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Uspekhi Mat. Nauk, 2004, Volume 59, Issue 2(356), Pages 9–36 (Mi umn715)  

This article is cited in 13 scientific papers (total in 13 papers)

Kolmogorov and Gödel's approach to intuitionistic logic: current developments

S. N. Artemovab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b City University of New York, Graduate Center

Abstract: Intuitionistic mathematics was created by Brouwer on the basis of constructive reasoning, where the existence of a proof was the criterion for truth. Kolmogorov and Gödel proposed interpreting intuitionistic logic on the basis of classical notions of a problem's solution and of provability. In 1933 Gödel made the first substantial step toward the building of such an interpretation. Despite much progress in the understanding of intuitionism, this task was not complete before the author's 1995 paper. This survey will cover the results of the past decade obtained within this framework.

DOI: https://doi.org/10.4213/rm715

Full text: PDF file (402 kB)
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English version:
Russian Mathematical Surveys, 2004, 59:2, 203–229

Bibliographic databases:

UDC: 510.23, 510.24, 510.25, 510.642, 510.643, 510.648
MSC: Primary 03B34, 03F45, 03F55; Secondary 03B70, 03B20, 03B80
Received: 04.11.2003

Citation: S. N. Artemov, “Kolmogorov and Gödel's approach to intuitionistic logic: current developments”, Uspekhi Mat. Nauk, 59:2(356) (2004), 9–36; Russian Math. Surveys, 59:2 (2004), 203–229

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Artemov S., Nogina E., “Introducing justification into epistemic logic”, J. Logic Comput., 15:6 (2005), 1059–1073  crossref  mathscinet  zmath  isi  elib
    2. Krupski V.N., “Reference constructions in the single-conclusion proof logic”, J. Logic Comput., 16:5 (2006), 645–661  crossref  mathscinet  zmath  isi  elib
    3. Brezhnev V., Kuznets R., “Making knowledge explicit: How hard it is”, Theoret. Comput. Sci., 357:1-3 (2006), 23–34  crossref  mathscinet  zmath  isi  elib
    4. Krupski N.V., “On the complexity of the reflected logic of proofs”, Theoret. Comput. Sci., 357:1-3 (2006), 136–142  crossref  mathscinet  zmath  isi  elib
    5. Krupski N., “Typing in reflective combinatory logic”, Ann. Pure Appl. Logic, 141:1-2 (2006), 243–256  crossref  mathscinet  zmath  isi  elib
    6. S.S.. Wainer, “2005 Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '05”, Bull. symb. log, 12:02 (2006), 310  crossref  zmath
    7. Artemov S., Iemhoff R., “The basic intuitionistic logic of proofs”, J. Symbolic Logic, 72:2 (2007), 439–451  crossref  mathscinet  zmath  isi  elib
    8. Artemov S., Nogina E., “Topological semantics of Justification Logic”, Computer Science - Theory and Applications, Lecture Notes in Computer Science, 5010, 2008, 30–39  crossref  mathscinet  zmath  isi
    9. Krupski V.N., “Symbolic Models for Single-Conclusion Proof Logics”, Computer Science - Theory and Applications, Lecture Notes in Computer Science, 6072, 2010, 276–287  crossref  mathscinet  zmath  isi
    10. Achilleos A., “A Complexity Question in Justification Logic”, Logic, Language, Information and Computation, Wollic 2011, Lecture Notes in Artificial Intelligence, 6642, eds. Beklemishev L., DeQueiroz R., Springer-Verlag Berlin, 2011, 8–19  mathscinet  zmath  isi
    11. Shamkanov D.S., “Strong Normalization and Confluence for Reflexive Combinatory Logic”, Logic, Language, Information and Computation, Wollic 2011, Lecture Notes in Artificial Intelligence, 6642, eds. Beklemishev L., DeQueiroz R., Springer-Verlag Berlin, 2011, 228–238  mathscinet  zmath  isi
    12. Antonis Achilleos, “A complexity question in justification logic”, Journal of Computer and System Sciences, 2014  crossref  mathscinet  isi
    13. Rodin A., “On the Constructive Axiomatic Method”, Log. Anal., 2018, no. 242, 201–231  crossref  isi
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