In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.
"Canonical extensions and relational completeness of some substructural logics." J. Symbolic Logic 70 (3) 713 - 740, September 2005. https://doi.org/10.2178/jsl/1122038911