Algorithmic Logic

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Algorithmic logic is a calculus in which one can express the semantical properties of programs and it allows to construct proofs of the formulas. In this way one can prove property like correctness by proving the corresponding formula that express the property.

Structure of AL

An algorithmic logic is a pair [math]\mathcal{AL} = \langle \mathcal{L}, \mathcal{C} \rangle [/math], where [math]\mathcal{L} [/math] is a formalized language of algorithmic logic and [math]\mathcal{C} [/math] is i a logical consequence operation defined by the notions of logical axioms, inference rules and the notion of (formal) proof. An algorithmic language [math]\mathcal{L} [/math] is a pair consisting of the alphabet of [math]\mathcal{L} [/math] and the set of weel-formed expressions, [math]\mathcal{L} = \langle A, WFF \rangle [/math], where [math] A [/math] is the alphabet, i.e. the set of admissible symbols and [math] WFF [/math] is the set of well formed expressions of the language.

History

The origins of algorithmic logic go to papers of Yanov, H. Thiele, Erwin Engeler. In 1969 the program of research was formulated in the Ph.D. thesis of A. Salwicki.

Bibliography

  1. [Mirkowska, Salwicki 1987] Szablon:Cytuj kiążkę
  2. [Kreczmar 1977a] Antoni Kreczmar. Effectivity problems of Algorithmic Logic. „Fundamenta Informaticae”, 1977. 
  3. [Kreczmar 1977b] Antoni Kreczmar. Programmability in Fields. „Fundamenta Informaticae”, s. 195-230, 1977. 
  4. [Kreczmar, Cioni 1984] Antoni Kreczmar, Gianna Cioni. Programmed deallocation without dangling reference. „Information Processing Letters”, s. 179-187, 1984. 
  5. [Banachowski, Kreczmar 1989] Lech Banachowski, Antoni Kreczmar: Elementy Analizy Algorytmów. Warszawa: WNT, 1989, s. 197. ISBN 8320411475.
  6. [Banachowski, Kreczmar, Rytter 1987] Lech Banachowski, Antoni Kreczmar, Wojciech Rytter: Analiza Algorytmów i Struktur Danych. Warszawa: WNT, 1987, s. 217. ISBN 8320407176.
  7. [Banachowski, Kreczmar, Rytter 1991] Lech Banachowski, Antoni Kreczmar, Wojciech Rytter: Analysis of Algorithms and Data Structures. New York: Addison-Wesley, 1991, s. 300. ISBN 020141693X.
  8. [Loglan 82] W.M. Bartol i in.: Report on the Loglan'82 programming language. Warszawa-Łódź: PWN, 1984, s. 165.
  9. [Kreczmar 1976] Antoni Kreczmar: On Memory Requirements of Strassen’s Algorithm. T. Proc. MFCS'76. Berlin: Springer, 1976, s. 404-407, seria: LNCS. ISBN 3540078541.
  10. [Grabowski, Kreczmar 1978] Michał Grabowski, Antoni Kreczmar: Dynamic theories of real and complex numbers. T. Proc. MFCS'78. Berlin: Springer Vlg, 1978, s. 239-249, seria: LNCS 64. ISBN 0387089217.
  11. [Kreczmar, Oktaba, Ratajczak, Litwiniuk 1983] Antoni Kreczmar, W.M. Bartol, H. Oktaba, A.I. Litwiniuk: Semantics and Implementation of Prefixing at Many Levels. T. proc. Logics of Programs and their Applications. Berlin: Springer Vlg, 1983, s. 45-80, seria: LNCS 148. ISBN 0387119817.
  12. [Kreczmar i in 1984] Antoni Kreczmar, Manfred Krause, Hans Langmaack, Andrzej Salwicki: Specification and Implementation Problems of Programming Languages Proper for Hierarchical Data Types. T. Rep. 8410. Kiel: Institut fuer Informatik, University of Kiel, 1984.
  13. [Kreczmar 1982] Antoni Kreczmar: The programming language Loglan'82 Basic constructs and facilities. Warszawa: Uniwersytet Warszawski, 1982, s. 66.
  14. [Kreczmar i in. 1986] Antoni Kreczmar, Manfred Krause, Hans Langmaack, Marek Warpechowski: Concatenation of program modules an algebraic approach to the semantics and implementation problems. Berlin: Springer, 1986, s. 134-156, seria: LNCS 208.
  15. [Kreczmar, Salwicki, Warpechowski 1990] Antoni Kreczmar, Andrzej Salwicki, Marek Warpechowski: Loglan'88 - Report on the Programming Language. Berlin: Springer Vlg, 1990, s. 133, seria: LNCS 414. ISBN 0387523251.
  16. [Cioni,Kreczmar 1989] Gianna Cioni, Antoni Kreczmar: Modules in High Level Programming Languages. T. Advanced Programming Methodologies. London: Academic Press, 1989, s. 247-340. ISBN 0121746909.
  17. [Cioni,Kreczmar, Vitale 1989] Gianna Cioni, Antoni Kreczmar, Ricardo Vitale: Storage Management. T. Advanced Programming Methodologies. London: Academic Press, 1989, s. 341-366. ISBN 0121746909.
  18. [Kreczmar, Mirkowska 1989] Antoni Kreczmar, Grażyna Mirkowska: Mathematical Foundations of Computer Science. Berlin: Springer Vlg, 1989, s. 620, seria: LNCS. ISBN 9783540514862.
  19. [Kreczmar 1977] Antoni Kreczmar: On finite and infinite computations. T. Proc. FCT'77. Bonn: Springer Vlg, 1977, s. 441-446, seria: LNCS 56. ISBN 0387084428.
  20. [Kreczmar 1977] Antoni Kreczmar. On infinite sets of polynomial relations. „Bull.Acad.Pol.Sci.Ser.Astr.Math.Phys.”. 25, 1977. PWN. 
  21. [Kreczmar 1979] Antoni Kreczmar: Some historical remarks on algorithmic logic. T. Algorithms in Modern Mathematics and Computer Science. Berlin: Springer Vlg, 1979, s. 999-1000, seria: LNCS. ISBN 0123456789.
  22. [Banachowski i in.] Lech Banachowski, Antoni Kreczmar, Grażyna Mirkowska, Helena Rasiowa, Andrzej Salwicki: An introduction to Algorithmic Logic - Metamathematical Investigations of Theory of Programs. T. 2: Banach Center Publications. Warszawa: PWN, 1977, s. 7-99, seria: Banach Center Publications. ISBN 123.
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