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An alternative semantics for quantified relevant logic

  • Edwin D. Mares (a1) and Robert Goldblatt (a2)

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(AB) → (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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An alternative semantics for quantified relevant logic

  • Edwin D. Mares (a1) and Robert Goldblatt (a2)

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