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Solution of Boolean equations

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Abstract

We reconstruct and refine the Boole-Jevons-Schroeder-Poretskii method of solving the inverse problems of logic, which through a misunderstanding is nowadays forgotten. We study characteristic examples of the application of the method with a suitable interpretation of the solutions that result. We give a brief presentation of the algebra of boolean expressions and the princples of its constructive implementation on a computer, making it possible in particular to automate the solution of systems of boolean equations.

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Literature Cited

  1. G. Boole,An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, London (1854).

  2. P. S. Poretskii,On Methods of Solving Logical Equalities and the Inverse Method of Mathematical Logic. An Essay in Construction of a Complete and Accessible Theory of Deduction on Qualitative Forms [in Russian], Kazan' (1884).

  3. N. I. Styazhkin,Formation of Mathematical Logic [in Russian], Nauka, Moscow (1967).

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  4. N. P. Brusentsov,Foundations of Information Theory [in Russian], New Millennium Foundation, Moscow (1994).

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  5. Yu. S. Vladimirova, “Constructive implementation of boolean algebra,” in:An Integrated System of Teaching, Program Construction, and Development of Didactic Materials [in Russian], VM&K, Moscow (1996), pp. 44–69.

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Authors
  1. N. P. Brusentsov
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  2. Yu. S. Vladimirova
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Additional information

Translated fromMetody Matematicheskogo Modelirovaniya, 1998, pp. 59–68.

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Brusentsov, N.P., Vladimirova, Y.S. Solution of Boolean equations. Comput Math Model 9, 287–295 (1998). https://doi.org/10.1007/BF02409862

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  • DOI: https://doi.org/10.1007/BF02409862

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