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Sequential method in propositional dynamic logic. (English) Zbl 0401.03005

MSC:
03B45 Modal logic (including the logic of norms)
68Q65 Abstract data types; algebraic specification
68W99 Algorithms in computer science
68N01 General topics in the theory of software
03B60 Other nonclassical logic
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[1] Fischer, M.J., Ladner, R.E.: Propositional modal logic of programs. Proceedings 9th Annual ACM Symposium on Theory of Computing, pp. 296-294, Boulder Co, 1977
[2] Gentzen, G.: Untersuchungen über das logische Schliessen I and II. Math. Z. 39, 176-210 and 405-431 (1935) · Zbl 0010.14501 · doi:10.1007/BF01201353
[3] Harel, D., Meyer, A.R., Pratt, V.R.: Computability and completeness in logics of programs. Proceedings 9th Annual Symposium on Theory of Computing, pp. 261-268, Boulder 1977
[4] Harel, D.: Logics of programs: Axiomatics and descriptive power. MIT, ph.D.thesis, May 1978
[5] Hughes, G.E., Cresswell, M.J.: An introduction to modal logic. London: Methuen 1968 · Zbl 0205.00503
[6] Manna, Z.: Mathematical theory of computation. New York: McGraw-Hill 1974 · Zbl 0353.68066
[7] Monk, D.: Mathematical logic. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0354.02002
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[10] Ohnishi, M., Matsumoto, K.: Gentzen method in modal calculi II. Osaka Math. J. 11, 115-120 (1959) · Zbl 0089.00602
[11] Parikh, R.: The completeness of propositional dynamic logic. Lecture Notes in Computer Science, vol. 64, pp. 403-415. Berlin-Heidelberg-New York: Springer 1978 · Zbl 0392.03017
[12] Pratt, V.R.: Semantical considerations in Floyd-Hoare logic. Proceedings 17th IEEE Symposium on Foundations of Computer Science, pp. 109-121. 1976
[13] Prawitz, D.: Comments on Gentzen-type procedures and the classical notion of truth. Lecture Notes in Mathematics vol. 500, pp. 290-319. Berlin-Heidelberg-New York: Springer 1975 · Zbl 0342.02022
[14] Sato, M.: A study of Kripke-type models for some modal logics by Gentzen’s sequential method. Publ. Res. Inst. Math. Sci. 13, 381-468 (1977) · Zbl 0405.03013 · doi:10.2977/prims/1195189814
[15] Segerberg, K.: A completeness theorem in the modal logic of programs. Notices of the American Mathematical Society, 24, A-552 (1977)
[16] Takeuti, G.: Proof theory. Amsterdam: North-Holland 1975 · Zbl 0355.02023
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