a1 School of Informatics, Indiana University, Bloomington, IN 47408-3912, USA E-mail:, email@example.com
a2 Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003., USA E-mail:, firstname.lastname@example.org
a3 Departament De Logica, Historia I Filosofia De La Ciencia, Universitat De Barcelona, Barcelona. E-08028, Spain E-mail:, email@example.com
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.
(Received November 22 2004)
* The authors wish to thank an anonymous referee and M. Dunn's student, Chunlai Zhou, for their careful reading of the manuscript and for their suggestions and corrections.
† Partially supported by grant NSF01-4-21760 of the USA National Science Foundation.
‡ Partially supported by the Spanish grant MTM2004-03101 and by the grant 2001FI 00281 of the Generalitat de Catalunya.