Skip to main content

Labelled Tableau Systems for Some Subintuitionistic Logics

Abstract

Labelled tableau systems are developed for subintuitionistic logics \(\mathbf {wK}_\sigma \), \(\mathbf {wKT}_\sigma \) and \(\mathbf {wK4}_\sigma \). These subintuitionistic logics are embedded into corresponding normal modal logics. Hintikka’s model systems are applied to prove the completeness of labelled tableau systems. The finite model property, decidability and disjunction property are obtained by labelled tableau method.

This is a preview of subscription content, access via your institution.

References

  1. Beth, E.W.: Semantic entailment and formal derivability. In: Hintikka, J. (ed.), The Philosophy of Mathematics, pp. 9–41. Oxford University Press. Originally published in Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afdeling Letterkunde, N.R. 19 no. 13 (Amsterdam 1955), pp. 309–342 (1969)

  2. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  3. Celani, S., Jansana, R.: A closer look at some subintuitionistic logic. Notre Dame J. Form. Logic 42(4), 225–255 (2001)

    MathSciNet  Article  MATH  Google Scholar 

  4. Corsi, G.: Weak logics with strict implication. Zeitschrift für mathematische Logik u. Grundlagen d 33, 389–406 (1987)

    MathSciNet  Article  MATH  Google Scholar 

  5. Dos̆en, K.: Modal tanslations into K and D. In: de Rijke, M. (ed.) Diamonds and Defaults, pp. 103–127. Kluwer Academic Publishers, Dordrecht (1993)

    Chapter  Google Scholar 

  6. Fitting, M.: Proof Methods for Modal and Intuitionistic Logics. D. Reidel, Dordrecht (1983)

    Book  MATH  Google Scholar 

  7. Goré, R.: Tableau methods for modal and temporal logics. In: D’Agostino, M., et al. (eds.) Handbook of Tableau Methods, pp. 297–396. Springer, Berlin (1999)

    Chapter  Google Scholar 

  8. Hintikka, J.: A new approach to sentential logic. Societas Scientiarum Fennica, Commentationes physica-mathematicae, 17(2) (1953)

  9. Hintikka, J.: Form and content in quantification theory. Acta Philosophica Fennica 8, 3–55 (1955)

    MathSciNet  MATH  Google Scholar 

  10. Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press, Ithaca (1962)

    Google Scholar 

  11. Kripke, S.: A completeness theorem in modal logic. J. Symb. Logic 24(1), 1–14 (1959)

    MathSciNet  Article  MATH  Google Scholar 

  12. Massacci, F.: Strongly analytic tableaux for modal logics. In: Proceedings of CADE-12, LNAI 814, Bundy, A. (ed.), pp. 723–737. Springer, Berlin (1994)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Minghui Ma.

Additional information

This work was supported by Guangdong Province Higher Vocational Colleges and Schools Pearl River Scholar Funded Scheme (2017–2019).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ma, M. Labelled Tableau Systems for Some Subintuitionistic Logics. Log. Univers. 13, 273–288 (2019). https://doi.org/10.1007/s11787-018-0201-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11787-018-0201-z

Keywords

  • Labelled tableau system
  • subintuitionistic logic
  • modal logic

Mathematics Subject Classification

  • Primary 03F03
  • Secondary 03B45