Talk:Resolution (logic)

message: I believe Resolution inference should in fact be merged into the current page, carrying over the references from there as additional references.  — Preceding unsigned comment added by Vkuncak (talk • contribs) 13:13, 23 June 2021 (UTC)
thread_title:  Merger proposal 

message: On 22 September 2005, [Paolo Liberatore] edited this page deleting a sentence at the beginning of the article. That sentence claimed that automated theorem proving is a branch of AI.  In the literature I have read, for example "Artificial Intelligence, a Modern Approach" (probably the most complete book about GOFAI), automated theorem proving is considered a subject of GOFAI. I agree with that and thus I think it should be included in the article changing "branch" for "subject", because there are other disciplines dealing with automated theorem proving.
[Ivan F. Villanueva B.]
: I don't mind either way. Maybe AI should be mentioned in automated theorem proving instead? If you have a strong opinion, be bold. BTW, I don't think the term GOFAI should be overused - it's a nice gag, but it should be enough to have a small paragraph linked from the main AI page. --Stephan Schulz 09:50, 23 September 2005 (UTC)
replies: text: Well, I have a strong opinion:  The GOFAI link was distracting and self-indulgent, and the gag isn't actually particularly funny.  Very bad style.  Taking Stephan at his word, I deleted it. Jorend 13:03, 31 March 2006 (UTC)
thread_title:  GOFAI 

message: I just started a computability section but I'm unsure of the facts -- my best try is there but tagged with question marks, could someone more expert than me check this and correct them please?
:Sorry, I've deleted your section again. Computability is a property of the problem, not of the method used. Resolution can be used to implement a complete refutation procedure for first-order clause sets, and a complete decision procedure for finite propositional logic clause sets. But you need extra conditions (fairness) and operations. --Stephan Schulz 13:01, 1 December 2006 (UTC)
thread_title:  Computability 

message: What are complementary literals? They seem to be a literal and its negation. If someone knows that this is correct, could you just parenthetically say that in the article? It's unnecessarily opaque right now. —The preceding unsigned comment was added by SpaceMoose (talk • contribs) 03:48, 3 March 2007 (UTC)
replies: text: I've tried, is it clearer now? The problem ist that one really needs to assume knowledge about clauses, literals, and atoms  to write a decent description of resolution.--Stephan Schulz 10:16, 3 March 2007 (UTC)
thread_title:  Quick question 

message: Does resolution actually have to be done on a disjunction of literals? What if a clause has conjunctions? Fresheneesz (talk) 07:50, 18 November 2007 (UTC)
replies: text: Resolution many other methods and systems require a normal form, here it is a "Conjunctive Normal Form" (CNF) and this is sufficient because every first order logic formula can be translated into a semantically equivalent formula in CNF. With my understanding (and the wiki page) the term "clause" refers only to a _disjunction_ or literals, thus by definition, a clause cannot have a conjunction. What you probably mean is that you have a general formula with a mixture of conjunctions and disjunctions and would like to apply this method. What you would do is you would convert your formula into CNF. This results in n clauses where you can perform pairwise resolution. See Conjunctive_normal_form#Conversion_into_CNF Methossant (talk) 22:35, 22 February 2009 (UTC)
thread_title:  Literals 

message: The presented rule of resolution is the binary resolution. It is incomplete : the set of clauses, a+b, a+-b, -a+b, -a+-b is inconsistent (+ is the disjunction, - is the negation) but with this single rule, you obtain only resolvant of length 2.
In order to have a complete system, you need 
either to add the factoring rule, from A+p+B+p+C (where p is a literal) deduce A+B+C
either to define a more complex resolution rule, combining binary resolution and factorization
either (following the Robinson founder of the resolution system) considering that a clause is a set of literals
Liviusbarbatus (talk) 14:12, 30 January 2008 (UTC)
thread_title:  Incomplete rule 

message: The article says if the empty clause can be derived, "the initial conjecture follows from the axioms". Are these axioms the knowledge base mentioned earlier (+ axioms of boolean algebra)?
84.238.30.199 (talk) 16:27, 12 October 2008 (UTC)
thread_title:  Axioms / knowledge base 

message: In the first paragraphs there seems to be a contradiction between the following two sentences. I suggest to rephrase the first one s.t. it does not say "all literals that have complements". PeterSchueller (talk) 08:15, 10 July 2009 (UTC)
thread_title:  Contradiction 

message: Isn't it confusing to assert that resolution is due to John Alan Robinson in 1965, in the first paragraph, and that it's used in DP-algorithm which publication date is more 1960 or 1962 for its revised version, at the end of the "Resolution in propositional logic" section ? It may be just that Davis and Putnam didn't call it that way, or that Robinson extended the idea, or that I'm just confused. The dates are from the bibliography from the resolution and the dpll articles.
131.254.10.81 (talk) 15:50, 27 July 2009 (UTC)
replies: text: I agree, and tried to rephrase the lead accordingly. Explanation of the role of MGU and Lifting Lemma in the article (maybe with an example contrasting DPLL and Robinson) still remains to be done. - Jochen Burghardt (talk) 23:48, 29 May 2014 (UTC)
thread_title:  Confusing date 

message: As this is my first participation on Wikipedia, I apologize if I am going against custom in one way or the other. In section "Resolution in propositional logic" the following is claimed
:"When the two clauses contain more than one pair of complementary literals, the resolution rule can be applied (independently) for each such pair; however, the result is always a tautology."
I cannot see how the last claim about always arriving at a tautology should be true. There are two cases, both of which are not going to be trivially true
# We arrive at a non-empty clause. It is satisfiable, since it can be made true by setting any of the literals to be true. On the other hand, since it is non-empty and there are no complements, then the entire clause can evaluate to false by setting all literals to false.
# We arrive at the empty clause, which is trivially false.
I assume, that there is some detail I've missed. Maybe it has to do with the goal of the resolution technique, described later in the article? Could this be elaborated?
--Soelvsten (talk) 07:25, 5 October 2020 (UTC)
replies: text: \frac{
\lnot d \lor a_1 \lor a_2 \lor \cdots \lor c ,
\quad d \lor b_1 \lor b_2 \lor \cdots \lor \neg c}
{\lnot d \lor a_1 \lor a_2 \lor \cdots \lor d \lor b_1 \lor b_2 \lor \cdots}
That is, the resolvent on the first pair (c , \lnot c), containing the disjunction on the second pair (\lnot d , d), is satistifed by every assignment of truth values, hence a tautology. I guess most theorem provers would simplify it to \text{true}, and then discard it. Resolving the clauses on \lnot d , d will obtain a similar result. - Jochen Burghardt (talk) 11:59, 5 October 2020 (UTC)
thread_title:  Exhaustively applying resolution rule leading to a tautology