Re: question regrading tautology and valid formula

On Oct 28, 1:23 pm, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Sat, 27 Oct 2007 17:08:34 -0000, translogi



<wilem...@xxxxxxxxxxxxxx> wrote:
On Oct 27, 4:03 pm, Min JIANG <mail.minji...@xxxxxxxxx> wrote:
Hi, all,

I'm studying modal logic, but one problem puzzles me. Can someone help
me to understand the differentia between tautology and valid formula
in modal logic? or they are the same?

TIA

Which book are you studying?
(different authers have different opinions about what a tautology and
a valid formula is

some posibilities (going from broad to narrow)

(very broad)
A valid formula is a well formed formula. It is not just a line of
(modal) logical symbols

(a bit less broad)
A valid formula is a formula that is satisfiable ( It can be true but
does not have to be true in every situation)

Can you give a reference where either of those is the definition?

A valid formula is a formula that is (probably true) biut not proven /
provable to be so.

Huh? Can you give a reference where the definition of "valid formula"
has the property that a formula can fail to be valid one day but
become valid the next day?

Or is a valid formula a formula that is a theorem
.

I know at least one author (Smullyan, but i don't know if he wrote
about modal logic) who has the opinion that
a tautology must be a propositional statement.
p -> p is a tautology

(Ax) ( Fx -> Fx) is not a tautology (but it is a theorem)

In the last situation the main connective is (Ax) and that is not a
propositional connective so it is not a tautology.

That's close to the standard definition. A tautology in
first-order logic must be a _substitution instance_ of
a tautology in propositional logic. For example,
AxP(x) -> AxP(x) is a tautology, according to the
definition that I _bet_ is what Smullyan actually
gives, even though it's not a formula of propositional
logic.



Maybe the auther of your book has one of these ideas in mind.
(Or maybe other ideas there are more posibilities)
Like Humpty Dumpty (Trough the looking-glass, Lewis Carroll) says, It
means just what I choose it to mean -- neither more nor less.

Not all metalogical terms in logic are not as rigourous defined as
logic itself is.

Good luck hope this helps,
Otherwise please state to wich book you are refering or a quote or
so.
(if it is not a such widly known book)

Or ask your lecturer.
He will find it a smart question

It shows that you have thought about it.

************************

David C. Ullrich

Addition



A valid formula is a formula that is (probably true) biut not proven /
provable to be so.

Huh? Can you give a reference where the definition of "valid formula"
has the property that a formula can fail to be valid one day but
become valid the next day?
<<<
No no definition

I meant more like the famous Con (T) or so that is true (valid?)
But cannot be proven to be so.
(I find it famous not infamous)

But my first intension was to show a lot of possibilities so that he
could think about it.

And it is interesting to notice that Smullyan and Smith do disagree
about this...

.

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