Journal of Symbolic Logic

An alternative semantics for quantified relevant logic

Robert Goldblatt and Edwin D. Mares

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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.

Article information

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

Dates
First available: 22 February 2006

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1140641167

Digital Object Identifier
doi:10.2178/jsl/1140641167

Mathematical Reviews number (MathSciNet)
MR2210060

Zentralblatt MATH identifier
05038892

Citation

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


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