September 26, 2019

Abstract: In this talk I present a new frame semantics for positive substructural and relevant propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation is the use of a single accessibility relation to relate collections of points to points. Different logics are modelled by varying the kinds of collections featuring in the relation: for example, they can be sets, multisets, lists or trees. In this talk I will focus on multiset frames, which are sound and complete for the logic RW+ (positive multiplicative and additive linear logic with distribution for the additive connectives, or equivalently, the relevant logic R+ without contraction).

This is joint work with Shawn Standefer.


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I’m Greg Restall, and this is my personal website. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews.

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