Collection Frames for Substructural Logics

Greg Restall (University of Melbourne)

Greg Restall (Melbourne) will present "Collection Frames for Substructural Logics" at 11 in Arts West North Wing 353 on 15 March.

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.