Sentence Tableau...

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Reply Sun 28 Jun, 2009 01:47 pm
Hello folks, have I constructed this sentence tableau correctly. I am presenting the arguments as

P
[P therefore Q]
R
[ [Q^R] therefore S]
Therefore S

1. P
2. [P therefore Q]
3. R
4. [ [Q^R] therefore S]
5. Therefore S

P (line 1)
|
R (line 3)
|
S (line 5)
___|____
| |
-P Q (line 2)
___ __|___
| | (line 4)
-Q S
-R
____

---------- Post added at 02:48 PM ---------- Previous post was at 02:47 PM ----------

Ew. It's all skewed. My formatting is messed up.
 
Horace phil
 
Reply Tue 30 Jun, 2009 05:15 pm
@Horace phil,
Come on people, I am mostly wondering how [ [Q^R] therefore S] would break down...
 
Zetetic11235
 
Reply Tue 30 Jun, 2009 06:54 pm
@Horace phil,
Here is what I have gathered


Facts: P = True , P->Q = True, R= True, Q^R -> S =True

So taking P and P -> Q, we derive Q by Modus Ponens
Then We take R and Q and get Q^R by conjunction
Then we take Q^R and Q^R -> S to get S by Modus Ponens.

Is this what you are presenting? This is correct if it is.
 
Horace phil
 
Reply Tue 30 Jun, 2009 09:04 pm
@Zetetic11235,
Thank you. I am more looking for how it would look on a sentence tableau
 
goapy
 
Reply Tue 30 Jun, 2009 10:48 pm
@Horace phil,
It would help if you could mention what text you're using (I've asked you this a few times, but you haven't responded).

Generally, a sentence tableau is just the same as a truth tree - although a few texts treat sentence tableau much more modestly than a full-blown truth tree proof system. In any case, the notation for truth trees often varies from text to text. So, knowing the precise system would be useful in order to construct a tableau (i.e. tree) for your problem.

However, here is a truth tree. It may have a different format than what you're using. The lines aren't numbered below the argument. Note that when checking for validity using a truth tree, the negation of the conclusion is used in the tree. Also, you have "therefore" on line 2 and on line 4, but I'm instead assuming that you mean "if/then".

http://i44.tinypic.com/35btjdi.jpg
 
Horace phil
 
Reply Wed 1 Jul, 2009 10:30 am
@goapy,
why the -S in line 5?
 
goapy
 
Reply Wed 1 Jul, 2009 11:49 am
@Horace phil,
Horace;74015 wrote:
why the -S in line 5?


Did you read my post? Particularly this part:

Note that when checking for validity using a truth tree, the negation of the conclusion is used in the tree.

A truth tree is used to check for validity by conducting an exhaustive search for counterexamples. If none are found, the argument is valid.

So, the opposite truth value of the conclusion is used, in order to check if there are any instances where the premises are true and the conclusion false.

None were found here, so the original argument is valid.
 
 

 
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