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Is multiset consequence trivial?

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    0466816 - ÚI 2022 RIV NL eng J - Journal Article
    Cintula, Petr - Paoli, F.
    Is multiset consequence trivial?
    Synthese. Roč. 199, Suppl. 3 (2021), s. 741-765. ISSN 0039-7857. E-ISSN 1573-0964
    R&D Projects: GA ČR GA13-14654S
    EU Projects: European Commission(XE) 689176 - SYSMICS
    Institutional support: RVO:67985807
    Keywords : contraction-free logics * multiset consequence * substructural logics * multiple conclusions
    OECD category: Pure mathematics
    Impact factor: 1.595, year: 2021
    Method of publishing: Limited access
    http://dx.doi.org/10.1007/s11229-016-1209-7

    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.
    Permanent Link: http://hdl.handle.net/11104/0265069

     
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