What is wrong with this logic tree?

Question

I have found this in a university text book and have been told it has many erros. What is wrong here?

enter image description here

Which textbook? Which page? – Carl Mummert Nov 23 '15 at 20:00 — Carl Mummert, Nov 23 '15 at 20:00

Shaun · Accepted Answer · 2014-01-08T13:17:21.860

2

The $Pb$ and $Qb$ magically appear and $\forall x(Px\to Qx)$ is improperly instantiated. The $(\neg Qb\wedge\forall x(Px\to Qx))$ should be negated (as should $Px$) and it's treated like $\vee$ instead of $\wedge$.

Each path of a tableau kind of represents a different scenario, so that what happens in one path doesn't influence what happens in another beyond the point where they branch.

Here's what I get:

enter image description here .

edited Jan 08 '14 at 13:17

answered Jan 07 '14 at 20:39

Shaun

44,997

Does this answer your question, @Joseph? $\ddot\smile$ – Shaun Jan 08 '14 at 09:19
[The code for the diagram above is available on request, but it'll take a while.] – Shaun Jan 08 '14 at 11:12
1

Sure it does, great! I just could not believe when I was told its in a textbook as an example! The code would be great, but as I don't need it specifically, I wouldn't bother. – user574859 Jan 09 '14 at 23:54

score 0 · Answer 2 · edited Nov 23 '15 at 20:25

0

This tree is fine, but it's not a tableau, it's syntax tree. Whoever told you it's wrong is confusing tableaux (which represent ways a formula can be falsified) and syntax trees (which represent the syntactic structure of a formula, breaking it down in simpler sub-formula until you reach atomic formula).

edited Nov 23 '15 at 20:25

Harish Chandra Rajpoot

37,450

answered Nov 23 '15 at 19:55

G.T.

17

What is wrong with this logic tree?

2 Answers2