Difference between revisions of "Implicative normal form"
From Encyclopedia of Mathematics
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A [[Propositional form|propositional form]] of the type | A [[Propositional form|propositional form]] of the type | ||
| − | + | $$C_1\supset(C_2\supset\dotsb(C_n\supset\bot)\cdots),$$ | |
| − | where all the | + | where all the $C_i$, $i=1,\dotsc,n$, have the form |
| − | + | $$C_{i1}\supset(C_{i2}\supset\dotsb(C_{im_i}\supset\bot)\cdots).$$ | |
| − | Here, each | + | Here, each $C_{ij}$ ($i=1,\dotsc,m$; $j=1,\dotsc,m_i$) 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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> A. Church, "Introduction to mathematical logic" , '''1''' , Princeton Univ. Press (1956)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A. Church, "Introduction to mathematical logic" , '''1''' , Princeton Univ. Press (1956)</TD></TR></table> | ||
Latest revision as of 13:03, 14 February 2020
A propositional form of the type
$$C_1\supset(C_2\supset\dotsb(C_n\supset\bot)\cdots),$$
where all the $C_i$, $i=1,\dotsc,n$, have the form
$$C_{i1}\supset(C_{i2}\supset\dotsb(C_{im_i}\supset\bot)\cdots).$$
Here, each $C_{ij}$ ($i=1,\dotsc,m$; $j=1,\dotsc,m_i$) 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
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