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I'm reading about negative normal forms. My text talks about transforming H¬x to 'negative normal form' so it reads ¬Hx.

If the two sentences are interchangeable, then they mean the same thing. So, suppose that H stands for reads a lot, and that x refers to someone named John. Could one think of ¬Hx translating in to it is not the case that John reads a lot, and of H¬x translating in to it is the case that John does not read a lot. (Although, I suppose they could both translate into any one English sentence that expresses their shared meaning.)

More importantly, why would anyone bother writing H¬x?

Hal
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  • I've actually never seen the notation of negating a variable before. It violates the syntactic rules of most treatments of first order logic. – Malice Vidrine Mar 22 '14 at 21:18
  • You can read about it here. http://en.wikipedia.org/wiki/Negation_normal_form – Hal Mar 22 '14 at 21:45
  • @malice Of course you have seen the negation of a variable before. Consider the law of the excluded middle: $ p \lor\lnot p $. OP is just confused about the interpretation of $x$ here. – MJD Mar 22 '14 at 21:54
  • @MJD: In first order logic I wouldn't typically consider propositional symbols "variables" on account of them not being something you can bind with quantifiers. But I side with Quine on this issue. – Malice Vidrine Mar 22 '14 at 22:01
  • Well, it's not at all clear that H here is a quantifier. In fact I'd guess it is more likely than not that it Isn't one and OP is confused about that too. – MJD Mar 22 '14 at 22:06

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The negation of $x$ in that expression is formally wrong - and in formal logic everything is super technical and formal.

"Negative normal form" refers to when the not operator is fully distributed. Consider $\neg (A\wedge B)$ vs $\neg A\vee \neg B$. See here for more details.

Stella Biderman
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