Geometric Models for Relevant Logics

Restall, Greg

doi:10.1007/978-3-030-71430-7_6

Outstanding Contributions to Logic

2021

DOI: 10.1007/978-3-030-71430-7_6

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Geometric Models for Relevant Logics

Greg Restall

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2022

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“…28 Elsewhere [42], Restall explores features of frames on geometric spaces, and options for extending geometric set frames with new points to bring in the empty set, in case one simply cannot do without and without . …”

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confidence: 99%

Collection Frames for Distributive Substructural Logics

Restall¹,

Standefer²

2022

The Review of Symbolic Logic

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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.

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mentioning

confidence: 99%

Collection Frames for Distributive Substructural Logics

Restall¹,

Standefer²

2022

The Review of Symbolic Logic

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Geometric Models for Relevant Logics

Cited by 1 publication

References 12 publications

Collection Frames for Distributive Substructural Logics

Collection Frames for Distributive Substructural Logics

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