Source: J. Symbolic Logic
Volume 71, Issue 1
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
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