Soft Computing

, Volume 21, Issue 1, pp 191–197 | Cite as

Deciding logics of linear Kripke frames with scattered end pieces

  • Arnold Beckmann
  • Norbert Preining


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.


Linear Order Initial Segment Force Relation Finite Model Persistency Condition 
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Conflict of interest

The authors declare that they have no conflict of interest.


  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 697–711Google Scholar
  2. Baaz M, Iemhoff R (2006) The skolemization of existential quantifiers in intuitionistic logic. Ann Pure Appl Log 142(1):269–295CrossRefzbMATHMathSciNetGoogle Scholar
  3. Baaz M, Preining N, Zach R (2007) First-order Gödel logics. Ann Pure Appl Log 147:23–47CrossRefzbMATHGoogle Scholar
  4. Beckmann A, Preining N (2007) Linear Kripke frames and Gödel logics. J Symb Log 71(1):26–44CrossRefzbMATHGoogle Scholar
  5. Minari P, Takano M, Ono H (1990) Intermediate predicate logics determined by ordinals. J Symb Log 55(3):1099–1124CrossRefzbMATHMathSciNetGoogle 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 660–696Google Scholar
  7. Takano M (1987) Ordered sets R and Q as bases of Kripke models. Stud Log 46:137–148CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Swansea UniversitySwanseaUK
  2. 2.Accelia Inc.TokyoJapan
  3. 3.Japan Advanced Institute of Science and TechnologyNomiJapan

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