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An alternative semantics for quantified relevant logic

Published online by Cambridge University Press:  12 March 2014

Edwin D. Mares  and
Robert Goldblatt
Edwin D. Mares
Affiliation:
Centre for Logic, Language and Computation, Victoria University of Wellington, New Zealand. E-mail: [email protected], E-mail: [email protected]
Robert Goldblatt
Affiliation:
Centre for Logic, Language and Computation, Victoria University of Wellington, New Zealand. E-mail: [email protected]
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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 ⋁ 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 163 - 187
Copyright
Copyright © Association for Symbolic Logic 2006

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