The Journal of Symbolic Logic

Research Article

Canonical extensions and relational completeness of some substructural logics  *

J. Michael Dunna1, Mai Gehrkea2  and Alessandra Palmigianoa3 

a1 School of Informatics, Indiana University, Bloomington, IN 47408-3912, USA E-mail:,

a2 Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003., USA E-mail:,

a3 Departament De Logica, Historia I Filosofia De La Ciencia, Universitat De Barcelona, Barcelona. E-08028, Spain E-mail:,


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.