Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations

• Autorzy: Satoru Niki
• Języki publikacji: EN

Abstrakty

EN

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.

Słowa kluczowe

EN

empirical negation; co-negation; Beth semantics; Kripke semantics; intuitionism

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2020
• Tom: 49
• Numer: 3
• Strony: 231-253

Daty

wydano

2020-11-04

Twórcy

autor

Satoru Niki

• Japan Advanced Institute of Science and Technology School of Information Science 923-1292, 1-1 Asahidai, Nomi Ishikawa, Japan

• https://orcid.org/0000-0002-0882-806X

Bibliografia

• [1] L. E. J. Brouwer, Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Zweiter Teil, [in:] A. Heyring (ed.), L.E.J. Brouwer Collected Works 1: Philosophy and Foundations of Mathematics, North-Holland (1975), pp. 191–221, DOI: http://dx.doi.org/10.1016/C2013-0-11893-4
• [2] J. L. Castiglioni, R. C. E. Biraben, Strict paraconsistency of truth-degree preserving intuitionistic logic with dual negation, Logic Journal of the IGPL, vol. 22(2) (2014), pp. 268–273, DOI: http://dx.doi.org/10.1093/jigpal/jzt027
• [3] M. De, Empirical Negation, Acta Analytica, vol. 28 (2013), pp. 49–69, DOI: http://dx.doi.org/10.1007/s12136-011-0138-9
• [4] 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.
• [5] K. Došen, Negation on the Light of Modal Logic, [in:] D. M. Gabbay, H. Wansing (eds.), What is Negation?, Kluwer Academic Publishing. (1999), DOI: http://dx.doi.org/10.1007/978-94-015-9309-04
• [6] T. M. Ferguson, Extensions of Priest-da Costa Logic, Studia Logica, vol. 102 (2013), pp. 145–174, DOI: http://dx.doi.org/10.1007/s11225-013-9469-4
• [7] 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
• [8] A. Heyting, Intuitionism: An Introduction, third revised ed., North Holland (1976).
• [9] M. Osorio, J. L. Carballido, C. Zepeda, J. A. Castellanos, Weakening and Extending Z, Logica Universalis, vol. 9(3) (2015), pp. 383–409, DOI: http://dx.doi.org/10.1007/s11787-015-0128-6
• [10] M. Osorio, J. A. C. Joo, Equivalence among RC-type paraconsistent logics, Logic Journal of the IGPL, vol. 25(2) (2017), pp. 239–252, DOI: http://dx.doi.org/10.1093/jigpal/jzw065
• [11] G. Priest, Dualising Intuitionistic Negation, Principia, vol. 13(2) (2009), pp. 165–184, DOI: http://dx.doi.org/10.5007/1808-1711.2009v13n2p165
• [12] C. Rauszer, A formalization of the propositional calculus of H-B logic, Studia Logica, vol. 33(1) (1974), pp. 23–34, DOI: http://dx.doi.org/10.1007/BF02120864
• [13] C. Rauszer, Applications of Kripke models to Heyting-Brouwer logic, Studia Logica, vol. 36(1) (1977), pp. 61–71, DOI: http://dx.doi.org/10.1007/BF02121115
• [14] G. Restall, Extending intuitionistic logic with subtraction (1997), unpublished.
• [15] R. Sylvan, Variations on da Costa C Systems and dual-intuitionistic logics I. Analyses of Cω and CCω, Studia Logica, vol. 49(1) (1990), pp. 47–65, DOI: http://dx.doi.org/10.1007/BF00401553
• [16] A. S. Troelstra, J. R. Moschovakis, A.S. Troelstra, D. van Dalen, Constructivism in Mathematics Corrections, URL: https://www.math.ucla.edu/~joan/ourTvDcorr030818 [accessed 20/Jul/2020].
• [17] A. S. Troelstra, D. van Dalen, Constructivism in Mathematics: An Introduction, vol. I, Elsevier (1988).
• [18] A. S. Troelstra, D. van Dalen, Constructivism in Mathematics: An Introduction, vol. II, Elsevier (1988).
• [19] D. van Dalen, L.E.J. Brouwer: Topologist, Intuitionist, Philosopher, Springer (2013), DOI: http://dx.doi.org/10.1007/978-1-4471-4616-2

Identyfikatory

DOI

10.18778/0138-0680.2020.12