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Collection frames for distributive substructural logics
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dc.contributor.author | Restall, Greg | |
dc.contributor.author | Standefer, Shawn | |
dc.date.accessioned | 2023-01-12T14:30:02Z | |
dc.date.available | 2023-01-12T14:30:02Z | |
dc.date.issued | 2023-12-13 | |
dc.identifier | 282875250 | |
dc.identifier | 0c040973-b1dc-4d87-9ac0-eb023b203f26 | |
dc.identifier | 85181019428 | |
dc.identifier | 000853706100001 | |
dc.identifier | 85181019428 | |
dc.identifier.citation | Restall , G & Standefer , S 2023 , ' Collection frames for distributive substructural logics ' , The Review of Symbolic Logic , vol. 16 , no. 4 , pp. 1120-1157 . https://doi.org/10.1017/S1755020322000272 | en |
dc.identifier.issn | 1755-0203 | |
dc.identifier.other | ORCID: /0000-0001-8257-6764/work/126554265 | |
dc.identifier.uri | https://hdl.handle.net/10023/26749 | |
dc.description | Funding: This research was supported by the Australian Research Council, Discovery Grant dp150103801. | en |
dc.description.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 B+ , that collection frames on multisets are sound and complete for RW+ (the relevant logic 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 R+. The completeness of set frames for R+ is, currently, an open question. | |
dc.format.extent | 38 | |
dc.format.extent | 646092 | |
dc.language.iso | eng | |
dc.relation.ispartof | The Review of Symbolic Logic | en |
dc.subject | Substructural logics | en |
dc.subject | Relevant logics | en |
dc.subject | Frame semantics | en |
dc.subject | Ternary relational frames | en |
dc.subject | BC Logic | en |
dc.subject | Mathematics (miscellaneous) | en |
dc.subject | Philosophy | en |
dc.subject | Logic | en |
dc.subject | T-NDAS | en |
dc.subject | AC | en |
dc.subject | MCC | en |
dc.subject | NCAD | en |
dc.subject.lcc | BC | en |
dc.title | Collection frames for distributive substructural logics | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Philosophy | en |
dc.identifier.doi | 10.1017/S1755020322000272 | |
dc.description.status | Peer reviewed | en |
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