A unifying theorem for algebraic semantics and dynamic logics

  • H. Andreka
  • I. Guessarian
  • I. Németi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 199)


A unified single proof is given which implies theorems in such diverse fields as continuous algebras of algebraic semantics, dynamic algebras of logics of programs and program verification methods for total correctness. The proof concerns ultraproducts and diagonalization.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ADJ]
    ADJ. Initial algebra semantics and continuous algebras. J. ACM 24 (1977), 68–95.Google Scholar
  2. [Andréka-Németi-Sain]
    H. Andréka, I. Németi, I. Sain, A complete logic for reasoning about programs via nonstandard model theory. Theoretical Computer Science 17 (1982) 193–212, 259–278.Google Scholar
  3. [Courcelle-Guessarian]
    B. Courcelle, I. Guessarian, On some classes of interpretations, JCSS 17 (1978), 388–413.Google Scholar
  4. [Guessarian]
    I. Guessarian, Algebraic semantics, LNCS 99 Springer Verlag, Berlin (1981).Google Scholar
  5. [Henkin-Monk-Tarski-Andréka-Németi]
    L. Henkin, D. Monk, A. Tarski, H. Andréka, I. Néméti, Cylindric set algebras, LN Maths 883, Springer Verlag, Berlin (1981).Google Scholar
  6. [Jonsson]
    B. Jonsson, The theory of binary relations, Proc. Séminaire de Mathématiques supérieures de l'Université de Montréal (1984).Google Scholar
  7. [Kfoury-Park]
    D.J. Kfoury, D.M. Park, On the termination of program schemas. Information and Control 29 (1975), 243–251.Google Scholar
  8. [Kozen]
    D. Kozen, On induction vs. *-continuity. In: Logics of Programs (Proc. New York 1981) Lecture Notes in Computer Science 131, Springer Verlag 1982, 167–176.Google Scholar
  9. [Németi 1]
    I. Németi, Dynamic algebras of programs FCT 81, LNCS 117 Springer Verlag, Berlin (1981), 281–290.Google Scholar
  10. [Németi 2]
    I. Németi. Every free algebra in the variety generated by separable dynamic algebras is separable and representable, TCS 17 (1982), 343–347.Google Scholar
  11. [Németi 3]
    I. Németi, Nonstandard dynamic logic. In: Logics of Programs (Proc. New York 1981) Lecture Notes in Computer Science 131, Springer-Verlag 1982, 311–348.Google Scholar
  12. [Nivat]
    M. Nivat, On the interpretation of recursive polyadic program schemes Symp. Mathematica 15, Rome (1975), 255–281.Google Scholar
  13. [Plotkin]
    G. Plotkin, A power domain construction. SIAM J. Comp. 5 (1976), 452–487.Google Scholar
  14. [Pratt]
    V. R. Pratt, Dynamic Logic. In: Logic, Methodology and Philosophy of Science VI. (Proc. Hannover 1979) Studies in Logic and the foundations of math. Vol. 104, North Holland (1982), 251–261.Google Scholar
  15. [Relterman-Trnkova]
    J. Relterman, V. Trnkova, From dynamic algebras to test algebras. Preprint, Charles University Prague, (1984).Google Scholar
  16. [Sain]
    I. Sain, On the applicability of a category-theoretic notion of ultraproducts (in Hungarian). Matematikai lapok 31, No 1, 3 (1983).Google Scholar
  17. [Sain-Hien]
    I. Sain, Bui Huy Hien, Category theoretic notions of ultraproducts, Studia Math. Sci. Hungar., to appear.Google Scholar
  18. [Scott]
    D. Scott, Data types as lattices, SIAM J. Comput. 5 (1976), 522–587.Google Scholar
  19. [Smyth]
    M. Smyth, Powerdomains, J. CCS 15 (1978), 23–36.Google Scholar
  20. [Tarski-Ng]
    K.C. Ng, A. Tarski, Relation algebras with transitive closure. Notices Amer. Math. Soc., vol. 24 (1977), p. A-29.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • H. Andreka
    • 1
  • I. Guessarian
    • 2
  • I. Németi
    • 1
  1. 1.Mathematical research Institute of the Hungarian Academy of SciencesH. Budapest - V
  2. 2.CNRS - LITPUniversité Paris 7Paris

Personalised recommendations