(with Shawn Standefer) “Collection Frames for Distributive Substructural Logics,” to appear in the Review of Symbolic Logic.

 download pdf

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.)


Do you like this, or have a comment? (I especially value feedback on work which is yet to be be published in final form.) If you do, please  share or reply on Twitter, or  email me.


← Proofs and Models in Philosophical Logic | Writing Archive

about

I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews.

elsewhere

subscribe

To receive updates from this site, you can subscribe to the  RSS feed of all updates to the site in an RSS feed reader, or follow me on Twitter at  @consequently, where I’ll update you if anything is posted.

search