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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

Abstract

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.

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

Information

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

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Vol.71 • No. 1 • March 2006
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