Dunn about finite Sugihara monoids.