Making dynamic logic first-order

  • Petr Hájek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 118)


Regular dynamic logic DL is given an alternative semantics admitting non-standard interpretation of arithmetical notions and, consequently, of finiteness; the interpretation of iteration of a program is made dependent on this, possibly non-standard notion of finiteness. Dynamic logic with this semantics is recursively axiomatizable: roughly speaking, Harel's axioms and deduction rules together with axioms of Peano arithmetic form a finitary sound and complete axiomatization of valid formulas.


Dynamic Logic Peano Arithmetic Deduction Rule Full Induction Complete Axiomatization 
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  1. 1.
    H. Andréka, I. Neméti, I. Sain: Completeness results in verification of programs and program schemes, MFCS 1979 (Bečvář, ed.) Lect. Notes in Comp. Sci vol. 74, p. 208–218, Springer-Verlag 1979Google Scholar
  2. 2.
    S. Feferman: Arithmetization of metamathematics in a general setting, Fund. Math. 49 (1960) 35–92Google Scholar
  3. 3.
    D. Harel: First order dynamic logic, Lect. Notes in Comp. Sci. vol. 68, Springer-Verlag 1979Google Scholar
  4. 4.
    J. A. Makowsky: Measuring the expressive power of dynamic logic — an application of abstract model theory, Automata, Languages and Programming (deBakker and van Leeuwen, eds.) Lect. Notes in Comp. Sci. vol. 85, p. 409–421, Springer-Verlag 1980Google Scholar
  5. 5.
    K. McAloon: Completeness theorems, incompleteness theorems and models of arithmetic, Trans. AMS 239 (1978) 253–277Google Scholar
  6. 6.
    V. R. Pratt: Dynamic logic and the nature of induction, MIT/LCS/TM-159, March 1980Google Scholar
  7. 7.
    J. R. Shoenfield, Mathematical Logic, Addison-Vesley 1967Google Scholar
  8. 8.
    C. Smoryński: Non-standard models of arithmetic, Univ. Utrecht, Dept. of Math., preprint nr. 153, April 1980Google Scholar
  9. 9.
    P. Vopěnka, P. Hájek: The Theory of Semisets, Academia Prague and North-Holland Publ. Comp. 1972Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Petr Hájek
    • 1
  1. 1.Mathematical Institute, ČSAVPragueCzechoslovakia

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