Deciding logics of linear Kripke frames with scattered end pieces

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.

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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 

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Correspondence to Norbert Preining.

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The authors declare that they have no conflict of interest.

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

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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

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Keywords

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