March 2006 An alternative semantics for quantified relevant logic
Robert Goldblatt, Edwin D. Mares
J. Symbolic Logic 71(1): 163-187 (March 2006). DOI: 10.2178/jsl/1140641167


The quantified relevant logic RQ is given a new semantics in which a formula ∀ x A is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of ‘extensional confinement’: ∀ x(A∨ B)→(A∨∀ xB), with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation.


Download Citation

Robert Goldblatt. Edwin D. Mares. "An alternative semantics for quantified relevant logic." J. Symbolic Logic 71 (1) 163 - 187, March 2006.


Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1100.03011
MathSciNet: MR2210060
Digital Object Identifier: 10.2178/jsl/1140641167

Rights: Copyright © 2006 Association for Symbolic Logic


This article is only available to subscribers.
It is not available for individual sale.

Vol.71 • No. 1 • March 2006
Back to Top