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Canonical extensions and relational completeness of some substructural logics*

Published online by Cambridge University Press:  12 March 2014

J. Michael Dunn ,
Mai Gehrke  and
Alessandra Palmigiano
J. Michael Dunn
Affiliation:
School of Informatics, Indiana University, Bloomington, IN 47408-3912, USAE-mail:, dunn@indiana.edu
Mai Gehrke
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003., USAE-mail:, mgehrke@nmsu.edu
Alessandra Palmigiano
Affiliation:
Departament De Logica, Historia I Filosofia De La Ciencia, Universitat De Barcelona, Barcelona. E-08028, SpainE-mail:, ccl47472@cconline.es
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 3 , September 2005 , pp. 713 - 740
Copyright
Copyright © Association for Symbolic Logic 2005

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Footnotes

*

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.

References

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