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UNIFICATION IN INTERMEDIATE LOGICS

Published online by Cambridge University Press:  22 July 2015

ROSALIE IEMHOFF  and
PAUL ROZIÈRE
ROSALIE IEMHOFF
Affiliation:
DEPARTMENT OF PHILOSOPHY UTRECHT UNIVERSITY JANSKERKHOF 13 3512 BL UTRECHT THE NETHERLANDSE-mail: r.iemhoff@uu.nl
PAUL ROZIÈRE
Affiliation:
UFR DE MATHÉMATIQUES UNIVERSITÉ PARIS 7 CASE 7012 75205 PARIS CEDEX FRANCEE-mail: roziere@pps.univ-paris-diderot.fr
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Abstract

This paper contains a proof–theoretic account of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments, the connection between valuations and most general unifiers is clarified, and it is shown how from the closure of a formula under the Visser rules a proof of the formula under a projective unifier can be obtained. This implies that in the logics considered, for the n-unification type to be finitary it suffices that the m-th Visser rule is admissible for a sufficiently large m. At the end of the paper it is shown how these results imply several well-known results from the literature.

Keywords

03B2003B5503B7003F03unificationadmissible rulesintermediate logicsfragments
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 3 , September 2015 , pp. 713 - 729
Copyright
Copyright © The Association for Symbolic Logic 2015 

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