Semantical analysis of superrelevant predicate logics with quantification (Q1109761)

The paper defines two generalisations of standard semantics for the quantified relevant logic RQ. The first (general relevant RPg models) are essentially Routley/Meyer (R/M) models, except that propositions may take values in an arbitrary \(C_ R\) matrix, instead of the usual two-element Boolean Algebra. The second (strictly general relevant RPg models) are essentially R/M models in which the world structure is the Cartesian product of those of two R/M models. The paper then establishes various results about these models, e.g., that they generate super-systems of RQ, and that there are super-systems of RQ that are incomplete with respect to any class of such models.