Journal of Symbolic Logic

An alternative semantics for quantified relevant logic

Robert Goldblatt and Edwin D. Mares

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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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J. Symbolic Logic Volume 71, Issue 1 (2006), 163-187.

First available in Project Euclid: 22 February 2006

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Mares, Edwin D.; Goldblatt, Robert. An alternative semantics for quantified relevant logic. J. Symbolic Logic 71 (2006), no. 1, 163--187. doi:10.2178/jsl/1140641167.

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