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- W4285088085 abstract "Abstract We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation 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 distributive substructural logic $mathsf {B}^+$ , that collection frames on multisets are sound and complete for $mathsf {RW}^+$ (the relevant logic $mathsf {R}^+$ , 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 $mathsf {R}^+$ . The completeness of set frames for $mathsf {R}^+$ is, currently, an open question." @default.
- W4285088085 created "2022-07-14" @default.
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- W4285088085 date "2022-07-13" @default.
- W4285088085 modified "2023-10-14" @default.
- W4285088085 title "COLLECTION FRAMES FOR DISTRIBUTIVE SUBSTRUCTURAL LOGICS" @default.
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- W4285088085 doi "https://doi.org/10.1017/s1755020322000272" @default.
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