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Mat. Sb. (N.S.), 1977, Volume 102(144), Number 2, Pages 314–323 (Mi msb2686)  

This article is cited in 17 scientific papers (total in 17 papers)

On admissible rules of intuitionistic propositional logic

A. I. Citkin


Abstract: This paper studies modus rules of deduction admissible in intuitionistic propositional logic (a rule is called a modus rule if it corresponds to some sequence and allows passage from the results of any substitution in the formulas in its antecedent to the result of the same substitution in its succedent). Examples of such rules are considered, as well as the derivability of certain rules from others by means of the intuitionistic propositional calculus. An infinite independent system of admissible modus rules is constructed. It is proved that a finite Gödel pseudo-Boolean algebra in which all modus rules are valid (i.e. the quasi-identities corresponding to them are valid) is isomorphic to a sequential union of Boolean algebras of power not greater than 4.
Figures: 3.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 31:2, 279–288

Bibliographic databases:

UDC: 517.12
MSC: Primary 02B05, 02C15, 02J05, 02D99, 02E05, 06A35; Secondary 02B99, 02E99, 06A25, 02H10, 06A40, 08A15
Received: 27.01.1976

Citation: A. I. Citkin, “On admissible rules of intuitionistic propositional logic”, Mat. Sb. (N.S.), 102(144):2 (1977), 314–323; Math. USSR-Sb., 31:2 (1977), 279–288

Citation in format AMSBIB
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\by A.~I.~Citkin
\paper On admissible rules of intuitionistic propositional logic
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 2
\pages 314--323
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=465801}
\zmath{https://zbmath.org/?q=an:0355.02016|0386.03011}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 279--288
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002303}
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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. V. V. Rybakov, “Bases of admissible rules of the modal system Grz and of intuitionistic logic”, Math. USSR-Sb., 56:2 (1987), 311–331  mathnet  crossref  mathscinet  zmath
    2. V. V. Rybakov, “Decidability of admissibility in the modal system $\mathrm{Grz}$ and in intuitionistic logic”, Math. USSR-Izv., 28:3 (1987), 589–608  mathnet  crossref  mathscinet  zmath
    3. V. V. Rybakov, “Criteria for admissibility of rules of inference with parameters in the intuituonistc propositional calculus”, Math. USSR-Izv., 37:3 (1991), 693–703  mathnet  crossref  mathscinet  zmath  adsnasa
    4. V. V. Rybakov, “Admissibility of rules of inference, and logical equations, in modal logics axiomatizing provability”, Math. USSR-Izv., 36:2 (1991), 369–390  mathnet  crossref  mathscinet  zmath  adsnasa
    5. Vladimir V. Rybakov, “Intermediate logics preserving admissible inference rules of heyting calculus”, MLQ-Math Log Quart, 39:1 (1993), 403  crossref  mathscinet  zmath
    6. V. V. Rybakov, “Hereditarily structurally complete modal logics”, J. symb. log, 60:01 (1995), 266  crossref
    7. V. V. Rybakov, “Logical consecutions in discrete linear temporal logic”, J. symb. log, 70:04 (2005), 1137  crossref
    8. B. R. Fedorishin, “An explicit basis for the admissible inference rules in the Gödel–Löb logic $GL$”, Siberian Math. J., 48:2 (2007), 339–345  mathnet  crossref  mathscinet  zmath  isi  elib
    9. Vitalii V. Rimatskii, “Yavnyi bazis dopustimykh pravil vyvoda logik konechnoi shiriny”, Zhurn. SFU. Ser. Matem. i fiz., 1:1 (2008), 83–91  mathnet
    10. V. V. Rimatskii, “An explicit basis for admissible inference rules in table modal logics of width 2”, Algebra and Logic, 48:1 (2009), 72–86  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    11. V. V. Rimatskii, “An explicit basis for the admissible inference rules of the modal logics extending $S4.1$ and $Grz$”, Siberian Math. J., 50:4 (2009), 692–699  mathnet  crossref  mathscinet  isi  elib
    12. Rutskii A.N., “Finitnaya approksimiruemost kak dostatochnoe uslovie razreshimosti po dopustimosti dlya tranzitivnykh modalnykh i superintuitsionistskikh logik”, Vestn. Krasnoyarskogo gos. ped. un-ta im. V. P. Astafeva, 2009, no. 3, 86–93  elib
    13. Alexander Citkin, “A note on admissible rules and the disjunction property in intermediate logics”, Arch. Math. Logic, 2011  crossref
    14. V. V. Rimatskii, “On construction of an explicit basis for admissible inference rules of modal logics extending $S4.1$”, Discrete Math. Appl., 21:5-6 (2011), 741–760  mathnet  crossref  crossref  mathscinet  elib
    15. G. V. Bokov, “Criterion for propositional calculi to be finitely generated”, Discrete Math. Appl., 23:5-6 (2013), 399–427  mathnet  crossref  crossref  mathscinet  elib
    16. J.P.. Goudsmit, “Admissibility and refutation: some characterisations of intermediate logics”, Arch. Math. Logic, 2014  crossref
    17. Alex Citkin, “Characteristic Inference Rules”, Log. Univers, 2015  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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