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Implicative normal form

From Encyclopedia of Mathematics
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A propositional form of the type

where all the C_i, i=1,\ldots,n, have the form

C_{i1}\supset(C_{i2}\supset\ldots(C_{im_i}\supset\bot)\ldots).

Here, each C_{ij} (i=1,\ldots,m; j=1,\ldots,m_i) is either a variable or the negation of a variable, and \bot is the logical symbol denoting falsehood. For each propositional formula A one can construct an implicative normal form B classically equivalent to it and containing the same variables as A. Such a B is called an implicative normal form of A.

References

[1] A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956)
How to Cite This Entry:
Implicative normal form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Implicative_normal_form&oldid=15924
This article was adapted from an original article by S.K. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article