Abstract
In the early seventies, several logicians developed a semantics for propositional systems of relevance logic. The essential ingredients of this semantics were a privileged point o, an ‘accessibility’ relation R and a special operator * for evaluating negation. Under the truth- conditions of the semantics, each formula A(Pl,…,Pn) could be seen as expressing a first order condition A+(pl,…,pn, o, R,*) on sets p1,…,pn and o, R, *, while each formula-scheme could be regarded as expressing the second-order condition ∀p1,…,∀pn A+(p1,…,pn, o, R, *). It could then be shown that many standard systems of propositional relevance logic were complete in the sense that their theorems were just those formulas true in all models whose components o, R and * conformed to the second-order conditions expressed by the axioms of the system.
I should like to thank Nuel Belnap for pointing out some slips in the original draft of the paper. Since writing the paper I have developed a semantics with respect to RQ which is both sound and complete. It is to appear in Entailment vol.11.
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© 1989 Kluwer Academic Publishers
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Fine, K. (1989). Incompleteness for Quantified Relevance Logics. In: Norman, J., Sylvan, R. (eds) Directions in Relevant Logic. Reason and Argument, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1005-8_16
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DOI: https://doi.org/10.1007/978-94-009-1005-8_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6942-7
Online ISBN: 978-94-009-1005-8
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