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The temporal logic of branching time. (English) Zbl 0533.68036
Summary: A temporal logic is defined which contains both linear and branching operators. The underlying model is the tree of all possible computations. The following metatheoretical results are proven: 1) an exponential decision procedure for satisfiability; 2) a finite model property; 3) the completeness of an axiomatization.

MSC:
68Q65 Abstract data types; algebraic specification
03B60 Other nonclassical logic
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[1] Abrahamson, K.R.: Modal logic of concurrent nondeterministic programs. Symposium on Semantics of Concurrent Computations, Lecture Notes in Computer Science 70, pp. 21-33. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0402.68010
[2] Ben-Ari, M., Manna, Z., Pnueli, A.: The temporal logic of branching time. Eight ACM Symposium on Principles of Programming Languages, Williamsburg, VA, pp. 164-176, 1981 · Zbl 0533.68036
[3] Emerson, A.E., Halpern, J.Y.: Decision procedures and expressiveness in the temporal logic of branching time. 14-th ACM Symposium on Theory of Computing, San Francisco, CA, pp. 169-180, 1982
[4] Floyd, R.W.: Nondeterministic algorithms. J. ACM14(4), 636-644 (1967) · Zbl 0153.47006 · doi:10.1145/321420.321422
[5] Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: The temporal analysis of fairness. Seventh ACM Symposium on Principles of Programming Languages, Las Vegas, NE, pp. 163-173, 1980
[6] Harel, D.: First Order Dynamic Logic, Lecture Notes in Computer Science 68. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0403.03024
[7] Harel, D., Kozen, D., Parikh, R.: Process Logic: expressiveness, decidability, completeness. 21-st IEEE Symposium on Foundation of Computer Science, pp. 129-142, 1980
[8] Kröger, A.: A uniform logical basis for the description, specification and verification of programs. IFIP Working Conference on Formal Description of Programming Concepts, St. Andrews, Canada, 1977 · Zbl 0373.68026
[9] Lamport, L.: ?Sometime? is sometimes ?not never?. Seventh ACM Symposium on Principles of Programming Languages, Las Vegas, NE, pp. 174-183, 1980
[10] Manna, Z.: Second order mathematical theory of computation. Second ACM Symposium on Theory of Computing, pp. 158-168, 1970
[11] Manna, Z., Pnueli, A.: The modal logic of programs. Automata, Languages and Programming, Lecture Notes in Computer Science 79, pp. 385-409. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0404.68011
[12] Pnueli, A.: The temporal semantics of concurrent programs. Theor. Comput. Sci.13, 45-60 (1981) · Zbl 0441.68010 · doi:10.1016/0304-3975(81)90110-9
[13] Pratt, V.R.: A near optimal method for reasoning about action. J. Comput. Syst. Sci.20, 231-254 (1980) · Zbl 0424.03010 · doi:10.1016/0022-0000(80)90061-6
[14] Prior, A.: Past, Present and Future. Oxford University Press 1967 · Zbl 0169.29802
[15] Rescher, N., Urquhart, A.: Temporal Logic. Berlin, Heidelberg, New York, Wien: Springer 1971 · Zbl 0229.02027
[16] Smullyan, R.M.: First Order Logic. Berlin, Heidelberg, New York: Springer 1968 · Zbl 0172.28901
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