 While the proof theory for quantifiers seems well behaved, the generalisation to model theory for substructural logics has proved difficult. Richard Routley (1980) showed that  adding the rules for the quantifiers to a very weak system of substructural logic \(\mathbf{B}\) fits appropriately with the ternary relational semantics, where quantifiers are interpreted as ranging over a domain of objects, constant across all of the points in the model. This fact does not apply for stronger logics, in particular, the relevant logic \(\mathbf{R}\).  Kit Fine (1989) showed that there exists a complex formula which holds in all constant domain frame models for \(\mathbf{R}\) but which is not derivable from the axioms. The details of Fine’s argument are not important for our purposes, but the underlying cause for the mismatch is relatively straightforward to explain. In the constant domain semantics, the universal generalisation \(\forall x Fx\) has exactly the same truth conditions—at every point in the model—as the family of instances \(Fx_1\), \(Fx_2\), \(Fx_3,\ldots\), \(Fx_\lambda,\ldots\), where the objects of the domains are enumerated by the values of the terms \(x_i\).  So, the quantified expression \(\forall x Fx\) is semantically indistinguishable from the (possibly infinite) conjunction \(Fx_1\land Fx_2\land Fx_3\land\cdots \). However, no conjunction of instances (even an infinite one) could be relevantly equivalent to the universally quantified claim \(\forall x Fx\), because the instances could be true in a circumstance (or could be made true by a circumstance) without also making true the generalisation—if there had been more things than those. So, constant domain models seem ill-suited to the project of a relevant theory of quantification. 