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Logic of Programs 1979: Logic of Programs pp 198-245 | Cite as

A survey of the logic of effective definitions

  • J. Tiuryn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 125)

Abstract

LED, the Logic of Effective Definitions, is an extension of first order predicate calculus used for making assertions about programs. Programs are modeled as effective definitional schemes (following Friedman). Logical properties of LED and its relations to classical logics and other programming logics are surveyed.

Key words

effective definitions logic of programs partial correctness completeness infinitary logic 

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References

  1. [1]
    Banachowski, L., Kreczmar, A., Mirkowska, G., Rasiowa, H. and Salwicki, A., An Introduction to Algorithmic Logic. Mathematical Investigations in the Theory of Programs. In Mazurkiewicz and Pawlak (eds) Math. Found of Comp. Sc. Banach Center Publications. Warsaw 1977, pp. 7–99.Google Scholar
  2. [2]
    Bell, J. and Machover, M., A Course in Mathematical Logic. North-Holland Publ. Co., Amsterdam 1977.Google Scholar
  3. [3]
    Bergstra, J. and Meyer, J. J. C. On the Quantifier Free Fragment of Logic of Effective Definitions. Leiden University Report (80–4), 1980.Google Scholar
  4. [4]
    Bergstra, J. and Tiuryn, J., Implicit Definability of Algebraic Structures by Means of Program Properties. Abstract: in Budach (ed.). Fundamentals of Comp. Th. Academie-Verlag Berlin 1979. The full version will appear in Fundamenta Informaticae.Google Scholar
  5. [5]
    Bergstra, J., and Tiuryn, J., Algorithmic Degrees of Algebraic Structures. Leiden University Report (79–6), 1979.Google Scholar
  6. [6]
    Bergstra, J., Tiuryn, J., and Tucker, J.V., Correctness Theories and Program Equivalence. Mathematisch Centrum Report (IW 119/79). Amsterdam 1979.Google Scholar
  7. [7]
    Chang, C.C. and Keisler, H.J., Model Theory. North-Holland Publ. Co., Amsterdam 1973.Google Scholar
  8. [8]
    Constable, R.L., A Constructive Programming Logic. In Gilchrist (ed.) Information Processing '77. Proc. of IFIP Congress '77. North-Holland Publ. Co. Amsterdam 1977, pp. 733–738.Google Scholar
  9. [9]
    Constable, R.L. and Gries, D., On Classes of Program Schemata. SIAM Journal on Computing 1 (1972) pp. 66–118.Google Scholar
  10. [10]
    Engeler, E., Algorithmic Logic. In de Bakker (ed.) Mathematical Centre Tracts (63) Amsterdam 1975, pp. 57–85.Google Scholar
  11. [11]
    Engeler, E., Generalized Galois Theory and its Application to Complexity. Berichte des Instituts für Informatik (24) ETH Zurich (1978).Google Scholar
  12. [12]
    Friedman, H., Algorithmic Procedures, Generalized Turing Algorithms, and Elementary Recursion Theory. In Gandy and Yates (eds) Logic Colloquium '69, North-Holland Publ. Co., Amsterdam 1971, pp. 361–390.Google Scholar
  13. [13]
    Goguen, J.A., Thatcher, J.W., and Wagner, E.G., An Initial Algebra Approach to the Specification Correctness and Implementation of Abstract Data Types. In Yeh (ed.) Current Trends in Programming Methodology, (vol. 3) Data Structuring. Prentice-Hall 1977. Automatic Computation Series.Google Scholar
  14. [14]
    Greibach, S.A., Theory of Program Structures: Schemes, Semantics, Verification. Lecture Notes in Comp. Sc. 36, Springer Verlag, Berlin 1975.Google Scholar
  15. [15]
    Harel, D., First-order Dynamic Logic. Lecture Notes in Comp. Sc. 68, Springer Verlag, Berlin 1979.Google Scholar
  16. [16]
    Keisler, H.J., Model Theory for Infinitary Logic. North-Holland Publ. Co., Amsterdam 1972.Google Scholar
  17. [17]
    Kfoury, D.J., Comparing Algebraic Structures up to Algorithmic Equivalence. In Nivat (ed.) Automata, Languages and Programming. North-Holland Publ. Co., Amsterdam 1972, pp. 253–264.Google Scholar
  18. [18]
    Kfoury, D.J., Translatability of schemes over restricted interpretations. Journal of Comp. and Syst. Sc. 8 (1974) pp. 387–408.Google Scholar
  19. [19]
    Kreczmar, A. Programmability in Fields. Fundamenta Informaticae I, 2. (1977) pp. 195–230.Google Scholar
  20. [20]
    Lopez-Escobar, E., An interpolation theorem for denumerably long sentences. Fundamenta Mathematicae LVII, (1965) pp. 253–272.Google Scholar
  21. [21]
    Meyer, A.R. and Grief, I., Can Partial Correctness Assertions Specify Programming Language Semantics? In Weihrauch (ed.) Theoretical Comp Sc. 4th GI Conference. Lecture Notes in Comp. Sc. 67, Springer Verlag, Berlin (1979) pp. 25–26.Google Scholar
  22. [22]
    Meyer, A.R. and Halpern, J.Y. Axiomatic Definitions of Programming Languages: A Theoretical Assessment. In Proceedings of the 7th Annual Symposium on the Principles of Programming Languages. pp. 203–212, January 1980.Google Scholar
  23. [23]
    Moldestad, J., Stoltenberg-Hansen, V. and Tucker, J.V., Finite Algorithmic Procedures and Computation Theories. To appear in Mathematica Scandanavia.Google Scholar
  24. [24]
    Parikh, R., The Completeness of Propositional Dynamic Logic. In Winkowski (ed.) Proc. of MFCS '78. Lecture Notes in Comp. Sc. 64, Springer Verlag, Berlin 1978, pp. 403–415.Google Scholar
  25. [25]
    Rasiowa, H., Algorithmic Logic. ICSPAS Report 281, Warsaw 1977.Google Scholar
  26. [26]
    Rasiowa, H., θ+-valued Algorithmic Logic As a Tool To Investigate Procedures. In Blikle (ed.) Proc. of MFCS '74 Lecture Notes in Comp. Sc. 28, Springer Verlag, Berlin 1974, pp. 423–450.Google Scholar
  27. [27]
    Rasiowa, H., Logic of Complex Algorithms. In Budach (ed.) Fundamentals of Comp. Th. Akademie Verlag, Berlin 1979. pp. 371–380.Google Scholar
  28. [28]
    Rogers, H., Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York 1967.Google Scholar
  29. [29]
    Salwicki, A., On Algorithmic Theory of Stacks. In Winkowski (ed.) Proc. of MFCS '78. Lecture Notes in Comp. Sc. 64. Springer Verlag, Berlin 1978.Google Scholar
  30. [30]
    Shepherdson, J.C., Computation Over Abstract Structures: Serial and Parallel Procedures and Friedman's Effective Definitional Schemes. In Shepherdson and Rose (eds.) Logic Colloquium '73. North-Holland, Amsterdam 1973, pp. 445–513.Google Scholar
  31. [31]
    Tiuryn, J., Algebraic Aspects of Logic Based on Term Algebra of r.e. trees. Warsaw University Report 1978.Google Scholar
  32. [32]
    Tiuryn, J., Completeness Theorem for Logic of Effective Definitions. To appear in Proc. Coll. Logic in Programming, Salgotarjan 1978, North-Holland Publishing Co.Google Scholar
  33. [33]
    Tiuryn, J., Logic of Effective Definitions. R.W.T.H.-Aachen Report 55, 1979. To appear in Fundamenta Informaticae.Google Scholar
  34. [34]
    Urzyczyn, P., On Algorithmically Trivial Structures. Warsaw University Report 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • J. Tiuryn
    • 1
    • 2
  1. 1.Institute of MathematicsWarsaw UniversityWarsawPoland
  2. 2.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridge

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