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A Note on the Completeness of Kozen's Axiomatisation of the Propositional μ-Calculus

Published online by Cambridge University Press:  15 January 2014

Igor Walukiewicz
Igor Walukiewicz*
Affiliation:
Basic Research in Computer Science, Centre of the Danish National Research Foundation (BRICS), Department of Computer Science, University of Aarhus, NY Munkegade, DK-8000 Aarhus C, Denmark E-mail: igw@mimuw.edu.pl
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Abstract

The prepositional μ-calculus is an extension of the modal system K with a least fixpoint operator. Kozen posed a question about completeness of the axiomatisation of the logic which is a small extension of the axiomatisation of the modal system K. It is shown that this axiomatisation is complete.

Information

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 2 , Issue 3 , September 1996 , pp. 349 - 366
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1] Bull, R. and Segerberg, K., Basic modal logic, Handbook of philosophical logic (Gabbay, D. and Guenther, F., editors), vol. 2, D. Reidel Publishing Company, 1984, pp. 1–89.Google Scholar
[2] Emerson, E. A., Temporal and modal logic, Handbook of theoretical computer science (Leeuven, J., editor), vol. B, Elsevier, 1990, pp. 995–1072.Google Scholar
[3] Emerson, E. A. and Jutla, C. S., The complexity of tree automata and logics ofprograms, 29th FOCS, 1988.Google Scholar
[4] Fitting, M., Proof methods for modal and intuitionistic logics, D. Reidel Publishing Company, 1983.CrossRefGoogle Scholar
[5] Harel, D., Dynamic logic, Handbook of philosophical logic, vol. II, D. Reidel Publishing Company, 1984, pp. 497–604.CrossRefGoogle Scholar
[6] Janin, D. and Waluoewicz, I., Automata for the μ-calculus and related results, MFCS '95, Lecture Notes in Computer Science, vol. 969, 1995, pp. 552–562.Google Scholar
[7] Kaivola, R., Axiomatising linear time μ-calculus, CONCUR '95, Lecture Notes in Computer Science, vol. 962, 1995, pp. 423–437.CrossRefGoogle Scholar
[8] Kozen, D., Results on thepropositional μ-calculus, Theoretical Computer Science, vol. 27 (1983), pp. 333–354.CrossRefGoogle Scholar
[9] Kozen, D., A finite model theorem for the propositional μ-calculus, Studia Logica, vol. 47 (1988), no. 3, pp. 234–241.CrossRefGoogle Scholar
[10] Kozen, D. and Tiurïn, J., Logics of programs, Handbook of theoretical computer science (Leeuven, J., editor), vol. B, Elsevier, 1990, pp. 789–840.Google Scholar
[11] Mostowskl, A. W., Regular expressions for infinite trees and a standard form of automata, Fifth symposium on computation theory (Skowron, A., editor), Lecture Notes in Computer Science, vol. 208, 1984, pp. 157–168.CrossRefGoogle Scholar
[12] Niwińskl, D., Fixed points vs. infinite generation, LICS '88, 1988, pp. 402–409.Google Scholar
[13] Niwiński, D. and Waluoewicz, I., Games for μ-calculus, Technical Report TR 94-03(192), Institute of Informatics, Warsaw Univeristy, 02 1994, to appear in Theoretical Computer Science ; available from: http://www.daimi.aau.dk/~igw/home.html.Google Scholar
[14] Rabin., M., Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 1–35.Google Scholar
[15] Slefkes, D., Büchi's monadic second order successor arithmetic, Lecture notes in mathematics, vol. 120, Springer-Verlag, 1970.Google Scholar
[16] Stirling, C. S., Modal and temporal logics, Handbook of logic in comuter science (Abramsky, S., Gabbay, D., and Maibaum, T., editors), Oxford University Press, 1991, pp. 477–563.Google Scholar
[17] Streett, R. S. and Emerson, E. A., An automata theoretic procedure for the propositional μ-calculus, Information and Computation, vol. 81 (1989), pp. 249–264.CrossRefGoogle Scholar
[18] Walukiewicz, I., On completeness of the μ-calculus, LICS '93, 1993, pp. 136–146.Google Scholar