On synonymy in proof-theoretic semantics

  • We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus \(\bf SC2Int\) for the bi-intuitionistic logic \(\bf 2Int\). A distinctive feature of \(\bf SC2Int\) is that it makes use of two kinds of sequents, one representing proofs, the other representing refutations. The structural rules of \(\bf SC2Int\), 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 co- implies-truth negation of \(\bf 2Int\). By assuming that the interaction rules have no impact on the identity of derivations, the concept of inherited identity between derivations in \(\bf SC2Int\) 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.

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Author:Sara AyhanORCiDGND, Heinrich WansingORCiDGND
Parent Title (English):Bulletin of the Section of Logic
Subtitle (English):The case of 2Int
Publisher:Lodz University Press
Place of publication:Lodz
Document Type:Article
Date of Publication (online):2024/04/12
Date of first Publication:2023/07/18
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:ConLog, Projekt ID: 101018280; bilateralismbi-intuitionistic logic \(\bf 2Int\); cut-elimination; identity of derivations; synonymy
First Page:187
Last Page:237
ConLog, Projekt ID: 101018280
Relation (DC):info:eu-repo/grantAgreement/EC/H2020/101018280
Institutes/Facilities:Institut für Philosophie I
Dewey Decimal Classification:Philosophie und Psychologie / Philosophie
faculties:Fakultät für Philosophie und Erziehungswissenschaft
Licence (English):License LogoCreative Commons - CC BY-NC-ND 4.0 - Attribution-NonCommercial-NoDerivatives 4.0 International