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An Alternative Semantics for Quantified Relevant Logic

Edwin D. Mares and Robert Goldblatt
The Journal of Symbolic Logic
Vol. 71, No. 1 (Mar., 2006), pp. 163-187
Stable URL: http://www.jstor.org/stable/27588440
Page Count: 25
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
An Alternative Semantics for Quantified Relevant Logic
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Abstract

The quantified relevant logic RQ is given a new semantics in which a formula ∀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': ∀x(A V B) → (A V ∀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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