An alternative semantics for quantified relevant logic

Journal of Symbolic Logic 71 (1):163-187 (2006)
Abstract
The quantified relevant logic RQ is given a new semantics in which a formula for all xA 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': for all x(A V B) -> (A V for all 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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DOI 10.2178/jsl/1140641167
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References found in this work BETA
Star and Perp: Two Treatments of Negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.
Completeness of Relevant Quantification Theories.Robert K. Meyer, J. Michael Dunn & Hugues Leblanc - 1974 - Notre Dame Journal of Formal Logic 15 (1):97-121.

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Citations of this work BETA
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
The Relevant Fragment of First Order Logic.Guillermo Badia - forthcoming - Review of Symbolic Logic:1-24.
Belief Revision, Probabilism, and Logic Choice.Edwin Mares - 2014 - Review of Symbolic Logic 7 (4):647-670.

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