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2020 | 49 | 4 | 359-375
Tytuł artykułu

Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations

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Abstrakty
EN
We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.
Rocznik
Tom
49
Numer
4
Strony
359-375
Opis fizyczny
Daty
wydano
2020-12-30
Twórcy
autor
  • Japan Advanced Institute of Science and Technology School of Information Science 923-1292, 1-1 Asahidai, Nomi Ishikawa, Japan
Bibliografia
  • [1] M. De, Empirical Negation, Acta Analytica, vol. 28 (2013), pp. 49–69, DOI: http://dx.doi.org/10.1007/s12136-011-0138-9
  • [2] M. De, H. Omori, More on Empirical Negation, [in:] R. Goreé, B. Kooi, A. Kurucz (eds.), Advances in Modal Logic, vol. 10, College Publications (2014), pp. 114–133.
  • [3] H. Friedman, Intuitionistic Completeness of Heyting's Predicate Calculus, Notices of the American Mathematical Society, vol. 22(6) (1975), pp. A648–A648.
  • [4] A. B. Gordienko, A Paraconsistent Extension of Sylvan's Logic, Algebra and Logic, vol. 46(5) (2007), pp. 289–296, DOI: http://dx.doi.org/10.1007/s10469-007-0029-8
  • [5] V. N. Krivtsov, An intuitionistic completeness theorem for classical predicate logic, Studia Logica, vol. 96(1) (2010), pp. 109–115, DOI: http://dx.doi.org/10.1007/s11225-010-9273-3
  • [6] S. Negri, Proof analysis in modal logic, Journal of Philosophical Logic, vol. 34(5–6) (2005), pp. 507–544, DOI: http://dx.doi.org/10.1007/s10992-005-2267-3
  • [7] S. Negri, Proof analysis in non-classical logics, [in:] C. Dimitracopoulos, L. Newelski, D. Normann, J. Steel (eds.), ASL Lecture Notes in Logic, vol. 28, Cambridge University Press (2007), pp. 107–128, DOI: http://dx.doi.org/10.1017/CBO9780511546464.010
  • [8] S. Negri, J. von Plato, Proof analysis: a contribution to Hilbert's last problem, Cambridge University Press (2011), DOI: http://dx.doi.org/10.1017/CBO9781139003513
  • [9] G. Priest, Dualising Intuitionistic Negation, Principia, vol. 13(2) (2009), pp. 165–184, DOI: http://dx.doi.org/10.5007/1808-1711.2009v13n2p165
  • [10] R. Sylvan, Variations on da Costa C Systems and dual-intuitionistic logics I. Analyses of C! and CC!, Studia Logica, vol. 49(1) (1990), pp. 47–65, DOI: http://dx.doi.org/10.1007/BF00401553
  • [11] A. S. Troelstra, D. van Dalen, Constructivism in Mathematics: An Introduction, vol. II, Elsevier (1988).
  • [12] W. Veldman, An Intuitionistic Completeness Theorem for Intuitionistic Predicate Logic, The Journal of Symbolic Logic, vol. 41(1) (1976), pp. 159–166, DOI: http://dx.doi.org/10.2307/2272955
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Bibliografia
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