Deciding logics of linear Kripke frames with scattered end pieces

Soft Computing volume 21, pages191–197(2017)Cite this article

Abstract

We show that logics based on linear Kripke frames—with or without constant domains—that have a scattered end piece are not recursively enumerable. This is done by reduction to validity in all finite classical models.

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

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. Baaz M, Iemhoff R (2005) On interpolation in existence logics. In: Logic for programming, artificial intelligence, and reasoning: 12th international conference, LPAR 2005, Montego Bay, Jamaica, December 2–6, 2005. Proceedings. Springer, Berlin, pp 697–711

  2. Baaz M, Iemhoff R (2006) The skolemization of existential quantifiers in intuitionistic logic. Ann Pure Appl Log 142(1):269–295

    Article  MATH  MathSciNet  Google Scholar 

  3. Baaz M, Preining N, Zach R (2007) First-order Gödel logics. Ann Pure Appl Log 147:23–47

    Article  MATH  Google Scholar 

  4. Beckmann A, Preining N (2007) Linear Kripke frames and Gödel logics. J Symb Log 71(1):26–44

    Article  MATH  Google Scholar 

  5. Minari P, Takano M, Ono H (1990) Intermediate predicate logics determined by ordinals. J Symb Log 55(3):1099–1124

    Article  MATH  MathSciNet  Google Scholar 

  6. Scott D (1979) Identity and existence in intuitionistic logic. In: Applications of sheaves: proceedings of the research symposium on applications of sheaf theory to logic, algebra, and analysis, Durham, July 9–21, 1977. Springer, Berlin, pp 660–696

  7. Takano M (1987) Ordered sets R and Q as bases of Kripke models. Stud Log 46:137–148

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Affiliations

  1. Swansea University, Swansea, UK

    Arnold Beckmann

  2. Accelia Inc., Tokyo, Japan

    Norbert Preining

  3. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Norbert Preining

Authors
  1. Arnold Beckmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Norbert Preining
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Norbert Preining.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by A. Di Nola, D. Mundici, C. Toffalori, A. Ursini.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Beckmann, A., Preining, N. Deciding logics of linear Kripke frames with scattered end pieces. Soft Comput 21, 191–197 (2017). https://doi.org/10.1007/s00500-016-2400-y

Download citation

Keywords

  • Linear Order
  • Initial Segment
  • Force Relation
  • Finite Model
  • Persistency Condition