An alternative semantics for quantified relevant logic

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 variableassignments 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) (AxB), 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: Journal
• Year: 2006
• Where: JSYML
• Authors: Robert Goldblatt, Edwin D. Mares
• Keywords: JSYML 2006, Quantified Relevant Logic, Relevant Model Structure, True Proposition