Workshop on Logic of Programs

Logic of Programs 1979: Logic of Programs pp 102-144 | Cite as

Propositional dynamic logics of programs: A survey

  • Rohit Parikh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 125)


Binary Relation Boolean Algebra Propositional Logic Kripke Model Dynamic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ab]
    Abrahamson, Karl, Modal Logic of Concurrent Nondeterministic Pograms, Proc. Conf. on Parallel Programs, Evian, France, 1979, 21–33.Google Scholar
  2. [AHU]
    Aho A.V., J.E. Hopcroft, and J.D. Ullman, The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.Google Scholar
  3. [BKMRS]
    Banachowski, L., A. Kreczmar, G. Mirkowska, H. Rasiowa, A. Salwicki., An Introduction to Algorithmic Logic; Metamathematical Investigations in the Theory of Programs, In Math. Found. of Comp. Sci. (eds. Mazurkiewicz and Pawlak), Banach Center Publications, Warsaw. 1977.Google Scholar
  4. [Be]
    Berman, F., A completeness technique for D-axiomatizable semantics, Proc. 11th ACM Symp. on Theory of Comp. (May 1979), 160–166.Google Scholar
  5. [BHP]
    Ben-Ari, M., Halpern, J., and Pnueli, A., Finite Models for Deterministic Propositional Dynamic Logic, Proceedings of the 8th ICALP conference, Jerusalem 1981, Springer LNCS 115, pp. 249–263.Google Scholar
  6. [BP2]
    Berman, F. and M. Paterson., Test-Free Propositional Dynamic Logic is Strictly Weaker than PDL, T.R. 77-10-02, Dept. of Computer Science, Univ. of Washington, Seattle. Nov. 1977.Google Scholar
  7. [BS]
    Bell, J.S. and A.B. Slomson, Models and Ultraproducts. North Holland, Amsterdam, 1971.Google Scholar
  8. [C]
    Conway, J.H. Regular Algebra and Finite Machines. Chapman-Hall, London, 1971.Google Scholar
  9. [CHMP]
    Chandra, A., Halpern, J., Meyer, A., and Parikh, R., Equations between Regular Terms and an Application to Process Logic, Proceedings of STOC 1981, pp. 384–390.Google Scholar
  10. [CO]
    Constable, R.L. and M.J. O'Donnell. A Programming Logic. Winthrop, Cambridge, Mass., 1978.Google Scholar
  11. [E]
    Engeler, E., Algorithmic properties of structures, Math. Systems Theory. 1, 183–195. 1967.Google Scholar
  12. [FL]
    Fischer, M.J. and R.E. Ladner., Propositional Modal Logic of Programs, Proc. 9th Ann. ACM Symp. on Theory of Computing, 286–294, Boulder, Col., May 1977.Google Scholar
  13. [F]
    Floyd, R.W., Assigning Meanings to Programs, In Mathematical Aspects of Computer Science (ed. J.T. Schwartz), 19–32, 1967.Google Scholar
  14. [G]
    Gabbay, D., Axiomatizations of Logics of Programs, Typescript, Nov. 1977.Google Scholar
  15. [GPSS]
    Gabbay G., Pnueli, A. Shelah, S. and Stavi, J., The Temporal Analysis of Fairness, 7th Annual ACM Symposium on POPL, Jan 1980, 163–173.Google Scholar
  16. [GM]
    Greif, I. and A. R. Meyer, Specifying Programming Language Semantics, Proc. 6th Ann. ACM Symp. on Principles of Programming Languages, 180–189, San Antonio, Texas, Jan. 1979.Google Scholar
  17. [Hs]
    Halmos, P.R. Lectures on Boolean Algebras. Springer Verlag, New York, 1974.Google Scholar
  18. [H1]
    Harel, D., Two Results on Process Logic, Information Processing Letters, 8 (1979) 195–198.Google Scholar
  19. [H2]
    Harel, D. First Order Dynamic Logic, Lecture Notes in Computer Science, no. 68, Springer Verlag 1979.Google Scholar
  20. [HKP]
    Harel, D., Kozen, D., Parikh, R., Process Logic: Expressiveness, Decidability, Completeness, Proc. IEEE-FOCS 1980, pp. 129–142.Google Scholar
  21. [HL]
    Hoare, C.A.R., and Lauer, P.E., Consistent and Complementary Formal Theories of the Semantics of Programming Languages. Acta Informatica 3, (1974) 135–153.Google Scholar
  22. [Ho]
    Hoare, C.A.R., An Axiomatic Basis for Computer Programming, CACM 12, 576–580, 1969.Google Scholar
  23. [HPS]
    Harel, D., Pnueli, A., and Stavi, J., Propositional Dynamic Logic of Recursive Programs, Research report, May 1981.Google Scholar
  24. [HR]
    Halpern, J., and Reif, J., The Propositional Dynamic Logic of Deterministic, Well-structured Programs, MIT-LCS TM no. 198, March 1981. To appear in Proc IEEE-FOCS 1981.Google Scholar
  25. [Ka]
    Kamp, H., Tense Logic and the Theory of Linear Order, Ph.D. thesis, UCLA 1968.Google Scholar
  26. [Ke]
    Keisler, H.J. Model Theory for Infinitary Logic. North Holland, Amsterdam, 1971.Google Scholar
  27. [K1]
    Kozen, D., A representation theorem for models of *-free PDL, Proc. 7th Int. Colloq. on Automata, Languages, and Programming, Lecture Notes in Computer Science 85, ed. Goos and Hartmanis, Springer-Verlag, Berlin, 1980, 351–362. Also Report RC7864, IBM Research, Yorktown Heights, New York, Sept. 1979.Google Scholar
  28. [K2]
    Kozen, D., On the duality of dynamic algebras and Kripke models, Report RC7893, IBM Research, Yorktown Heights, New York, Oct. 1979.Google Scholar
  29. [K3]
    Kozen, D., On the representation of dynamic algebras, Report RC7898, IBM Research, Yorktown Heights, New York, Oct. 1979.Google Scholar
  30. [K4]
    Kozen, D., On the representation of dynamic algebras II, Report RC8290, IBM Research, Yorktown Heights, New York, May 1980.Google Scholar
  31. [K5]
    Kozen, D., On induction vs. *-continuity, Report RC8468, IBM Research, Yorktown Heights, New York, Sept. 1980.Google Scholar
  32. [K6]
    Kozen, D., Semantics of Probabilistic Programs, 20th IEEE-FOCS Symposium, San Juan, 1979, 101–114.Google Scholar
  33. [KP]
    Kozen, D. and Parikh, R., An elementary Completeness Proof for PDL, TCS vol 14 (1981) pp. 113–118.Google Scholar
  34. [Kr]
    Kripke, S., Semantical considerations on Modal Logic, Acta Philosophica Fennica, 83–94, 1963.Google Scholar
  35. [LP]
    Litvinchouk, S.D. and V.R. Pratt., A Proof-checker for Dynamic Logic, Proc. 5th Int. Joint Conf. on AI, 552–558, Boston, Aug. 1977.Google Scholar
  36. [Ma]
    Manna, Z., Mathematical Theory of Computation. McGraw-Hill, 1974.Google Scholar
  37. [Me]
    Meyer, A., WSIS is not elementary decidable, Proceedings of the Boston Logic Colloquium, edited by R. Parikh, Springer Lecture Notes in Mathematics vol. 453, 1974, pp. 132–154.Google Scholar
  38. [Mi]
    Mirkowska, G., Complete Axiomatisation of Algorithmic Properties of Program Schemes with Bounded Nondeterministic Interpretations, 12th Annual ACM-STOC Symposium (1980), 14–21.Google Scholar
  39. [MSM]
    Meyer, A., Street, R., and Mirkowska, G., The Deducibility Problem in Propositional Dynamic Logic, Proc. 8th ICALP, Springer LNCS 115 (1981) pp. 238–248.Google Scholar
  40. [N]
    Nemeti, I., Every free algebra in the variety generated by the representable dynamic algebras is separable and representable, manuscript, Hungarian Academy of Sciences, Budapest, 1980.Google Scholar
  41. [Ni]
    Nishimura, H., Descriptively Complete Process Logic, typescript, Kyoto University, Dec. 1979.Google Scholar
  42. [OP]
    Owicki, S., A Consistent and Complete Deductive System for the Verification of Parallel Programs, Proc. 8th Ann. ACM Symp. on Theory of Computing, 73–86. Hershey PA. May 1976.Google Scholar
  43. [Pa1]
    Parikh, R., A Completeness Result for PDL, Manuscript dated 11/29/77.Google Scholar
  44. [Pa2]
    Parikh, R., A Completeness Result for PDL, Symposium on Mathematical Foundations of Computer Science, Zakopane, Poland, Springer LNCS 64, Sept. 1978, pp. 403–415.Google Scholar
  45. [Pa3]
    Parikh, R., Second Order Process Logic, 19th IEEE Symposium on Foundations of Computer Science. Oct. 1978 pp. 177–183.Google Scholar
  46. [Pa4]
    Parikh, R., Propositional Logics of Programs, Proc. 7th Ann. ACM Symp. on Principles of Programming Languages, Las Vegas, Jan. 1980. pp. 186–192.Google Scholar
  47. [Pa5]
    Parikh, R., Some Applications of Topology to Program Semantics, to appear in Math. Systems theory.Google Scholar
  48. [Pn]
    Pnueli, A., The Temporal Logic of Programs, 18th IEEE Symposium on Foundations of Computer Science, 46–57. Oct. 1977, pp. 46–57.Google Scholar
  49. [Pr1]
    Pratt, V.R., Semantical Considerations on Floyd-Hoare Logic, Proc. 17th Ann. IEEE Symp. on Foundations of Comp. Sci., 109–121. Oct. 1976, pp. 109–121.Google Scholar
  50. [Pr2]
    Pratt, V.R., A Practical Decision Method for Propositional Dynamic Logic, Proc. 10th Annual ACM Symposium on Theory of Computing, 326–337, San Diego, Calif., May 1978.Google Scholar
  51. [Pr3]
    Pratt, V.R., Process Logic, Proc. 6th Ann. ACM Symp. on Principles of Programming Languages, Jan. 1979.Google Scholar
  52. [Pr4]
    Pratt, V.R., Models of Program Logics, 20th IEEE-FOCS Symposium, San Juan, 1979, 115–122.Google Scholar
  53. [Pr5]
    Pratt, V.R., Dynamic Algebras: Examples, Constructions, Applications, MIT/LCS/TM-138, July 1979.Google Scholar
  54. [Pr6]
    Pratt, V.R., Dynamic Logic, Proc. 6th International Congress for Logic, Philosophy, and Methodology of Science, Hanover, W. Germany, Aug. 1979.Google Scholar
  55. [Pr7]
    Pratt, V.R., Dynamic algebras and the nature of induction, Proc. 12th ACM Symp. on Theory of Computing (May 1980), 22–28.Google Scholar
  56. [R]
    Redko, V.N., On Defining Relations for the Algebra of Regular Events (Russian) Ukrain. Math. Z. 16 (1964), 120–126.Google Scholar
  57. [Re]
    Reif, J., Logics for Probabilistic Computation, 12th Annual ACM-STOC Symposium (1980), 8–13.Google Scholar
  58. [Ra]
    Rabin, M., Decidability of Second Order Theories and Automata on Infinite Trees, Transactions of the Amer. Math. Soc., 141 (1969) 1–35.Google Scholar
  59. [RT1]
    Reiterman, J. and V. Trnkova, Dynamic algebras which are not Kripke structures, Proc. 9th Symp. on Math. Found. of Computer Science (Aug. 1980), 528–538.Google Scholar
  60. [RT2]
    Reiterman, J. and V. Trnkova, private communication.Google Scholar
  61. [Sa1]
    Salomaa, A., Two Complete Axiom Systems for the Algebra of Regular Events, Jour. ACM 13 (1966), 158–169.Google Scholar
  62. [Sa2]
    Salwicki, A., Formalized Algorithmic Languages, Bull. Acad. Pol. Sci., Ser. Sci. Math. Astr. Phys. Vol. 18. No. 5. 1970.Google Scholar
  63. [Seg]
    Segerberg, K., A Completeness Theorem in the Modal Logic of Programs, Preliminary report. Notices of the AMS, 24, 6, A-552. Oct. 1977.Google Scholar
  64. [Sem]
    Semyonov, A.L., Some Algorithmic Problems for Systems of Algorithmic Algebras, Doklady vol. 239 (1978).Google Scholar
  65. [St1]
    Stockmeyer, L., The Complexity of Decision Procedures, MIT project MAC report TR-133, July 1974.Google Scholar
  66. [St2]
    Street, R., Propositional Dynamic Logic of Looping and Converse, Proc. 13th ACM-STOC Symposium (1981), pp. 375–383.Google Scholar
  67. [Va]
    Valiev, B., On Axiomatisation of Deterministic Propositional Dynamic Logic, Symposium on Mathematical Foundations of Computer Science, Olomouc, Czechoslovakia, Sept. 1979, 482–491.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Rohit Parikh
    • 1
  1. 1.Math DeptBoston Univ. and Laboratory for Computer Science, MITUSA

Personalised recommendations