Re: completeness what is it exactly



Jan Burse wrote:
translogi schrieb:

In propositional logic you are onlu talking about formula's with
constants.
(truth and falsehood)

Most (or even all) axioms are not sentences in this view.

Yes, propositional logic consists only of closed
formulas. All formulas are closed in SAT.

Would someone please explain to me why propositional logic
does not have variables? Or does not have free variables?
Or whatever? I must have missed the memo.

Your propositional formulae at the bottom of this post
sure look to me like they contain free variables.

(Lets not consider QSAT, where one can quantify over
propositional variables, i.e. exists p.p, and one
might have prepositional constants and variables.
Example for a constant being f (bottom, _|_))

But there are formuals and schemas, even for propositional
logic.

A formula (small cap):

p -> p

A schema (upper cap):

P -> P

Stands for the following formulas (small cap):

p -> p
q -> q
(p -> q) -> (p -> q)
etc..

--
hz
.

Relevant Pages

  • Re: The problem with counterfeit rooster sauce
    ... the batch/date criterion and the bottom emboss criterion. ... under my cap is *slightly* larger than the cap, ... just a slight wideness to the neck. ...
    (rec.food.cooking)
  • Re: Question about old 451
    ... bottom which prevents the mic from slipping into it, ... flange would sit between the cap and pre amp body. ... C'est suisse, et tres, tres precis." ...
    (rec.audio.pro)
  • Re: Is anyone out there doing Extended Maceration?
    ... mushes up the cap. ... of the fermentation bin and pumped from the ... bottom and sucked up the seeds and let the wine ...
    (rec.crafts.winemaking)
  • Re: Question about old 451
    ... bottom which prevents the mic from slipping into it, ... flange would sit between the cap and pre amp body. ... cap down then the top of the ball could be screwed back on to complete ...
    (rec.audio.pro)
  • Re: FMA - 26
    ... snip out what you don't need. ... Fine, fine, so I snipped off the bottom and not the top. ... Sue me. ... Cap. ...
    (rec.arts.anime.misc)