Description

• Title:
  Fractional-Valued Modal Logic and Soft Bilateralism
• Creator:
  Piazza, Mario;
  Pulcini, Gabriele;
  Tesi, Matteo
• Contributor:
  Piazza, Mario - Scuola Normale Superiore, Classe di Lettere e Filosofia;
  Pulcini, Gabriele - University of Rome “Tor Vergata”, Department of Literary, Philosophical and Art History Studies;
  Tesi, Matteo - Scuola Normale Superiore, Classe di Lettere e Filosofia;
  Piazza, Mario - mario.piazza@sns.it;
  Pulcini, Gabriele - gabriele.pulcini@uniroma2.it;
  Tesi, Matteo - matteo.tesi@sns.it
• Description:
  In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) of rational numbers [14]. In this paper, after clarifying our conception of bilateralism – dubbed “soft bilateralism” – we generalize the fractional method to encompass extensions and weakenings of \(\mathbf{K}\). Specifically, we introduce well-behaved hypersequent calculi for the deontic logic \(\mathbf{D}\) and the non-normal modal logics \(\mathbf{E}\) and \(\mathbf{M}\) and thoroughly investigate their structural properties.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0/
• Date:
  2023.10.26;
  2023.08.16
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;3;
  52
• Subject:
  modal logic;
  general proof theory (including proof-theoretic semantics);
  many-valued logics
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/48183 ;
  2449-836X;
  10.18778/0138-0680.2023.17
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other