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An Investigation into Intuitionistic Logic with Identity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We 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.
Rocznik
Tom
48
Numer
4
Opis fizyczny
Daty
wydano
2019-12-31
Twórcy
  • Department of Logic and Cognitive Science, Faculty of Psychology and Cognitive Science, Adam Mickiewicz University, Poznań, Poland
  • Department of Logic and Cognitive Science, Faculty of Psychology and Cognitive Science, Adam Mickiewicz University, Poznań, Poland
Bibliografia
  • [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/1093890617
  • [2] J. G. Granström, Treatise on intuitionistic type theory, Springer Science & Business Media, Dordrecht, 2011. http://dx.doi.org/10.1007/978-94-007-1736-7
  • [3]J. R. Hindley, Basic simple type theory, Cambridge University Press, Cambridge, 1997. https://doi.org/10.1017/CBO9780511608865
  • [4] S. C. Kleene, Introduction to Metamathematics, Amsterdam: North-Holland Publishing Co.; Groningen: P. Noordhoff N.V., 1952.
  • [5] P. Łukowski, Intuitionistic sentential calculus with identity, Bulletin of the Section of Logic, Vol. 19, No. 3 (1990), pp. 92–99.
  • [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/10.2307/420956
  • [7] S. Negri and J. von Plato, Structural Proof Theory, Cambridge University Press, Cambridge, 2001. https://doi.org/10.1017/CBO9780511527340
  • [8] S. Negri and J. von Plato, Proof Analysis: a Contribution to Hilbert’s Last Problem, Cambridge University Press, Cambridge, 2011.
  • [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/s00153-003-0209-8
  • [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/BFb0064874
  • [11] A. S. Troelstra and H. Schwichtenberg, Basic Proof Theory, Camridge University Press, Cambridge, second edition, 2000. https://doi.org/10.1017/CBO9781139168717
  • [12] L. Viganò, Labelled non-classical logics, Kluwer Academic Publishers, Boston, 2000. https://doi.org/10.1007/978-1-4757-3208-5
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_48_4_02
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