Definition talk:Tableau Confutation

The only cited source for this explicitly specifies:
 * By a confutation of a hypothesis set $\mathbf H$ in propositional logic we mean a finite propositional tableau $\mathbf T$ with root $\mathbf H$ such that every branch of $\mathbf T$ is contradictory.

Thus I believe we need to revert to that definition here, rather than specify it as an "also defined as". The finite nature of the confutation should, I believe, be the primary definition until such time as evidence can be provided to back up the contention that the confutation need not be finite.

The reason I worry is because I am minded of the Lewis Carroll sketch "What the tortoise said to Achilles" which sent him down an infinite regress chasing a never-ending ladder of modus ponendo ponens. I'm worried that if it is not necessary for a tableau to be finite, then it may be possible to construct such a logical argument and thus invalidate an otherwise valid argument.

If my suggestion is held to, then I believe we may need to revisit quite a lot of the proofs (in particular restoring Finished Tableau has Finished Branch or is Confutation).

Please note that I will not be able to resolve any questions in full detail until March, as I am about to fly out again for 2 months, and I will not be taking my Keisler and Robbin with me. --prime mover (talk) 07:29, 5 January 2014 (UTC)


 * The preprint version of KR does not specify a confutation needs to be finite. Tableau Confutation implies Unsatisfiable does not restrict to the finite case, so no hypothesis set that is satisfiable could ever have a confutation -- the infinitude does not matter here.


 * Through careful analysis of the arguments presented on PW (effectively mirroring the published KR) and the preprint KR I have access to, I have determined that:


 * Infinite confutations are not necessary (i.e. any hypothesis set with an infinite confutation also has a finite one), and therefore equivalent to the published KR version.


 * It is in this light that I decided to set up this page as it is -- it enriches our capability to construct confutations, without compromising the conclusions we may draw from obtaining one. &mdash; Lord_Farin (talk) 12:34, 5 January 2014 (UTC)


 * The relevant result has been proved and linked. I consider the discussion closed now. &mdash; Lord_Farin (talk) 16:54, 4 October 2017 (EDT)


 * I'll defer to you -- I'm not planning on revisiting mathematical logic for a while. --prime mover (talk) 18:32, 4 October 2017 (EDT)