Description

• Title:
  On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\)
• Creator:
  Ayhan, Sara;
  Wansing, Heinrich
• Contributor:
  Ayhan, Sara - Ruhr University Bochum, Department of Philosophy I, Universitätsstraße 150, D-44780 Bochum, Germany;
  Wansing, Heinrich - Ruhr University Bochum, Department of Philosophy I, Universitätsstraße 150, D-44780 Bochum, Germany;
  Ayhan, Sara - sara.ayhan@rub.de;
  Wansing, Heinrich - Heinrich.Wansing@rub.de
• Description:
  We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus \(\mathtt{SC2Int}\) for the bi-intuitionistic logic \(\mathtt{2Int}\). A distinctive feature of \(\mathtt{SC2Int}\) is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of \(\mathtt{SC2Int}\), in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through two different negation connectives, the well-known implies-falsity negation and the less well-known coimplies-truth negation of \(\mathtt{2Int}\). By assuming that the interaction rules have no impact on the identity of derivations, the concept of inherited identity between derivations in \(\mathtt{SC2Int}\) is introduced and the notions of positive and negative synonymy of formulas are defined. Several examples are given of distinct formulas that are either positively or negatively synonymous. It is conjectured that the two conditions cannot be satisfied simultaneously.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2023.10.12;
  2023.07.18
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;2;
  52
• Subject:
  bilateralism;
  bi-intuitionistic logic \(\mathtt{2Int}\);
  cut-elimination;
  identity of derivations;
  synonymy
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/48071 ;
  2449-836X;
  10.18778/0138-0680.2023.18
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other