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An Investigation into Intuitionistic Logic with Identity

dc.contributor.authorChlebowski, Szymon
dc.contributor.authorLeszczyńska-Jasion, Dorota
dc.date.accessioned2021-05-05T15:51:48Z
dc.date.available2021-05-05T15:51:48Z
dc.date.issued2019-12-31
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/35365
dc.description.abstractWe define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;4en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectNon-Fregean logicsen
dc.subjectintuitionistic logicen
dc.subjectadmissibility of cuten
dc.subjectpropositional identityen
dc.subjectcongruenceen
dc.titleAn Investigation into Intuitionistic Logic with Identityen
dc.typeOther
dc.page.number259–283
dc.contributor.authorAffiliationChlebowski, Szymon - Department of Logic and Cognitive Science, Faculty of Psychology and Cognitive Science, Adam Mickiewicz University, Poznań, Polanden
dc.contributor.authorAffiliationLeszczyńska-Jasion, Dorota - Department of Logic and Cognitive Science, Faculty of Psychology and Cognitive Science, Adam Mickiewicz University, Poznań, Polanden
dc.identifier.eissn2449-836X
dc.references[1] S. L. Bloom and R. Suszko, Investigations into the sentential calculus with identity, Notre Dame Journal of Formal Logic, Vol. 13, No. 3 (1972), pp. 289–308. http://dx.doi.org/10.1305/ndjfl/1093890617en
dc.references[2] J. G. Granström, Treatise on intuitionistic type theory, Springer Science & Business Media, Dordrecht, 2011. http://dx.doi.org/10.1007/978-94-007-1736-7en
dc.references[3]J. R. Hindley, Basic simple type theory, Cambridge University Press, Cambridge, 1997. https://doi.org/10.1017/CBO9780511608865en
dc.references[4] S. C. Kleene, Introduction to Metamathematics, Amsterdam: North-Holland Publishing Co.; Groningen: P. Noordhoff N.V., 1952.en
dc.references[5] P. Łukowski, Intuitionistic sentential calculus with identity, Bulletin of the Section of Logic, Vol. 19, No. 3 (1990), pp. 92–99.en
dc.references[6] S. Negri and J. von Plato, Cut elimination in the presence of axioms, Bulletin of Symbolic Logic, Vol. 4, No. 04 (1998), pp. 418–435. https://doi.org/10.2307/420956en
dc.references[7] S. Negri and J. von Plato, Structural Proof Theory, Cambridge University Press, Cambridge, 2001. https://doi.org/10.1017/CBO9780511527340en
dc.references[8] S. Negri and J. von Plato, Proof Analysis: a Contribution to Hilbert’s Last Problem, Cambridge University Press, Cambridge, 2011.en
dc.references[9] S. Negri, J. von Plato, and T. Coquand, Proof-theoretical analysis of order relations, Archive for Mathematical Logic, Vol. 43, No. 3 (2004), pp. 297–309. https://doi.org/10.1007/s00153-003-0209-8en
dc.references[10] R. Suszko, Abolition of the Fregean axiom, [in:] R. Parikh (ed.), Logic Colloquium, pp. 169–239, Berlin, Heidelberg, 1975, Springer. https://doi.org/10.1007/BFb0064874en
dc.references[11] A. S. Troelstra and H. Schwichtenberg, Basic Proof Theory, Camridge University Press, Cambridge, second edition, 2000. https://doi.org/10.1017/CBO9781139168717en
dc.references[12] L. Viganò, Labelled non-classical logics, Kluwer Academic Publishers, Boston, 2000. https://doi.org/10.1007/978-1-4757-3208-5en
dc.contributor.authorEmailChlebowski, Szymon - szymon.chlebowski@amu.edu.pl
dc.contributor.authorEmailLeszczyńska-Jasion, Dorota - dorota.leszczynska@amu.edu.pl
dc.identifier.doi10.18778/0138-0680.48.4.02
dc.relation.volume48


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