Talk:Logical consequence/Archive (Logical implication)

Material implication

What the hell is the difference between Logical implication and the Material conditional ????? I propose a merge. Fresheneesz 07:35, 11 October 2006 (UTC)

A logical implication is a valid material implication (or material conditional). These are two different but often confused notions. The pages should remain separate, but the page on logical implication needs to be updated so as to reflect this distinction. 128.112.210.248 22:29, 7 November 2006 (UTC)

Actually both pages are a mess. Nortexoid 06:04, 10 December 2006 (UTC)

Actually, interwiki links are a mess here. --VictorAnyakin (talk) 11:50, 21 April 2008 (UTC)

Introduction

The introduction of the article had been changed to read:

Logical implication is not to be confused with material implication (AKA material conditional).

In ordinary language, material implication is often expressed by sentences of the following form:

• If P then Q.

Here P and Q are propositional variables that represent propositions in a given language. In a statement of the form "if P then Q", the first term, P, is called the antecedent and the second term, Q, is called the consequent; and the statement as a whole is called a conditional. Assuming that the conditional is true, then the truth of the antecedent is a sufficient condition for the truth of the consequent, while the truth of the consequent is a necessary condition for the truth of the antecedent.

A sentence is valid (not to be confused with the property of an argument being valid) if and only if it is true on every interpretation. (See also logical truth, tautology.)

A logical implication is a valid material implication.

The rest of this article appears to be about material implications.

I found this introduction confusing, since it looks like discussion of the article rather than an introduction to the article. So I replaced the introduction with an earlier version. The above introduction is probably salvageable if it is modified to stop talking about what shouldn't be confused and start talking about what is to be understood. Michael Slone (talk) 23:52, 9 December 2006 (UTC)

Possible merge with Entailment

They are exactly the same concept, so why are there two distinct pages for them? This one is actually quite poorly written. I like the introduction though. Just kidding, I wrote it. This page should be scrapped (except for the great intro.) and redirected to Entailment. Is anybody going to make a stink about it if I do it? Nortexoid 23:38, 6 January 2007 (UTC)

Now that I've drastically edited the article, I don't think a redirect is in order, but rather a merge is. There is some useful information in the Entailment article that could be placed in this one, and then Entailment could be redirected to this article. Nortexoid 01:46, 7 January 2007 (UTC)

I'll support a merge, without really knowing much about entailment. I'll trust your judgment. Fresheneesz 21:49, 7 January 2007 (UTC)

I support a merge, or just redirect--Philogo 13:19, 5 December 2008 (UTC)

Sorry, I reverted the redirect. I disagree with a redirect without first merging the material. If anything, Entailment should rd here. This page has more information and better pictures. Fresheneesz (talk) 00:57, 6 December 2008 (UTC)

I merged the articles as best I could and replaced the redirect. Entailment is in dire need of work. There is even a section in entailment on how it is and isn't the same as logical implications.... I'm gonna leave that up to someone else to fix. Fresheneesz (talk) 01:20, 6 December 2008 (UTC)

I should point out that it is semi-standard in the literature to take logical implication to be the syntactic notion of derivability (of sentences from sets of sentences) and entailment the semantic notion of truth preservation (from sets of sentences to sentences). In this case, a merge is inappropriate, and so I retract my previous suggestion. Nortexoid (talk) 22:00, 6 December 2008 (UTC)

Gah, well wonderful. Would you be willing to fix the damage I caused then? Fresheneesz (talk) 00:24, 7 December 2008 (UTC)

Apologies. I made my initial suggestion nearly two years ago, when I was a fool. I believe, optimistically, that I'm becoming less of a fool as the years pass. In any case, would it not suffice to simply undo the last few edits to get back to the original (on both the pages for entailment and logical implication)? I would be more comfortable if someone else did it. Nortexoid (talk) 09:30, 7 December 2008 (UTC)

I have redirected this article to Entailment since (a) we do not need two articles on the same subject (b) Entailement has the better material (c) Entailment is (IMHO) a better title cos folks are confused enough about implicatiions as it is. If any materail was in this article that would enhance Entailment then it can cut and pasted across. OK?--Philogo 13:53, 9 December 2008 (UTC)

It does not appear to redirect now. Does anybody think that Logical Implication is anthing other than Entailment? If so, what is the difference? If not, what reason can there be for having two articles on the same subject?Philogo (talk) 17:50, 15 November 2010 (UTC)

I will support a merge, however please make sure it is under either the "logical connectives" or "logical consequence" category.Greg Bard (talk) 18:38, 15 November 2010 (UTC)

Go aheadPhilogo (talk) 14:06, 17 November 2010 (UTC)

Fresheneesz' partial revert

Yes, a lot was changed, but it would be appreciated it somebody qualified in disagreement reverted the article and gave good reasons for doing so. I notice that you ask what the difference between logical implication and the material conditional is at the top of the page. I feel your revert was unwarranted, simply because the article in its current state is awful. E.g., what exactly is the relevance of the Symbolization section, or for that matter the following section on Comparison with other conditional statements? What is all that talk of the Cond(x,y) function for? Nortexoid 21:47, 7 January 2007 (UTC)

I agree it was awful, maybe I shouldn't have reverted. I just felt like too much stuff I found useful was removed. I merged the two intros together, cause yours had lots of good stuff - but lacked some neccessary links and wording that made it a little hard to understand. I dunno about the Cond(x,y) junk - i'll look at merging some of the rest of the two versions right now. Btw, you have to admit, half a year ago, it was a little vauge (according to the articles) what the difference between material conditional and logical implication was. I don't need a degree in logic to know what makes sense. Fresheneesz 21:52, 7 January 2007 (UTC)

One thing I have a problem with is the model theory stuff. Is that really neccessary to understand logical implication? I'm not exactly sure what a "set T of formulas" would be - except that I suppose it could be a set of sets... Its just not clear to me. Fresheneesz 21:57, 7 January 2007 (UTC)

It's more general, as I clarified in the introduction, to use the model-theoretic (or valuation or interpretation) terminology rather than the valid material conditional one, because the logic may not have the appropriate semantic equivalent of the deduction theorem. E.g., if the logic does not have the property that if A logically implies B, then "if A then B" is valid, then "A implies B" cannot be stated as ""if A then B" is valid". They happen to be equivalent in classical logic but not for e.g. some many-valued logics.

"set Γ of formulas" means that the set Γ contains as elements formulas of some formal language L. Formulas are strings or sequences of symbols of L, usually constructed according to some inductive definition of 'formula'. But none of this has anything to do with the article. I suppose those terms (e.g. 'formula', 'set') could be linked to their respective pages. Nortexoid 00:09, 8 January 2007 (UTC)

Ok, I added back in your philosopical issues section, and killed the definition section (since thats covered in the intro). You can use your discretion on pruning the other sections - I just ask that you try to improve them, trim them, or truncate them, rather than deleting them entirely. Fresheneesz 22:01, 7 January 2007 (UTC)

Btw, pictures are nice - if you can get one or make one, I would personally be appreciative. Fresheneesz 22:01, 7 January 2007 (UTC)

p → q ≡ p ∧ q ∨ ¬p ∧ ¬q ∨ p ∧ ¬q

I wrote this: p → q ≡ p ∧ q ∨ ¬p ∧ ¬q ∨ p ∧ ¬q

It helped me understand the implied operator. Might it help improve the article, if someone could perhaps help me get it out of unicode into that fancy formulae format that wikipedia uses? --Nerd42 (talk) 03:29, 14 October 2009 (UTC)

A simple explanation

Logical implication can be confusing without a simple explanation of the concept that it is supposed to formalise. The exisiting article is difficult even for some experienced specialists:

http://en.wikipedia.org/wiki/Logical_implication

Logical implication can be used in many professions. Uses include:

• Establishing proof about certain aspects of software design procedures.

• Writing technical manuals for software.

• Writing universal and existential quantifications which can readily be converted into code loops.

• Helping to ensure code is correct - that is, for the debugging of code. It can be used in preconditions, midconditions, loop invariant conditions and postconditions of method specifications.

Currently there are several pages for the same thing, and confusion amongst the authors. This suggests that the fundamental concept of logical implication is not properly understood. Here are some comments from the 'talk' page:

---

"What the hell is the difference between Logical implication and the Material conditional ????? I propose a merge."

"... both pages are a mess"

"... interwiki links are a mess here"

"... The above introduction is probably salvageable if it is modified to stop talking about what shouldn't be confused and start talking about what is to be understood"

---

I added a simple explanation of 'logical implication' to the 'Logical implication' page. I think that logical implication has a real world origin, although this may not be verifiable. —Preceding unsigned comment added by DavidMortimer (talk • contribs) 09:15, 6 April 2010 (UTC)

merged into entailment

Please see Talk:Entailment#Duplication of content. - dcljr (talk) 19:51, 15 January 2011 (UTC)

Note this article was merged into entailment by consensus - see Talk:Entailment#Merger proposal

In accordance with merge procedures this page has been cleared and redirects to Entailment —  Philogos (talk) 02:13, 26 April 2011 (UTC).