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CONSERVATIVITY OF HEYTING IMPLICATION OVER RELEVANT QUANTIFICATION

Published online by Cambridge University Press:  09 July 2009

ROBERT GOLDBLATT
ROBERT GOLDBLATT*
Affiliation:
Centre for Logic, Language and Computation, Victoria University of Wellington
*
*CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, P.O. BOX 600 WELLINGTON, NEW ZEALAND. E-mail:rob.goldblatt@vuw.ac.nz
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Abstract

It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting implication is thereby reduced to the question of conservatively adding the axioms for identity. Some results in this direction are also obtained. The conservative presence of Heyting implication allows the development of an alternative model theory for quantified relevant logics.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 2 , June 2009 , pp. 310 - 341
Copyright
Copyright © Association for Symbolic Logic 2009

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