Abstract
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” W n,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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References
Amir, A.: Expressive Completeness Failure in Branching Time Structures, Journal Comp. Syst. Sc. 34 (1987), 27–42
Gabbay,D.: Expressive Functional Completeness in Tense Logic, in U. Mönnich (ed.), Aspects of Philosophical Logic, 1981
Gabbay,D.; Pnueli,A.; Shelah,S.; Stavi,J.: On the Temporal Analysis of Fairness, Proc. 7th Ann. ACM Sympos. PoPL, 1980, 163–173
Goldblatt, R.: Logics of Time and Computation, CSLI Lecture Notes, No. 7, Stanford 1987
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, 1987
Heinemann, B.: A note on Expressive Completeness of Modal Logic, Informatik-Berichte Nr. 138, Hagen 12/1992
Heinemann, B.: Some Comments on Expressiveness of Modal Logic, Informatik-Berichte Nr. 147, Hagen 10/1993
Heinemann, B.: Modal Logic on Wheels, Informatik-Berichte Nr. 151, Hagen 12/1993
Kamp, J.A.W.: Tense Logic and the Theory of Linear Order, Ph.D. Thesis, University of California, Los Angeles, 1968
Schlingloff, B.-H.: On the Expressive Power of Modal Logics on Trees, A. Nerode, M. Taitslin (eds.), LFCS — TVER '92, LNCS 620, 1992
Thomason, S.K.: Reduction of second-order logic to modal logic I, Zeit.Math.Logik Grundl. Math. 21, 107–114
Wolper, P.: Temporal Logic Can Be More Expressive, Information and Control 56 (1983), 72–99
van Benthem, J.F.A.K.: Modal Logic and Classical Logic, Bibliopolis, Napoli, 1982
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© 1994 Springer-Verlag Berlin Heidelberg
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Heinemann, B. (1994). On expressive completeness of modal logic. In: Nerode, A., Matiyasevich, Y.V. (eds) Logical Foundations of Computer Science. LFCS 1994. Lecture Notes in Computer Science, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58140-5_16
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DOI: https://doi.org/10.1007/3-540-58140-5_16
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