Collection Frames for Substructural Logics

March 15, 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.

• The talk is a Melbourne Logic Seminar.

• The slides for the talk are available here.