Greg Restall - Quantifiers in Frames for Substructural Logics

I outline different options for modelling standard (additive/extensional) quantifiers in frames for substructural logics. The ``natural'' constant domain semantics for RQ has been shown (by Kit Fine) to be stronger than the ``natural'' proof theory for RQ. Fine has also given a baroque semantics for which the proof theory is sound and complete.

In this paper sketch two new approaches for exploring this issue.

> Frames for Distributive Lattice Logic with one-place modal operators.

> Frames for Positive Relevant Logics (logics without negation)