Talk:Automated theorem proving

message: there's a large (and important) class of techniques and provers that are barely even mentioned in this article, namely inductive theorem provers.
i've searched, but cannot find an article on inductive theorem proving and the techniques in use in that field.
should this article be expanded beyond first order theorem proving and model checking? 137.195.27.231 16:01, 29 October 2007 (UTC)
thread_title: inductive theorem proving?

message: Should this article be merged with Computer-assisted proof?
S Sepp 14:33, 21 January 2006 (UTC)
thread_title: merge?

message: I don't know what the policy on spelling proper names is, but the theorem prover listed as "Vampire" is spelt "Vampyre" by the project itself (see http://www.cs.ucla.edu/~rupak/Vampyre/). Perhaps a spell-change is in order? —Preceding unsigned comment added by 74.130.8.62 (talk • contribs) 
:this seems to me to be a different theorem prover albeit with a similar name.
:there doesn't seem to be any doubt that the correct spelling is "vampire" if you do a google search on "vampire theorem prover manchester"
:81.77.83.84 19:18, 29 October 2007 (UTC)
replies: text: Yes, that's a different system. --Stephan Schulz 19:51, 29 October 2007 (UTC)
thread_title:  vampire / vampyre 

message: Hi,
I'm missing some seemingly relevant references to Schmidhuber's universal self-referential Gödel-machines. They are `machines' (not `incarnated' as in the Turing Machine) that can rewrite themselves based on expected progress of a proof. I'm not an expert of this research in particular, but I think it is certainly relevant and a candidate for inclusion on this page.
A pointer for Schmidhubers work can be found here: http://www.idsia.ch/~juergen/goedelmachine.html
Regards, Erik de Bruijn  —Preceding unsigned comment added by 85.147.200.8 (talk) 17:51, 28 October 2007 (UTC)
thread_title:  Schmidhuber missing 

message: Could someone that speaks Chinese possibly check the link to his home page to determine his institutional affiliation? (None is listed) Nahaj (talk) 14:50, 14 August 2008 (UTC)
thread_title:  Wen-Tsun Wu affiliation? 

message: In the section on "decidability" there is a reference to the "first-order theory of the natural numbers" used in Gödel's incompleteness theorem. I couldn't find a reference for this theory in itself. Is it just Peano arithmetic? If you know, please fix the link.  —Preceding unsigned comment added by Ezrakilty (talk • contribs) 13:36, 19 August 2008 (UTC)
thread_title:  Gödel's arithmetic system? 

message: The article should have a section on results from algebraic geometry on theorem proving, e.g. Characteristic set and Wu's method.  A good introductory reference is Cox, Little and O'Shea's Ideals, Varieties and Algorithms. Akriasas (talk) 12:32, 21 December 2008 (UTC)
thread_title:  algebraic methods? 

message: I fail to see why deontic theorem proving is given a special section.
Any modal logic "extends the first-order predicate calculus".
Other than to showcase this one specific author, what does this section add to the page?
(And if it is necessary, why wouldn't the same logic apply to any of categories of logics?)  —Preceding unsigned comment added by 155.101.224.65 (talk) 20:38, 20 May 2009 (UTC)
thread_title:  deontic theorem proving? 

message: I recently removed several interactive theorem provers (diff) from the list, but someone added them back. In my opinion, those don't belong there, because
*they are interactive, not completely automated, so they don't belong here.
*ITPs should listed in their own article.
If there are no objections within the next couple of days, I will re-remove them. – Adrian Willenbücher (talk) 05:26, 6 September 2010 (UTC)
thread_title:  Interactive theorem provers 

message: The section confuses decidability and complexity issues, and needs to be rewritten.
The following changes should be made:
The section needs to define properly "decidability" - that is, giving a true/false (yes/no) answer to any question, and related concept of "semi-decidability" - that true (viz. false) can be answered, but not necessarily that false (viz. true) can be answered in all cases.  Refer to Gödel incompleteness and the halting problem.
Note that the incompleteness theorem and halting problem show the non-existence of "universal" functions that can decide on all functions at all inputs. That does not imply the non-existence of functions which can decide about some functions and some inputs. In practice, one can decide many problems precisely by limiting the scope of functions or inputs.
Complexity classes are not related to decidability, so belong in a separate section. (Whether or not a problem is decidable is unrelated to how hard a problem is.) It's better to give a brief discussion about the difficulty (measured in time and space, i.e. memory usage) of solving problems and refer to a separate page about complexity classes.  —Preceding unsigned comment added by 94.173.19.247 (talk) 10:45, 14 February 2011 (UTC)
thread_title:  "Decidability of the problem" section is confused 

message: I think the authors of Jape are Bornat and Sufrin, not Neto. See the links.
Rmkeller (talk) 00:12, 28 February 2011 (UTC)
thread_title:  Wrong authors for Jape? 

message: G. Gonthier might be added to the notable people.  — Preceding unsigned comment added by 93.97.194.200 (talk) 15:19, 10 June 2011 (UTC)
replies: text: Benjamin Werner might also be added.  — Preceding unsigned comment added by 93.97.194.200 (talk) 15:21, 10 June 2011 (UTC)
thread_title:  Gonthier 

message: This article really needs a section on the history and development of the field. I came here looking for information on how it got started - and there's nothing on that. Noel (talk) 23:14, 1 September 2012 (UTC)
replies: text: Good point. I have some overview knowledge, but mostly only primary sources. However, I have a (unread so far) copy of ). I'll see if I can cobble something together. --Stephan Schulz (talk) 00:36, 2 September 2012 (UTC)

text: There also is . --Stephan Schulz (talk) 21:00, 2 September 2012 (UTC)

text: And another interesting source: . --Stephan Schulz (talk) 23:47, 26 September 2012 (UTC)

text: And another:  --Stephan Schulz (talk) 12:44, 4 May 2013 (UTC)
thread_title:  History of the field 

message: I've been working on various AI articles: inference engine, expert systems, etc. and needed to link to this page. BTW, this article is in great shape compared to what some of the AI articles were like. But I want to cast a strong vote to get rid of the "notable people" section. There is no such section on other articles that I've edited. We don't have a list of the notable inference engine or expert system people. If they are notable they are talked about and/or referenced in the article itself and if not then they aren't that notable. These lists are IMO just vanity or buddy lists where everyone adds themselves or their favorite researchers. Especially when they have lots of red links, I think the red links should just go immediately without further discussion but I'm not going to do it as I'm editing other articles now but just wanted to voice my opinion. RedDog (talk) 14:29, 6 December 2013 (UTC)
thread_title:  Vote We Should Remove Notable people section or put it off on a separate list page 

message: "DPLL" is only a special algorithms for the propositional satisfiability problem (SAT), and a more appropriate link, under "Popular techniques", should be to
https://en.wikipedia.org/wiki/Boolean_satisfiability_problem
Oliver Kullmann (talk) 17:11, 5 June 2016 (UTC)
thread_title:  Link to "DPLL" should be updated to link to "SAT" 

message: Under "See also" it seems sensible to add a link to
https://en.wikipedia.org/wiki/List_of_long_mathematical_proofs
since this contains proofs found by ATP (especially SAT solving).  — Preceding unsigned comment added by Oliver Kullmann (talk • contribs) 17:13, 5 June 2016 (UTC)
thread_title:  Add link to page with long proofs 

message: I noticed that someone has added yet another person to this section that I've never heard of. I've edited several pages like this (e.g., Expert system Artificial intelligence Knowledge-based system Knowledge-based software assistant and none of them have a section like this. If someone is truly notable their name will come up and can be linked to somewhere in the actual body of the article. Just having a laundry list like this seems to be of no value to me and seems like it's primarily about people adding their names or names of their friends or people they really like for some reason. I don't see any objective criteria used to determine who gets put in that section and who doesn't. E.g., someone like David Luckham is very well known but most of the other names are not. I think we should just get rid of this section all together or if not we should at least have some criteria so that people aren't just adding vanity references to little known researchers. --MadScientistX11 (talk) 17:03, 10 September 2019 (UTC)
replies: text: I agree. Would delete the section. And, if necessary, incorporate the works of the scientists. --ZaaraTE (talk) 17:20, 10 September 2019 (UTC)

text: I also agree. Saung Tadashi (talk) 21:17, 10 September 2019 (UTC)
thread_title:  Notable People Section: Do We Need it? 

message: Recently, OpenAI and Meta have created AI models that automatically write proofs, using the Lean proof assistant/language. I think this could at least be mentioned in Applications, after the sentence on automated theorem provers being integrated with proof assistants.
https://openai.com/research/formal-math
https://ai.meta.com/blog/ai-math-theorem-proving/ RedrickSchu (talk) 19:27, 14 March 2024 (UTC)
thread_title:  Do we need a section on AI-written proofs?