Axioms of algorithmic logic univocally determine semantics of programs

  • Andrzej Salwicki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 88)


Among many execution methods for programs that can be conceived of, only the standard notion of computation satisfies axioms of algorithmic logic AL and makes inference rules of AL sound. In this sense the axiomatic system of algorithmic logic specifies the semantics of programs. Next, we shall prove that by the relaxing of requirements, e.g. by the rejection of an axiom or an inference rule we shall create a liberal axiomatic system which allows nonstandard (i.e. transfinite and successful) runs of programs.


Inference Rule Completeness Theorem Algorithmic Logic Algorithmic Property Complete Axiomatization 
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. [1]
    Andreka H., Nemeti, I., Completeness of Floyd logic, Bulletin of section of logic vol. 7 (1978)Google Scholar
  2. [2]
    Banachowski, L., Modular approach to the logical theory of programs Proc. MFCS '74 Symp. A. Blikle ed. Lecture Notes Comp. Sci. 28Google Scholar
  3. [3]
    Bartol, W. M., On configurations of objects in LOGLAN computations Institute of Informatics, University of Warsaw, manuscript, 1980Google Scholar
  4. [4]
    Blikle, A., A survey of input-output semantics and program verification, ICS PAS Reports 344, Warsaw 1979Google Scholar
  5. [5]
    Cook, S.A., Soundness and completeness of an axiom system for program verification, SIAM Journal on Computing, 7 (1978) no 1Google Scholar
  6. [6]
    Csirmaz, L., Programs and program verifications in a general setting, Preprint 4 of the Mathematical Institute of the Hungarian Academy of Sciences, Budapest 1980Google Scholar
  7. [7]
    Dijkstra, E.W., A discipline of programming, Prentice Hall, 1976Google Scholar
  8. [8]
    Floyd, R.W., Assigning meaning to programs in Mathematical ASpects of Computer Science Proc. of Symp. in Applied Mathematics, AMS Providence, Rhode Island 1967Google Scholar
  9. [9]
    Greif, I., Meyer, A.R., Specifying the semantics of while programs, M.I.T. Lab. for Comp. Sci. TM-130, MIT, Cambridge, Mass. April 79Google Scholar
  10. [10]
    Grzegorczyk, A., An outline of mathematical logic, Polish Scientific Publishers and North-Holland, Warsaw, 1977Google Scholar
  11. [11]
    Harel, D., First-Order dynamic logic in Lecture notes Comp. Sci. vol.68, Springer Vlg, 1979, BerlinGoogle Scholar
  12. [12]
    Hoare, C.A., Wirth, N., An axiomatic definition of the programming language PASCAL, Acta Informatica 2 (1973) 335–355Google Scholar
  13. [13]
    Kozen, D., On the duality between dynamic algebras and Kripke models, IBM research report RC 7893, Oct. 1979Google Scholar
  14. [14]
    Kreczmar, A., Programmability in fields, Fundamenta Informaticae 1 (1977) 195–230Google Scholar
  15. [15]
    Oktaba, H., On algorithmic theory of reference, Institute of Informatics, University of Warsaw, manuscript, 1980Google Scholar
  16. [16]
    Meyer, A.R., Halpern, J.Y., Axiomatic definitions of programming languages, A theoretical assessment, Proc. 7-th POPL Symp. Las Vegas 1980 203–212Google Scholar
  17. [17]
    Mirkowska, G., Algorithmic logic and its applications in programs Fundamenta Informaticae 1 (1977) 1–17, 147–165Google Scholar
  18. [18]
    Mirkowska, G., Complete axiomatization of algorithmio properties of program schemes with bounded nondeterministic interpretations, Proc 12-th STOC symp. Los Angeles, April 1980, 21–32Google Scholar
  19. [19]
    Mirkowska, G., Model existence theorem for algorithmic logic of nondeterministic programs, 1978, to appear in Fundamenta Inform.Google Scholar
  20. [20]
    Mirkowska, G., Salwicki, A., A complete axiomatic characterization of algorithmic properties of block-structured programs with procedures in Proc. MFCS '76 A. Mazurkiewicz ed. Lecture Notes Comp. Sci. vol. 45 pp 602–603, Springer Vlg, 1976, BerlinGoogle Scholar
  21. [21]
    Reiterman, J., Trnkova, V., Dynamic algebras which are not Kripke structures, this volumeGoogle Scholar
  22. [22]
    Salwicki, A., On the predicate calculi with iteration quantifiers, Bull. Pol. Acad. Sci. Ser. Math. 18 (1970) 278–282Google Scholar
  23. [23]
    Salwicki, A., On algorithmic theory of stacks, in Proc MFCS'78 Zakopane J. Winkowski ed. Lecture Notes Comp. Scie. vol 64, Springer 1978 BerlinGoogle Scholar
  24. [24]
    Salwicki, A., On algorithmic theory of dictionaries, to appear in Proc. Alg. Logic Seminar, Zürich 1979 E. Engeler ed. Lecture Notes Comp. Sci.Google Scholar
  25. [25]
    Salwicki, A., Programmability and recursiveness, to appearGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Andrzej Salwicki
    • 1
  1. 1.Mathematical InstitutePolish Academy of SciencesWarsaw

Personalised recommendations