Abstract
We prove a finite model theorem and infinitary completeness result for the propositional μ-calculus. The construction establishes a link between finite model theorems for propositional program logics and the theory of well-quasi-orders.
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M. J. Fischer and R. E. Ladner, Prepositional Dynamic Logic of regular programs, J. Comput. Syst. Sci. 18:2 (1979), pp. 194–211.
D. Kozen, Results on the propositional μ-calculus, in: E. Schmidt (ed.), Proc. 9th Int. Colloq. Automata, Languages, and Programming 1982, Lect. Notes in Comput. Sci. 140, Springer, 1982, pp. 348–359.
D. Kozen and R. Parikh, A decision procedure for the propositional μ-calculus, in: E. Clarke and D. Kozen (eds.), Proc. Workshop on Logics of Programs 1983, Lect. Notes in Comput. Sci. 164, Springer, 1984, pp. 313–326.
R. Laver, Well-quasi-ordering s and sets of finite sequences, Proc. Camb. Phil. Soc. 79 (1976), pp. 1–10.
R. Laver, Better-quasi-orderings and a class of trees, in: Studies in Foundations and Combinatorics, Advances in Mathematics Supplementary Studies, v.1 (1978), pp. 31–48.
C. St. J. A. Nash-Williams, On well-quasi-ordering infinite trees, Proc. Camb. Phil. Soc. 61 (1965), pp. 697–720.
C. St. J. A. Nash-Williams, On better-quasi-ordering transfinite sequences, Proc. Camb. Phil. Soc. 64 (1968), pp. 273–290.
V. R. Pratt, A decidable μ-calculus (preliminary report), Proc. 22nd IEEE Symp. Found. Comput. Sci., 1981, pp. 421–427.
R. Streett, Propositional Dynamic Logic of looping and converse, Proc. 13th ACM Symp. Theory of Comput., 1981, pp. 375–383.
R. Streett and E. A. Emerson, An elementary decision procedure for the μ-calculus, in: J. Paredaens (ed.), Proc. 11th Int. Colloq. Automata, Languages, and Programming 1984, Lect. Notes in Comput. Sci. 172, Springer, 1984, pp. 465–472.
D. Scott and J. de Bakker, A theory of programs, unpublished notes, Vienna, 1969.
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Kozen, D. A finite model theorem for the propositional μ-calculus. Stud Logica 47, 233–241 (1988). https://doi.org/10.1007/BF00370554
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DOI: https://doi.org/10.1007/BF00370554