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Programs and logics

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Abstract

We use the algebraic theory of programs as in Blikle [2], Mazurkiewicz [5] in order to show that the difference between programs with and without recursion is of the same kind as that between cut free Gentzen type formalizations of predicate and prepositional logics.

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References

  1. J. W. de Bakker, Recursive procedures, Mathematical Center Tracts 24, Math. Centrum, Amsterdam 1971.

    Google Scholar 

  2. A. Blikle, An analysis of programs by algebraic means, Banach Center Publications, Vol. 2, Warszawa 1977, pp. 167–213.

    Google Scholar 

  3. G. Gentzen, Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, Vol. 39 (1934–35).

  4. Z. Manna and A. Purcell, Axiomatic approach to total correctness of programs, Memo AIM-210, Stanford Artificial Intelligence Laboratory (1973).

  5. A. Mazurkiewicz, Proving algorithms by tail functions, Information and Control 18 (1971), pp. 220–226.

    Google Scholar 

  6. G. Mirkowska, Algorithmic logic with nondeterministic programs, Fundamenta Informaticae 111.1. (1980), pp. 45–64.

    Google Scholar 

  7. H. Rasiowa, ω+-valued algorithmic logic as a tool to investigate procedures, Proc. MECS '74, Lecture Notes in Computer Science 28, Springer (1974).

  8. H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, PWN Warszawa 1963, 3rd ed. (1970).

    Google Scholar 

  9. G. Rousseau, Sequents in many-valued logic, Fundamenta Mathematicae (1967).

  10. A. Salwicki, Formalized algorithmic languages, Bulletin de l'Académie Polonaise des Sciences 18 (1970), pp. 227–232.

    Google Scholar 

  11. D. Scott, The lattice of flow diagrams, IFIP WG 2.2 Bulletin no 5, (1970).

  12. A. Wasilewska, A formalization of the modal propositional S4 calculus, Studia Logica XXXVII (1971), pp. 133–149.

    Google Scholar 

  13. A. Wasilewska, A sequence formalization for SCI, Studia Logica XXXV, 3 (1976), pp. 214–217.

    Google Scholar 

  14. A. Wasilewska, On the Gentzen type formalization, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik Bd. 25.s (1980), pp. 439–444.

    Google Scholar 

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Wasilewska, A. Programs and logics. Stud Logica 44, 125–137 (1985). https://doi.org/10.1007/BF00379762

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  • DOI: https://doi.org/10.1007/BF00379762

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