Rough Sets pp 121-136 | Cite as

Logical Theory of Approximations

  • Lech Polkowski
Part of the Advances in Soft Computing book series (AINSC, volume 15)


It may seem surprising that the first formalized system aimed at capturing basic laws of thought and rules for reasoning had been conceived before the propositional calculus was recognized as a legitimate subject of independent study by the Stoic school. But such had been the case with the system of logic created by Aristotle of Stagira and known as The Syllogistic. One of reasons seems to be that propositional calculus was used by Aristotle intuitively, as a tool not in need of formalization, in his reasoning about syllogisms and the necessity for its more formal study had not been felt before the Stoic school undertook such a study.


Propositional Calculus Deductive System Logical Theory Minor Premise Sentential Calculus 
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Works quoted

  1. [Bocheński6l]
    I. M. Bocheński, A History of Formal Logic, Notre Dame Univ. Press, 1961.Google Scholar
  2. [Łukasiewicz63]
    Jan Łukasiewicz, Elements of Mathematical Logic,Oxford — Warsaw, 1963Google Scholar
  3. [Łukasiewicz57]
    Jan Łukasiewicz, Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic,2nd ed., Oxford, 1957.Google Scholar
  4. [Łukasiewicz39]
    Jan Łukasiewicz, On Aristotle’s Syllogistic, (in Polish), Compt. Rend. Acad. Polon. Lettr., Cracovie, 44 (1939).Google Scholar
  5. [Slupecki49]
    J. Slupecki, On Aristotle’s Syllogistic, Studia Philosophica (Poznan), 4(1949–50), pp. 275–300.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Lech Polkowski
    • 1
    • 2
  1. 1.Polish-Japanese Institute of Information TechnologyWarsawPoland
  2. 2.Department of Mathematics and Computer ScienceUniversity of Wormia and MazuryOlsztynPoland

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