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Is multiset consequence trivial?
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SYSNO ASEP 0466816 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Is multiset consequence trivial? Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Paoli, F. (IT)Source Title Synthese. - : Springer - ISSN 0039-7857
Roč. 199, Suppl. 3 (2021), s. 741-765Number of pages 25 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords contraction-free logics ; multiset consequence ; substructural logics ; multiple conclusions Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA13-14654S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UIVT-O - RVO:67985807 UT WOS 000742032000011 EID SCOPUS 84986278287 DOI https://doi.org/10.1007/s11229-016-1209-7 Annotation Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction - whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in (affine) linear logic does not motivate cut. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2022 Electronic address http://dx.doi.org/10.1007/s11229-016-1209-7
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