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On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\)

dc.contributor.authorAyhan, Sara
dc.contributor.authorWansing, Heinrich
dc.date.accessioned2023-10-12T10:06:03Z
dc.date.available2023-10-12T10:06:03Z
dc.date.issued2023-07-18
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/48071
dc.description.abstractWe 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.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;2en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectbilateralismen
dc.subjectbi-intuitionistic logic \(\mathtt{2Int}\)en
dc.subjectcut-eliminationen
dc.subjectidentity of derivationsen
dc.subjectsynonymyen
dc.titleOn Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\)en
dc.typeOther
dc.page.number187-237
dc.contributor.authorAffiliationAyhan, Sara - Ruhr University Bochum, Department of Philosophy I, Universitätsstraße 150, D-44780 Bochum, Germanyen
dc.contributor.authorAffiliationWansing, Heinrich - Ruhr University Bochum, Department of Philosophy I, Universitätsstraße 150, D-44780 Bochum, Germanyen
dc.identifier.eissn2449-836X
dc.referencesA. Almukdad, D. Nelson, Constructible falsity and inexact predicates, The Journal of Symbolic Logic, vol. 49 (1984), pp. 231–233, DOI: https://doi.org/10.2307/2274105en
dc.referencesS. Ayhan, Meaning and identity of proofs in a bilateralist setting: A two-sorted typed lambda-calculus for proofs and refutations, manuscript in preparation.en
dc.referencesS. Ayhan, Uniqueness of Logical Connectives in a Bilateralist Setting, [in:] M. Blicha, I. Sedlár (eds.), The Logica Yearbook 2020, College Publications, London (2021), pp. 1–16.en
dc.referencesS. Drobyshevich, A bilateral Hilbert-style investigation of 2-intuitionistic logic, Journal of Logic and Computation, vol. 29(5) (2019), pp. 665–692, DOI: https://doi.org/10.1093/logcom/exz010en
dc.referencesS. Drobyshevich, S. Odintsov, H. Wansing, Moisil’s modal logic and related systems, [in:] K. Bimbó (ed.), Essays in Honour of Michael Dunn, College Publications, London (2022), pp. 150–177.en
dc.referencesR. Goré, Dual Intuitionistic Logic Revisited, [in:] R. Dyckhoff (ed.), Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2000, Springer-Verlag, Berlin (2000), pp. 252–267, DOI: https://doi.org/10.1007/10722086_21en
dc.referencesN. Kamide, H. Wansing, Proof theory of Nelson’s paraconsistent logic: A uniform perspective, Theoretical Computer Science, vol. 415 (2012), pp. 1–38, DOI: https://doi.org/10.1016/j.tcs.2011.11.001en
dc.referencesN. Kamide, H. Wansing, Proof Theory of N4-related paraconsistent logics, College Publications, London (2015).en
dc.referencesT. Kowalski, H. Ono, Analytic cut and interpolation for bi-intuitionistic logic, The Review of Symbolic Logic, vol. 10(2) (2017), pp. 259–283, DOI: https://doi.org/10.1017/S175502031600040Xen
dc.referencesS. Negri, J. von Plato, Structural proof theory, Cambridge University Press, Cambridge/New York (2001), DOI: https://doi.org/10.1017/CBO9780511527340en
dc.referencesL. Postniece, Proof Theory and Proof Search of Bi-Intuitionistic and Tense Logic, Ph.D. thesis, The Australian National University, Canberra (2010).en
dc.referencesD. Prawitz, Natural Deduction: A Proof-Theoretical Study, Almqvist & Wiksell, Stockholm (1965).en
dc.referencesC. Rauszer, A formalization of the propositional calculus of H-B logic, Studia Logica, vol. 33(1) (1974), pp. 23–34, DOI: https://doi.org/10.1007/BF02120864en
dc.referencesF. von Kutschera, Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle, Archiv für mathematische Logik und Grundlagenforschung, vol. 12 (1969), pp. 104–118, DOI: https://doi.org/10.1007/BF01969697en
dc.referencesH. Wansing, Falsification, natural deduction and bi-intuitionistic logic, Journal of Logic and Computation, vol. 26(1) (2016), pp. 425–450, DOI: https://doi.org/10.1093/logcom/ext035en
dc.referencesH. Wansing, On Split Negation, Strong Negation, Information, Falsification, and Verification, [in:] K. Bimbó (ed.), J. Michael Dunn on Information Based Logics. Outstanding Contributions to Logic, vol. 8, Springer (2016), pp. 161–189, DOI: https://doi.org/10.1007/978-3-319-29300-4_10en
dc.referencesH. Wansing, A more general general proof theory, Journal of Applied Logic, vol. 25 (2017), pp. 23–46, DOI: https://doi.org/10.1016/j.jal.2017.01.002en
dc.referencesH. Wansing, A note on synonymy in proof-theoretic semantics, [in:] T. Piecha, K. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Outstanding Contributions to Logic, Springer (forthcoming).en
dc.referencesH. Wansing, S. Ayhan, Logical multilateralism (2023), submitted.en
dc.contributor.authorEmailAyhan, Sara - sara.ayhan@rub.de
dc.contributor.authorEmailWansing, Heinrich - Heinrich.Wansing@rub.de
dc.identifier.doi10.18778/0138-0680.2023.18
dc.relation.volume52


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