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On a class of functionally complete multi-valued logical calculi

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References

  1. G. Epstein,The lattice theory of Post algebras,Transactions of the American Mathematical Society, Vol. 95 (1960), pp. 300–317.

    Google Scholar 

  2. S. V. Jablonskij,On superposition of functions in P k (Russian), SbornikProblemy Kibernetiki, Moscow Vol. 9 (1963).

  3. S. V. Jablonskij,Functional constructions in k-valued logics (Russian),Trudy Matematičeskogo Instituta im. V. A. Steklova, (Moscow) Vol. 51 (1958).

  4. L. J. Kohout,The Pinkava many-valued complete logic systems and their applications in the design of many-valued switching circuits, in: IEEE 74CH0845-8C (1974), pp. 261–284.

  5. L. J. Kohout,Application of multi-valued logics to the study of human movement control and of movement disorders, in: IEEE 76CH1111-4C (1976), pp. 224–231.

  6. L. J. Kohout andB. R. Gaines,Protection as a general systems problem,Int. Journal Gen. Syst. Vol. 3, No. 1 (1976), pp. 2–23.

    Google Scholar 

  7. L. J. Kohout andV. Pinkava,The functional completeness of Pi-algebras and its relevance to biological modelling and to technological applications of many-valued logics, in: E. H. Mamdani and B. R. Gaines (Eds.),Discrete Systems and Fuzzy Reasoning, EES-MMS-DSFR-76, Queen Mary College, University of London (workshop proceedings).

  8. V. Pinkava,Some further properties of the Pi-logics, in: IEEE75CH0959 (1975), pp. 20–26.

  9. V. Pinkava,“Fuzzification” of binary and finite multi-valued logical calculi,International Journal of Man Machines Studies 8 (1976), pp. 717–730.

    Google Scholar 

  10. V. Pinkava andL. J. Kohout,Enumerably infinite-valued functionally complete Pi-logic algebras, see [7]. in: E. H. Mamdani and B. R. Gaines (Eds.),Discrete Systems and Fuzzy Reasoning, EES-MMS-DSFR-76, Queen Mary College, University of London (workshop proceedings).

  11. V. Pinkava,Arrangements of formulas and minimisation in Pi-algebras, see [7], in: E. H. Mamdani and B. R. Gaines (Eds.),Discrete Systems and Fuzzy Reasoning, EES-MMS-DSFR-76, Queen Mary College, University of London (workshop proceedings).

  12. D. A. Pospelov,Logical Methods of Analysis and Synthesis of Schemas (in Russian), Moscow 1968.

  13. E. L. Post,Introduction to a general theory of elementary propositions,American Mathematics (1921), pp. 163–185.

  14. D. A. Rabinovič andU. L. Ivaskiv,On a class of canonic forms representing three-valued functions (Russian), Izvestija ANSSSRTexničeskaja Kibernetika (1963), No. 5.

  15. I. G. Rosenberg,La structure de fonctions de plusieurs variables sur un ensemble fini,Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences Paris (1965), pp. 3817–3819.

  16. I. G. Rosenberg,Über die funktionale Vollständigkeit in den mehrwertigen Logiken,Rozpravy ČSAV,Řada Matematických a Prirodnich Věd, 80 (1970).

  17. I. G. Rosenberg,Completeness, closed classes and relations in multi-valued logics, in: IEEE74CH0845-8C (1974).

  18. I. G. Rosenberg,Some algebraic and combinatorial aspects of multiple-valued circuits, in: IEEE76CH1111-4C (1976), pp. 9–23.

  19. I. B. Rosser andA. R. Turquette,Many valued logic, North Holland 1952.

  20. I. I. Žegalkin An arithmetization of symbolic logic (Russian),Matematičeskii Sbornik 35 (1928), pp. 311–378 and 36 (1929), pp. 205–338.

    Google Scholar 

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Allatum est die 1 Juli 1975

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Pinkava, V. On a class of functionally complete multi-valued logical calculi. Stud Logica 37, 205–212 (1978). https://doi.org/10.1007/BF02124805

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