(with Shawn Standefer) “Collection Frames for Substructural Logics,” article in progress.
You are welcome to download and read this document. I especially welcome feedback on it. As it is not yet published in final form, if you want to cite the paper, please check with me first. Thanks.
We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalization of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for the basic positive substructural logic B+, that collection frames on multisets are sound and complete for RW+ (the relevant logic R+, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic R+. (The completeness of set frames for R+ is, currently, an open question.)
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.