Re: Maximal/ly

"David C. Ullrich" wrote:

On Thu, 23 Mar 2006 18:02:27 GMT, Frederick Williams
<Frederick.Williams1@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

A set, S, of propositional formulae is said to be "maximal consistent"
(or just "maximal") if S is consistent and, for each propositional
formula phi, either phi in S or not-phi in S. But in Goldblatt [1] I
came across "maximally consistent". Wondering if I has misremembered
the jargon I rummaged around and found "maximal" in another Goldblatt
[2] and in Lemmon [3].

I wouldn't mind if somebody told me which is correct. I wouldn't mind
even more if they justified their answer.

I don't think it's going to matter to anyone which term you
use, but it seems clear to me that "maximal consistent" is
correct.

We're talking about a maximal element of the class of
consistent sets. So that would be a

maximal [consistent set]

or in English, "maximal consistent set".
Here "consistent set" is modified by "maximal".

Yes, that's what I thought.

On the other hand, in the spelling "maximally consistent set"
the word "maximally" appears to be modifying "consistent".
So a "maximally consistent set" would be a set S such
that the _consistency_ of S was some "maximal" sort of
consistency. But there's no such thing

Ditto.

Thanks.
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