Is multiset consequence trivial?

0466816 - ÚI 2022 RIV NL eng J - Článek v odborném periodiku
Cintula, Petr - Paoli, F.
Is multiset consequence trivial?
Synthese. Roč. 199, Suppl. 3 (2021), s. 741-765. ISSN 0039-7857. E-ISSN 1573-0964
Grant CEP: GA ČR GA13-14654S
GRANT EU: European Commission(XE) 689176 - SYSMICS
Institucionální podpora: RVO:67985807
Klíčová slova: contraction-free logics * multiset consequence * substructural logics * multiple conclusions
Obor OECD: Pure mathematics
Impakt faktor: 1.595, rok: 2021
Způsob publikování: Omezený přístup
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.
Trvalý link: http://hdl.handle.net/11104/0265069