Collection Frames for Substructural LogicsGreg 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.
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