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Propositional Algebra P1

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Intelligent Decision Technologies (IDT 2017)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 39))

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Abstract

In this semi-expository paper we investigate the propositional algebra P1, some properties and its relationship with Curry algebra P1. We show as in the classical case that both structures are equivalent in the sense of Bourbaki. Some results on the extension to the propositional algebras Pn (1 ≤ n ≤ ω) are also made.

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References

  1. Abe, J.M.: A note on curry algebras. Bull. Sect. Logic Pol. Acad. Sci. 16(4), 151–158 (1987)

    MATH  Google Scholar 

  2. Abe, J.M.: An introduction to the theory of curry systems. Scientiae Mathematicae Japonicae, Scientiae Mathematicae Japonicae, 76(2), 175–194 (2013), :e-2013, 175–194, ISSN 1346–0862, publicado pela International Society for Mathematical Sciences, Osaka, Japãor (2013)

    Google Scholar 

  3. Abe, J.M.: Curry algebras and propositional algebra C1. Int. J. Knowl. Based Intell. Eng. Syst. ISSN: 1327–2314, 5(2), 127–132 (2013)

    Google Scholar 

  4. Abe, J.M.: Curry algebras N1. Atti Acc. Lincei Rend. Fis. 7(9), 125–128 (1996)

    Google Scholar 

  5. Abe, J.M.: Curry algebras Pτ, Logique et Analyse, 161–162–163, 5–15 (1998)

    Google Scholar 

  6. Abe, J.M., Nakamatsu, K., Akama, S.: A Note on Monadic Curry System P1. Lecture Notes in Computer Science, vol. 5712, pp. 388–394. Springer, Berlin/Heidelberg (2009)

    Google Scholar 

  7. Abe, J.M., Nakamatsu, K., Akama, S.: A Note on Monadic Curry System P1. Lecture Notes in Computer Science—LNAI, vol. 5712, pp. 388–394, ISSN 0302–9743. Springer, Berlin/Heidelberg, Alemanha (2009). doi:10.1007/978-3-642-04592-9_49

  8. Abe, J.M., Nakamatsu, K., Akama, S.: An Algebraic Version of the Monadic System C1. New Advances In Intelligent Decision Technologies, Series: Studies in Computational Intelligence, vol. 199, pp. 341–349. Springer, Berlin/Heidelberg (2009)

    Google Scholar 

  9. Abe, J.M., Nakamatsu, K.: Curry systems for algebraization of some non-classical logics. Int. J. Reasoning-Based Intel. Syst. 59–69, ISSN: 17550556, , Indersciences Enterprize, UK (2011)

    Google Scholar 

  10. Abe, J.M., Akama, S., Nakamatsu, K.: Monadic Curry Algebras Qτ, Lecture Notes in Computer Science, vol. 4693, pp. 893–900. Springer (2007)

    Google Scholar 

  11. Barros, C.M., da Costa, N.C.A., Abe, J.M.: Tópico de teoria dos sistemas ordenados: vol. II. Sistemas de Curry, Coleção Documentos, Série Lógica e Teoria da Ciência, IEA-USP 20, 132p (1995)

    Google Scholar 

  12. Curry, H.B.: Foundations of Mathematical Logic. Dover, New York (1977)

    MATH  Google Scholar 

  13. da Costa, N.C.A., Marconi, D.: A note on paracomplete logic. Atti Acc. Lincei Rend. Fis. 80(8), 504–509 (1986)

    Google Scholar 

  14. da Costa, N.C.A.: Logics that are both paraconsistent and paracomplete. Atti Acc. Lincei Rend. Fis. 83, 29–32 (1990)

    Google Scholar 

  15. da Costa, N.C.A.: On the theory of inconsistent formal systems. Notre Dame J. Formal Logic 15, 497–510 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  16. Eytan, M.: Tableaux of Hintikka et Tout ça: un Point de Vue Algebrique. Math. Sci. Humaines 48, 21–27 (1975)

    MathSciNet  Google Scholar 

  17. Halmos, P.R.: Algebraic Logic. Chelsea Publishing Co., New York (1962)

    MATH  Google Scholar 

  18. Kleene, S.C.: Introduction to Metamathematics. Van Nostrand, Princeton (1952)

    MATH  Google Scholar 

  19. Mortensen, C.: Every quotient algebra for C 1 is trivial. Notre Dame J. Formal Logic 21, 694–700 (1977)

    Article  MathSciNet  Google Scholar 

  20. Rosenbloom, P.C.: The Elements of Mathematical Logic, Dover (1950)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate Program in Production Engineering, ICET - Paulista University, R. Dr. Bacelar 1212, CEP, São Paulo, SP, 04026-002, Brazil

    Jair Minoro Abe

  2. Institute for Advanced Studies, University of São Paulo, São Paulo, Brazil

    Jair Minoro Abe

  3. School of Human Science and Environment/H.S.E., University of Hyogo, Kobe, Japan

    Kazumi Nakamatsu

  4. C-Republic, Tokyo, Japan

    Seiki Akama

  5. Santa Cecília University, Santos, Philippines

    João I. S. Filho

Authors
  1. Jair Minoro Abe
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  2. Kazumi Nakamatsu
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  3. Seiki Akama
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  4. João I. S. Filho
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Corresponding author

Correspondence to Jair Minoro Abe .

Editor information

Editors and Affiliations

  1. FCT, Universidade Nova de Lisboa, Caparica, Portugal

    Rui Neves-Silva

  2. Faculty of Education, Science, Technology and Mathematics, University of Canberra, Canberra, Australia

    Lakhmi C. Jain

  3. KES International, Shoreham-by-sea, United Kingdom

    Robert J. Howlett

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Abe, J.M., Nakamatsu, K., Akama, S., Filho, J.I.S. (2015). Propositional Algebra P1 . In: Neves-Silva, R., Jain, L., Howlett, R. (eds) Intelligent Decision Technologies. IDT 2017. Smart Innovation, Systems and Technologies, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-19857-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-19857-6_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19856-9

  • Online ISBN: 978-3-319-19857-6

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