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dc.contributor.authorRestall, Greg
dc.contributor.authorStandefer, Shawn
dc.date.accessioned2023-01-12T14:30:02Z
dc.date.available2023-01-12T14:30:02Z
dc.date.issued2023-12-13
dc.identifier282875250
dc.identifier0c040973-b1dc-4d87-9ac0-eb023b203f26
dc.identifier85181019428
dc.identifier000853706100001
dc.identifier85181019428
dc.identifier.citationRestall , 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/S1755020322000272en
dc.identifier.issn1755-0203
dc.identifier.otherORCID: /0000-0001-8257-6764/work/126554265
dc.identifier.urihttps://hdl.handle.net/10023/26749
dc.descriptionFunding: This research was supported by the Australian Research Council, Discovery Grant dp150103801.en
dc.description.abstractWe 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.extent38
dc.format.extent646092
dc.language.isoeng
dc.relation.ispartofThe Review of Symbolic Logicen
dc.subjectSubstructural logicsen
dc.subjectRelevant logicsen
dc.subjectFrame semanticsen
dc.subjectTernary relational framesen
dc.subjectBC Logicen
dc.subjectMathematics (miscellaneous)en
dc.subjectPhilosophyen
dc.subjectLogicen
dc.subjectT-NDASen
dc.subjectACen
dc.subjectMCCen
dc.subjectNCADen
dc.subject.lccBCen
dc.titleCollection frames for distributive substructural logicsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Philosophyen
dc.identifier.doi10.1017/S1755020322000272
dc.description.statusPeer revieweden


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