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.
This work was supported in part by The National Science Foundation, Grant Nos. MCS 7719754 and MCS 8010707, and by a grant to the M.I.T. Laboratory for Computer Science by the IBM Corporation.
Preview
Unable to display preview. Download preview PDF.
References
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.
Bell, J. and Machover, M., A Course in Mathematical Logic. North-Holland Publ. Co., Amsterdam 1977.
Bergstra, J. and Meyer, J. J. C. On the Quantifier Free Fragment of Logic of Effective Definitions. Leiden University Report (80–4), 1980.
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.
Bergstra, J., and Tiuryn, J., Algorithmic Degrees of Algebraic Structures. Leiden University Report (79–6), 1979.
Bergstra, J., Tiuryn, J., and Tucker, J.V., Correctness Theories and Program Equivalence. Mathematisch Centrum Report (IW 119/79). Amsterdam 1979.
Chang, C.C. and Keisler, H.J., Model Theory. North-Holland Publ. Co., Amsterdam 1973.
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.
Constable, R.L. and Gries, D., On Classes of Program Schemata. SIAM Journal on Computing 1 (1972) pp. 66–118.
Engeler, E., Algorithmic Logic. In de Bakker (ed.) Mathematical Centre Tracts (63) Amsterdam 1975, pp. 57–85.
Engeler, E., Generalized Galois Theory and its Application to Complexity. Berichte des Instituts für Informatik (24) ETH Zurich (1978).
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.
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.
Greibach, S.A., Theory of Program Structures: Schemes, Semantics, Verification. Lecture Notes in Comp. Sc. 36, Springer Verlag, Berlin 1975.
Harel, D., First-order Dynamic Logic. Lecture Notes in Comp. Sc. 68, Springer Verlag, Berlin 1979.
Keisler, H.J., Model Theory for Infinitary Logic. North-Holland Publ. Co., Amsterdam 1972.
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.
Kfoury, D.J., Translatability of schemes over restricted interpretations. Journal of Comp. and Syst. Sc. 8 (1974) pp. 387–408.
Kreczmar, A. Programmability in Fields. Fundamenta Informaticae I, 2. (1977) pp. 195–230.
Lopez-Escobar, E., An interpolation theorem for denumerably long sentences. Fundamenta Mathematicae LVII, (1965) pp. 253–272.
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.
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.
Moldestad, J., Stoltenberg-Hansen, V. and Tucker, J.V., Finite Algorithmic Procedures and Computation Theories. To appear in Mathematica Scandanavia.
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.
Rasiowa, H., Algorithmic Logic. ICSPAS Report 281, Warsaw 1977.
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.
Rasiowa, H., Logic of Complex Algorithms. In Budach (ed.) Fundamentals of Comp. Th. Akademie Verlag, Berlin 1979. pp. 371–380.
Rogers, H., Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York 1967.
Salwicki, A., On Algorithmic Theory of Stacks. In Winkowski (ed.) Proc. of MFCS '78. Lecture Notes in Comp. Sc. 64. Springer Verlag, Berlin 1978.
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.
Tiuryn, J., Algebraic Aspects of Logic Based on Term Algebra of r.e. trees. Warsaw University Report 1978.
Tiuryn, J., Completeness Theorem for Logic of Effective Definitions. To appear in Proc. Coll. Logic in Programming, Salgotarjan 1978, North-Holland Publishing Co.
Tiuryn, J., Logic of Effective Definitions. R.W.T.H.-Aachen Report 55, 1979. To appear in Fundamenta Informaticae.
Urzyczyn, P., On Algorithmically Trivial Structures. Warsaw University Report 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tiuryn, J. (1981). A survey of the logic of effective definitions. In: Engeler, E. (eds) Logic of Programs. Logic of Programs 1979. Lecture Notes in Computer Science, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11160-3_7
Download citation
DOI: https://doi.org/10.1007/3-540-11160-3_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11160-3
Online ISBN: 978-3-540-38631-5
eBook Packages: Springer Book Archive