Poretsky's law of forms
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Short description: Theorem in Boolean algebra
In Boolean algebra, Poretsky's law of forms shows that the single Boolean equation [math]\displaystyle{ f(X)=0 }[/math] is equivalent to [math]\displaystyle{ g(X)=h(X) }[/math] if and only if [math]\displaystyle{ g=f\oplus h }[/math], where [math]\displaystyle{ \oplus }[/math] represents exclusive or.
The law of forms was discovered by Platon Poretsky.
See also
- Archie Blake (mathematician)
- Blake–Poretsky law
References
- "O sposobach reschenija lopgischeskich rawenstw i ob obrathom spocobe matematischeskoi logiki" (in ru). Collected Reports of Meetings of Physical and Mathematical Sciences Section of Naturalists' Society of Kazan University (2). 1884. (NB. This publication is also referred to as "On methods of solution of logical equalities and on inverse method of mathematical logic".)
- "Chapter 3: The Blake Canonical Form". Boolean Reasoning - The Logic of Boolean Equations (reissue of 2nd ed.). Mineola, New York: Dover Publications, Inc.. 2012. p. 100. ISBN 978-0-486-42785-0. https://books.google.com/books?id=QPzCAgAAQBAJ&q=%22Poretsky%27s+law+of+forms%22. [1]
- The Algebra Of Logic. 1914. p. 53, section 0.43.
- A Survey of Symbolic Logic. 1918. p. 145, section 7.15.
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