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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 1, Pages 47–68 (Mi izv1547)  

This article is cited in 22 scientific papers (total in 22 papers)

Predicate and set-theoretic calculi based on logic without contractions

V. N. Grishin


Abstract: In this paper the author studies the effect of eliminating the contraction rules from the Gentzen predicate calculus, and also from set-theoretic systems based on this calculus. It turns out that the predicate calculus without contraction rules is complete relative to finite models, and eliminating contraction rules from set-theoretic systems does not change the number of derivable formulas as long as the systems contain certain natural axioms.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:1, 41–59

Bibliographic databases:

UDC: 51.01.16
MSC: Primary 03B20; Secondary 03G25
Received: 14.05.1980

Citation: V. N. Grishin, “Predicate and set-theoretic calculi based on logic without contractions”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981), 47–68; Math. USSR-Izv., 18:1 (1982), 41–59

Citation in format AMSBIB
\Bibitem{Gri81}
\by V.~N.~Grishin
\paper Predicate and set-theoretic calculi based on logic without contractions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 1
\pages 47--68
\mathnet{http://mi.mathnet.ru/izv1547}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=607576}
\zmath{https://zbmath.org/?q=an:0478.03009|0464.03027}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 41--59
\crossref{https://doi.org/10.1070/IM1982v018n01ABEH001382}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Andrzej Wroński, “Remarks on a survey article on many valued logic by A. Urquhart”, Stud Logica, 46:3 (1987), 275  crossref
    2. Jean-Yves Girard, “Light Linear Logic”, Information and Computation, 143:2 (1998), 175  crossref
    3. V. N. Grishin, “On the weight of the comprehension axiom in a theory based on logic without contractions”, Math. Notes, 66:5 (1999), 533–540  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Francesco Paoli, “★-autonomous Lattices”, Stud Logica, 79:2 (2005), 283  crossref  mathscinet  zmath
    5. Shunsuke Yatabe, Hiroyuki Inaoka, “On Evans's Vague Object from Set Theoretic Viewpoint”, J Philos Logic, 35:4 (2006), 423  crossref  mathscinet  zmath
    6. Joan Gispert, Antoni Torrens, “Bounded BCK-algebras and their generated variety”, MLQ - Math Log Quart, 53:2 (2007), 206  crossref  mathscinet  zmath  isi
    7. Joan Gispert, Antoni Torrens, “Boolean representation of bounded BCK-algebras”, Soft Comput, 12:10 (2008), 941  crossref  zmath  isi
    8. Kai Brünnler, Dieter Probst, Thomas Studer, “On contraction and the modal fragment”, MLQ - Math Log Quart, 54:4 (2008), 345  crossref  isi
    9. Richard McKinley, “Soft Linear Set Theory”, Journal of Logic and Algebraic Programming, 76:2 (2008), 226  crossref
    10. Antoni Torrens, “Semisimplicity and the discriminator in bounded BCK-algebras”, Algebra univers, 2010  crossref
    11. Diego Castaño, José Patricio Díaz Varela, Antoni Torrens, “Indecomposability of free algebras in some subvarieties of residuated lattices and their bounded subreducts”, Soft Comput, 2010  crossref
    12. Patrick Baillot, Damiano Mazza, “Linear logic by levels and bounded time complexity”, Theoretical Computer Science, 411:2 (2010), 470  crossref
    13. Andrew Bacon, “Non-classical Metatheory for Non-classical Logics”, J Philos Logic, 2012  crossref
    14. Edwin Mares, Francesco Paoli, “Logical Consequence and the Paradoxes”, J Philos Logic, 2013  crossref
    15. S. Yatabe, “On the crispness of   and arithmetic with a bisimulation in a constructive naive set theory”, Logic Journal of IGPL, 2013  crossref
    16. Andrew Bacon, “Paradoxes of Logical Equivalence and Identity”, Topoi, 2013  crossref
    17. MAJID ALIZADEH, FARZANEH DERAKHSHAN, HIROAKIRA ONO, “UNIFORM INTERPOLATION IN SUBSTRUCTURAL LOGICS”, The Review of Symbolic Logic, 2014, 1  crossref
    18. L. Tranchini, “Proof-theoretic semantics, paradoxes and the distinction between sense and denotation”, Journal of Logic and Computation, 2014  crossref
    19. ROHAN FRENCH, DAVID RIPLEY, “CONTRACTIONS OF NONCONTRACTIVE CONSEQUENCE RELATIONS”, The Review of Symbolic Logic, 2014, 1  crossref
    20. DAVID RIPLEY, “NAIVE SET THEORY AND NONTRANSITIVE LOGIC”, The Review of Symbolic Logic, 2015, 1  crossref
    21. David Ripley, “Contraction and closure”, Thought: A Journal of Philosophy, 4:2 (2015), 131  crossref
    22. T.F.jetland Øgaard, “Paths to Triviality”, J Philos Logic, 2015  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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