On expressive completeness of modal logic

  • Bernhard Heinemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 813)


We have studied the problem of expressive completeness for modal logic. In case of a simple class of frames, the homogeneous ones, expressive completeness could be shown. Moreover, within a class of special finite hamiltonian binary ramified frames, called wheels, the complete ones have been classified by means of simple numerical invariants.

In the meantime, the question of expressive completeness could be answered for all binary ramified frames. The corresonding results will appear elsewhere.

Certain frames of ramification degree > 2 (e.g. “wheels” Wn,k,l) are unrollable into fan-like structures. For those frames the problem of expressive completeness may be studied in a similar way as in the present note.


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  1. [Ami]
    Amir, A.: Expressive Completeness Failure in Branching Time Structures, Journal Comp. Syst. Sc. 34 (1987), 27–42Google Scholar
  2. [Gab]
    Gabbay,D.: Expressive Functional Completeness in Tense Logic, in U. Mönnich (ed.), Aspects of Philosophical Logic, 1981Google Scholar
  3. [Gab/Pnu/She/Sta]
    Gabbay,D.; Pnueli,A.; Shelah,S.; Stavi,J.: On the Temporal Analysis of Fairness, Proc. 7th Ann. ACM Sympos. PoPL, 1980, 163–173Google Scholar
  4. [Gol]
    Goldblatt, R.: Logics of Time and Computation, CSLI Lecture Notes, No. 7, Stanford 1987Google Scholar
  5. [Haf/Tho]
    Hafer,T.; Thomas,W.: Computational Tree Logic CTL* and Path Quantifiers in the Monadic Theory of the Binary Tree, in T. Ottmann (ed.), ICALP 1987, LNSC 267, 1987Google Scholar
  6. [He1]
    Heinemann, B.: A note on Expressive Completeness of Modal Logic, Informatik-Berichte Nr. 138, Hagen 12/1992Google Scholar
  7. [He 2]
    Heinemann, B.: Some Comments on Expressiveness of Modal Logic, Informatik-Berichte Nr. 147, Hagen 10/1993Google Scholar
  8. [He 3]
    Heinemann, B.: Modal Logic on Wheels, Informatik-Berichte Nr. 151, Hagen 12/1993Google Scholar
  9. [Kam]
    Kamp, J.A.W.: Tense Logic and the Theory of Linear Order, Ph.D. Thesis, University of California, Los Angeles, 1968Google Scholar
  10. [Sch]
    Schlingloff, B.-H.: On the Expressive Power of Modal Logics on Trees, A. Nerode, M. Taitslin (eds.), LFCS — TVER '92, LNCS 620, 1992Google Scholar
  11. [Tho]
    Thomason, S.K.: Reduction of second-order logic to modal logic I, Zeit.Math.Logik Grundl. Math. 21, 107–114Google Scholar
  12. [Wol]
    Wolper, P.: Temporal Logic Can Be More Expressive, Information and Control 56 (1983), 72–99Google Scholar
  13. [van Ben]
    van Benthem, J.F.A.K.: Modal Logic and Classical Logic, Bibliopolis, Napoli, 1982Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Bernhard Heinemann
    • 1
  1. 1.Fachbereich InformatikFernUniversität HagenHagen

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