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From: PiperAlpha167 on 24 Feb 2010 03:45
It might be worth noticing that the formula in 2) is the (unique) perfect disjunctive normal form for 1).
That makes them truth-functionally equivalent.
From: mrsenim on 24 Feb 2010 04:04
> It might be worth noticing that the formula in 2) is
> the (unique) perfect disjunctive normal form for 1).
> That makes them truth-functionally equivalent.

Will you please write some words about the detail of "(unique) perfect disjunctive normal form" ? How can we write it for a given formula?

Thanks!
From: PiperAlpha167 on 24 Feb 2010 16:58
> > It might be worth noticing that the formula in 2)
> is
> > the (unique) perfect disjunctive normal form for
> 1).
> > That makes them truth-functionally equivalent.
>
> Will you please write some words about the detail of
> "(unique) perfect disjunctive normal form" ? How can
> we write it for a given formula?
>
> Thanks!

Here's a bit more detail.

The 'perfect' qualifier on DNF is from Stolyar.
Note that the formula in 1) has exactly three valuations that make it true.
Write out the characteristic sentence (from Bergmann) associated with each of these valuations.
Each one will be an iterated conjunction.
Form an iterated disjunction of these sentences.
The result will be the aforementioned disjunctive form for 1), and it'll be the formula in 2).

Disregarding the order of the conjuncts and disjuncts, the result is unique.
What makes it unique is that every atom in the formula of 1) has a literal represention in each of the disjuncts, with the understanding
that 'literal' here means either the atom or else its negation.

That's all I have time for. Good luck.
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