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

Satoru Niki

Bulletin of the Section of Logic (2020)

  • Volume: 49, Issue: 4, page 359-375
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Satoru Niki. "Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations." Bulletin of the Section of Logic 49.4 (2020): 359-375. <http://eudml.org/doc/296792>.

@article{SatoruNiki2020,
abstract = {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.},
author = {Satoru Niki},
journal = {Bulletin of the Section of Logic},
keywords = {empirical negation; co-negation; labelled sequent calculus; intuitionism},
language = {eng},
number = {4},
pages = {359-375},
title = {Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations},
url = {http://eudml.org/doc/296792},
volume = {49},
year = {2020},
}

TY - JOUR
AU - Satoru Niki
TI - Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 4
SP - 359
EP - 375
AB - 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.
LA - eng
KW - empirical negation; co-negation; labelled sequent calculus; intuitionism
UR - http://eudml.org/doc/296792
ER -

References

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  8. [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. [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. [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. [11] A. S. Troelstra, D. van Dalen, Constructivism in Mathematics: An Introduction, vol. II, Elsevier (1988). 
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