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Rules of inference with parameters for intuitionistic logic

  • Vladimir V. Rybakov (a1)


An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed.



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[1]Mints, G. E., Derivability of admissible rules, Zapiski Nauchnykh Seminarov L0M1, vol. 32 (1972), pp. 8599; English translation, Journal of Soviet Mathematics, vol. 6(1976), no. 4, pp. 417-421.
[2]Rybakov, V. V., A criterion for the admissibility of inference rules in the modal system S4 and intuitionistic logic, Algebra i Logika, vol. 23 (1984), pp. 546572; English translation, Algebra and Logic, vol. 23(1984), pp. 369-384.
[3]Rybakov, V. V., Decidability of admissibility in the modal system Grzand in intuitionistic logic, Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya, vol. 50 (1986), pp. 598616; English translation, Mathematics of the USSR Izvestiya, vol. 28 (1987), pp. 589-608.
[4]Rybakov, V. V., Equations in a free topo-Boolean algebra and the substitution problem, Doklady Akademii Nauk SSSR, vol. 287 (1986), pp. 554557; English translation, Soviet Mathematics Doklady, vol. 33 (1986), pp. 428-431.
[5]Rybakov, V. V., The elementary theories of free topo-Boolean and pseudo-Boolean algebras, Matematicheskie Zametki, vol. 37 (1985), pp. 797802; English translation, Mathematical Notes of the Academy of Sciences of the USSR, vol. 37 (1985), pp. 435-438.
[6]Tsitkin, A. I., On admissible rules of intuitionistic prepositional logic, Matematicheskiĭ Sbornik, vol. 102 (144) (1977), pp. 314323; English translation in Mathematics of the USSR Sbornik, vol. 31 (1977), pp. 279-288.
[7]Shekhtman, V. B., Rieger-Nishimura lattices, Doklady Akademii Nauk SSSR, vol. 241 (1978), pp. 12881291; English translation, Soviet Mathematics Doklady, vol. 19 (1978), pp. 1014-1018.
[8]Schütte, Kurt, Vollständige Systeme modaler und intuitionistischer Logik, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 42, Springer-Verlag, Berlin, 1968.
[9]Ershov, Yu. L. and Goncharov, S. S. (editors), Logical notebook: unsolved questions of mathematical logic, Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk, 1986. (Russian)
[10]Friedman, Harvey, One hundred and two problems in mathematical logic, this Journal, vol. 40 (1975), pp. 113129.


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