Skip to main content

A Possibilistic Intuitionistic Logic

  • Conference paper
  • 1286 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6437))

Abstract

We define what we call “Possibilistic Intuitionistic Logic (PIL)”; We present results analogous to those of the well-known intuitionistic logic, such as a Deduction Theorem, a Generalized version of the Deduction Theorem, a Cut Rule, a weak version of a Refutation Theorem, a Substitution Theorem and Glivenko’s Theorem.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. van Gelder, A., Ross, K.A., et al.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)

    MathSciNet  MATH  Google Scholar 

  2. Carballido, J.L., Osorio, M., et al.: Equivalence for the G 3′ −stable models sematics. J. Applied Logic 8(1), 82–96 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Inc., New york (1994)

    Google Scholar 

  4. De Jongh, D.H.J., Hendrix, L.: Characterizations of strongly equivalent logic programs in intermediate logics. Theory and Practice of Logic Programming 3(3), 259–270 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lifschitz, V., Pearce, D., et al.: Strongly equivalent logic programs. ACM Trans. Comput. Logic 2(4), 526–541 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Marek, V., Truszczyn’ski, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 169–181. Springer, Heidelberg (1999)

    Google Scholar 

  7. Mendelson, E.: Introduction to mathematical logic, 4th edn. Chapman & Hall / CRC (1997)

    Google Scholar 

  8. Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nicolas, P., Garcia, L., et al.: Possibilistic uncertainty handling for answer set programming. Annals Math. Artif. Intell. 47, 139–181 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Osorio, M., Nieves, J.C.: Possibilistic well-founded semantics. In: MICAI 2009: Advances in Artificial Intelligence, vol. 5845, pp. 15–26 (2009)

    Google Scholar 

  11. Osorio, M., Nieves, J.C.: Pstable semantics for possibilistic logic programs. In: Gelbukh, A., Kuri Morales, Á.F. (eds.) MICAI 2007. LNCS (LNAI), vol. 4827, pp. 294–304. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Osorio, M., Navarro, J.A., et al.: Ground non-monotonic modal logic S5: new results. J. Log. Computation 15(5), 787–813 (2005)

    Article  MATH  Google Scholar 

  13. Osorio, M., Navarro, J.A., et al.: Equivalence in answer set programming. In: Pettorossi, A. (ed.) LOPSTR 2001. LNCS, vol. 2372, pp. 57–75. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. Pearce, D.: Stable inference as intuitionistic validity. The Journal of Logic Programming 38(1), 79–91 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Shannon, C.: A mathematical theory of communication. Bell System Technical Journal 27, 379–426, 623–656 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  16. Van Dalen, D.: Logic and structure. Springer, Heidelberg (March 2004)

    Book  MATH  Google Scholar 

  17. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Estrada, O., Arrazola, J., Osorio, M. (2010). A Possibilistic Intuitionistic Logic. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds) Advances in Artificial Intelligence. MICAI 2010. Lecture Notes in Computer Science(), vol 6437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16761-4_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16761-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16760-7

  • Online ISBN: 978-3-642-16761-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics