Relevant predication: Grammatical characterisations

This paper reformulates and decides a certain conjecture in Dunn's Relevant Predication 1: The Formal Theory (Journal of Philosophical Logic 16, 347–381, 1987). This conjecture of Dunn's relates his object-language characterisation of a property's being relevant in a variable x to certain grammatical characterisations of relevance, analogous to some given by Helman, in Relevant Implication and Relevant Functions (to appear in Entailment: The Logic of Relevance and Necessity, vol. 2, by Alan Ross Anderson, Nuel Belnap, and J. Michael Dunn et al.) In the course of the investigation this paper also investigates Kit Fine's semantics for quantified relevance logics, which appears in his appropriately titled Semantics for Quantified Relevance LogicsMany thanks go to Nuel Belnap who suggested this research topic, and whose comments and inspiration were most appreciated.