NON-CONTRACTIVE LOGICS, PARADOXES, AND MULTIPLICATIVE QUANTIFIERS.
The paper investigates from a proof-theoretic perspective various non-contractive logical systems, which circumvent logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Grišin and Cantini). Systems with multiplicative quantifiers were proposed in the 2010...
| Publicado en: | Review of Symbolic Logic Vol. 17; no. 4; pp. 996 - 1018 |
|---|---|
| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Cambridge University Press
Dec2024
|
| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=182028153&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 182028153 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 17550203 8OI1 jtl: Review of Symbolic Logic issn: 17550203 maglogo: N pubinfo: dt: Dec2024 vid: 17 iid: 4 pid: 15979 pub: Cambridge University Press artinfo: ui: 182028153 10.1017/S1755020323000138 ppf: 996 ppct: 22 formats: tig: atl: NON-CONTRACTIVE LOGICS, PARADOXES, AND MULTIPLICATIVE QUANTIFIERS. aug: au: NICOLAI, CARLO PIAZZA, MARIO TESI, MATTEO affil: DEPARTMENT OF PHILOSOPHY KING'S COLLEGE, LONDON, UK E-mail SCUOLA NORMALE SUPERIORE DI PISA CLASSE DI LETTERE E FILOSOFIA PISA, ITALY su: Paradox Set theory Display systems Logic Additives sug: subj: Paradox Set theory Display systems Logic Additives keyword: contraction-free truth theories cut-elimination exponentials multiplicative quantifiers paradoxes ab: The paper investigates from a proof-theoretic perspective various non-contractive logical systems, which circumvent logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Grišin and Cantini). Systems with multiplicative quantifiers were proposed in the 2010s (Zardini), but they turned out to be inconsistent with the naive rules for truth or comprehension. We start by presenting a first-order system for disquotational truth with additive quantifiers and compare it with Grišin set theory. We then analyze the reasons behind the inconsistency phenomenon affecting multiplicative quantifiers. After interpreting the exponentials in affine logic as vacuous quantifiers, we show how such a logic can be simulated within a truth-free fragment of a system with multiplicative quantifiers. Finally, we establish that the logic for these multiplicative quantifiers (but without disquotational truth) is consistent, by proving that an infinitary version of the cut rule can be eliminated. This paves the way to a syntactic approach to the proof theory of infinitary logic with infinite sequents. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
|---|