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The text is not coherent in that it assumes that the reader knows that 0 means false and the 1 means true. This is not universal knowledge. What is confusing is that while the text describes functions as true or false, the truth table does not.— Precedingunsigned comment added by213.113.4.17 (talk)14:02, 23 March 2017 (UTC)[reply]

yes i found it confusing as well~2026-10790-1 (talk)06:54, 6 January 2026 (UTC)[reply]

According to the sources I've checked, the logical equivalence sign is not technically a connective -- this conflicts with what the page currently implies when it says "≡" can be used synonymously with "↔".

Source "Discrete Mathematics and its Applications" by Kenneth Rosen. Quote: "The symbol ≡ is not a logical connective and p ≡ q is not a compound proposition but rather is the statement that p ↔ q is a tautology."

Unfortunately there seems to be complete confusion in the Wikipedia about all the logic topics connected with arrows. But this confusion seems to come from the logicans themselves. We also have the articlesIf and only if,Logical equivalence andLogical equality.

I'd also say that "p ≡ q is not a compound proposition but rather is the statement that p ↔ q is a tautology", but for sure there's some logic author somewhere, who uses "≡" to express this operation (the negation of theexclusive or). Seems, that no logic sign beyond${\displaystyle \wedge }$ and${\displaystyle \vee }$ is generally accepted.Lipedia (talk)10:35, 3 September 2010 (UTC)[reply]

I am not joking, after reading this wikipedia article, I feel like I understand less about biconditionals than before. Sadly, this is true for so many other math related wikipedia articles.

Don't misunderstand, I'm quite familiar and comfortable with working with logic/math, but this page seems to be nothing more than a random collection of grammatically and information-ally correct but contextually and stylistically bankrupt sentences.

I suppose this is just the result of multiple authors though. Oh well.thank you

In the section on colloquial usage it says that the only unambiguous way of putting the biconditional in English is to say, "b if a and a if b". Should aif and only if b not be included here?Davkal22:31, 8 June 2006 (UTC)[reply]

I would also like to put in a brief note to include the formulation "just in case" which is commonly used in philosophy as th biconditional even though the usual English meaning of "just in case" is "as a precaution against...", as in, e.g., "I took my umbrella just in case it started raining".Davkal22:33, 8 June 2006 (UTC)[reply]

The misleading and confusing expression "just in case", should never replace its correct, and easily understood equivalent, "if, and only if" (also, in more technical writing, "if and only if"). The following explains the error:

• Language Log: "Just in Case"
• Southern California Philosophy for philosophy graduate students: "Just in Case".Dr Lindsay B Yeates (talk)22:10, 9 April 2014 (UTC)[reply]

I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at:Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also seeTalk:Logical connective.

I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts.

Gregbard08:56, 28 June 2007 (UTC)[reply]

Not quite the same, as A = B = C may mean they all have the same truth value, while A iff B iff C may mean A iff (B iff C). —Arthur Rubin |(talk)20:06, 28 June 2007 (UTC)[reply]

...which also means they have the same truth value. The convention that I have seen, and believe is convenient is the the equal with two bars (=) means "same numerical value as," the one with three bars${\displaystyle \equiv }$ means "has the same truth value as," and one with four bars (which I don't think we can make yet) means "is the same set as."

I would like to see this article deal with this one:${\displaystyle \equiv }$. I think that would include as least some of the material fromlogical equality, but not so much (if any) fromlogical equivalence.Gregbard20:36, 28 June 2007 (UTC)[reply]

Just thought I should point out that the merger withif and only if has already been proposed, discussed, opposed and rejected -- seeTalk:If_and_only_if#Merge. Also, I'm not an expert on logic, but it seems as ifif and only if,logical biconditional andlogical equality are related but distinct ideas, being frommathematical logic,propositional calculus, andelectronic engineering (I think), respectively. Even if they're the same thing, that doesn't necessarily make a merger the right option; they seem to be written with different target audiences in mind, and it's often worth including different treatments of the same idea, for people from different backgrounds, such as withquantum mechanics andintroduction to quantum mechanics.James pic (talk)17:46, 1 April 2008 (UTC)[reply]

I have removed the templates regarding the merger withif and only if, there seems to be little support for that one. --_{tiny plastic} Grey Knight⊖07:59, 18 June 2008 (UTC)[reply]

In section Biconditional Elimination there is the same text than in pageBiconditional elimination. please do somethingSnushka (talk)10:28, 19 June 2009 (UTC)[reply]

Please seeTalk:If and only if.Melchoir (talk)23:48, 21 February 2010 (UTC)[reply]

At the moment in theRules of Inference section it is told, that this is a connective infirst-order logic, which ispredicate logic. Shouldn't it read "zeroth-order logic", or simply "propositional calculus"?Lipedia (talk)00:17, 1 August 2010 (UTC)[reply]

EQV( ) should be true, not false. —Arthur Rubin(talk)05:44, 1 August 2010 (UTC)[reply]

Well, I replaced for, which I don't like.

Operations are not usually done without arguments, so I don't know if we can ask, which one is more common. I used the xor version, because I felt it's inacceptable that adding an argument to EQV( ) shouldnt change the result.

And because I've seen theall XOR nothing matrix before:

Relations like the subset relation are nonexistential quantifications combined by AND, and thustheir negations are existential quantifications combined by OR. Just for fun I replaced this OR by a XOR, andthere you can see this matrix with the zero line. (Comparethis overview.) So the xor version seemed more legitimate to me.Watchduck (talk)13:35, 1 August 2010 (UTC)[reply]

In spite of the fact that someone changed my skin on this site....

I look at this as logical equality, rather than logical biconditional. To be precise, I look at the alternative form of EQV(X) as:

${\displaystyle \underset{A\in X}{\bigwedge }\underset{B\in X}{\bigwedge }\left(A\leftrightarrow B\right),}$

making in clearly a generalization of the two-element logical biconditional, given that${\displaystyle A\leftrightarrow A}$ is always true. —Arthur Rubin(talk)16:40, 1 August 2010 (UTC)[reply]

I think that saying "p if and only ifq"just becausep andq have the same truth value is a ratherabsurd definiton. That would mean, since it is both currently true that I am on a laptop and I am on Wikipedia, that it is currently true that I am on a laptop if and only if I am on Wikipedia!That just isn't what "if and only if" means! It's NEVER true that I am on a laptop if and only if I am on Wikipedia! A counterexample exists: I could be on a laptop, BUT NOT on Wikipedia. Another counterexample would be that I could be on Wikipedia, but on an iPhone and hence NOT on a laptop!

"p if and only ifq" is supposed to be true when IT IS ALWAYS THE CASE thatp andq have the same truth value! That is, when IT IS IMPOSSIBLE thatp andq have different truth values!

I'm afraid NOBODY reading this page has ANY IDEA what it means for a logical biconditonal to be true! I don't care how many "respected publications" this bogus definition can be found in!

Rewrite this page, and rewrite the books! This Wikipedia article is an embarrassment for thewhole human race! -Hanlon1755 (talk)18:30, 4 July 2012 (UTC)[reply]

This article accurately describes thematerial biconditional (seematerial conditional). There are also biconditionals corresponding to thestrict conditional andlogical implication. I won't remove the{{disputed}} tag, but I don't think it's completely justified. —Arthur Rubin(talk)10:34, 5 July 2012 (UTC)[reply]

And we are supposed to report what "the books" call it (seeWP:OR), although I'm sure there are some which use the strict biconditional. —Arthur Rubin(talk)10:35, 5 July 2012 (UTC)[reply]

Nonsense. We only needone definition of logical biconditional, and I can tell you right now this sad, sad page does not have it. -Hanlon1755 (talk)17:40, 5 July 2012 (UTC)[reply]

Do you have a definition? —Arthur Rubin(talk)17:55, 5 July 2012 (UTC)[reply]

Of course! "p if and only ifq" meansp andqALWAYS have the same truth value. -Hanlon1755 (talk)20:22, 5 July 2012 (UTC)[reply]

That's not the definition of "material biconditional", which is the usual definition of biconditional. —Arthur Rubin(talk)10:11, 9 July 2012 (UTC)[reply]

Well,if that's true and a biconditional means simply bothp andq, or neither, that certainly isn't self-evident at all. Look at the mess I'm in! I think in this case this definition should be justified. It should be a theorem rather than a definition. This definition seems very synthetic and arbitrary. -Hanlon1755 (talk)00:55, 10 July 2012 (UTC)[reply]

"p ↔ q" means "p → q" and "p ← q" ("q → p"), forany definition of the conditional "→". Seems the appropriate definition ofbiconditional. —Arthur Rubin(talk)03:00, 10 July 2012 (UTC)[reply]

That's not the definition I was disputing, Arthur. I agree that p ↔ q means p → q and q → p. I just dispute the definiton where p ↔ q means both p and q, or neither. I don't care that this is "equivalent" to p → q and q → p; I would also have disputed the definition ofmaterial conditional, as this weird definition is implied by it. -Hanlon1755 (talk)02:28, 11 July 2012 (UTC)[reply]

In fact, I still don't believe it! -Hanlon1755 (talk)02:12, 15 July 2012 (UTC)[reply]

XNOR, read "exclusive nor", is logically erroneous (it should be "not xor/exclusive or"), I hope that can be taken as an objective fact(?). The correct acronym should of course be NXOR, but - probably due to easier articulation - XNOR has prevailed, but that have had the unfortunate consequence that many seems to think that it really is an "exclusive NOR" (and IMHO, they're not to blame for that).I made an edit earlier today, where a comment (in parens) were added to note the learning reader about this, but it was quickly reverted by @Adakiko, why?2A01:799:965:9400:809C:C3B0:7357:4FE (talk)13:36, 24 April 2025 (UTC)[reply]

The comment was at the end of the 1st paragraph:... which means "both or neither"(the nomenclature can be confusing though, as it is actually the negation of XOR).2A01:799:965:9400:809C:C3B0:7357:4FE (talk)13:38, 24 April 2025 (UTC)[reply]

Your edits appear to be editorializing. SeeMOS:EDITORIAL and, maybe,wp:synthesis. Thank youAdakiko (talk)01:55, 25 April 2025 (UTC)[reply]

Disclaimer: I'm not a native speaker of English, so the wording of my edit can probably be improved.

That said, I assume it was the word "actually" that raised your concern(?); I find it apt here, since the name/term "exclusive NOR" implies an incorrect working of this operator (ref the comment of the original edit for argumentation) and the comment points out what "it actually is/does."

Perhaps you could suggest an alternative wording?2A01:799:965:9400:809C:C3B0:7357:4FE (talk)18:50, 25 April 2025 (UTC)[reply]

I wonder how many people actually consider that? To me, it's just another word that does not make literal sense. I have designed a considerable amount of digital circuitry and never thought about that. I don't remember anyone else bringing it up. It's just a black box that does something and has an acronym that I never spent too much time deciphering. I don't believe that the XNOR/NXOR issue is significant enough to go in the lead section, especially when it sounds like editorializing. Please ask at thewp:Help desk and get someone else's opinion. That's about all I can offer. Thank youAdakiko (talk)10:24, 26 April 2025 (UTC)[reply]

I will address you, @Adakiko, since you appearantly have taken an editor's role for this and other related articles, ie. the prerogative of deleting content with (what I still assume to be) undisputed factual content:

I put it in the only place where the XNOR operator is referred to, I think putting it elsewhere would little sense unless one makes a separate section for it (which, I guess, would only inflate what at least I consider an issue, even more).

The note was of course not intended for you, as you know the working of it, and perhaps even not for "you as learner", since you seem happy with blackbox knowledge and words/acronyms that doesn't make litteral sense; there are, however, people whos mind works differently from yours (I'm one), that try to note systems to ease learning/remembering. Maybe someone that wants to have a working knowledge of the subject without being a proffesional (like you), and then meaningful/consistent systems makes things easier.

I have come over multiple questions on stackoverflow, quora, etc. where people ask eg. about if/why not some exclusive operator exist, evedently based on the misconception that "any locical op can have an exclusive variant"; furthermore, in the typical comment discussions following, some participants that seem to think they understand this, come up with various explanations and/or justifications, sometimes based on even other "imaginary operators" such as XAND (which of course is just another faulty name for NXOR).

Having read these posts and discussions (over some time, I must admit, so it's just the impression I'm left with) I attribute this misconception to the confusing XNOR acronym, since it appears to be an "exclusive variant of NOR" (which of course is an oxymoron).

Needless to say, trying to reform a bad/unfortunate system is mute (math is full of them, due of course to historic development), but at least noting an incosistency of an otherwise consistent system is something any good teacher or reference would do (XNOR is the only erroneous acronym of the logical operators/gates).

Unless you you disagree in the factual contents of the note I suggested, I think it would serve the readers of Wikipedia, as well as the community, better if you could suggest or implement improvements/solutions (eg. change of wording, positioning, etc.) instead of just reverting an edit whose contents is undisputed (I assume), partly based on your personal opinion concerning what is important. If one really cares about making Wikipedia better, I think one should be cautious with just bluntly deleting genuine/correct content additions due to a eg. a "suspicious word" (which sometimes could actuall be apt) since it can be very discouraging and the community will lose valuable contributors (that are not necessarily native English speakers, but still use/prefer the English wiki and want to contribute to/improve it). IMHO, it's counter productive at best, and that it should rather be on you to get someone else's opinion before deleting objectively factual content.2A01:799:965:9400:809C:C3B0:7357:4FE (talk)12:45, 26 April 2025 (UTC)[reply]

TLDR - Ask at thewp:Help desk someone there who is more familiar with the policy will give you suggestions. Don'twp:Editorialize. I am done here. BTW:MrOllie (talk ·contribs ·count) undidyour edit on XNOR gate for "editorializing".Adakiko (talk)19:09, 26 April 2025 (UTC)[reply]

Yes he did that, but then I reformulated, and apearantly he seemed ok with that (I had also not given a comment/motivation for the edit the first time).

You reverted that edit 2 days later, just after you reverted this.

I acknowledge that my previous reply was long, but please be respectful and read it, I think it goes with being "an editor".2A01:799:965:9400:809C:C3B0:7357:4FE (talk)21:55, 26 April 2025 (UTC)[reply]

I am not OK with the revised version, and I fully support Adakiko's reversion. Wikipedia isn't a place to include your personal thoughts on the topic.MrOllie (talk)01:37, 27 April 2025 (UTC)[reply]

I just assumed that since the edit was left inplace (after removal of "unfortunate", which I agree is my personal opinion) that it was deemed ok...

I have not gotten any arguments against the the factual content of the note I wanted to add, namely that a consistent naming of the gate/logic operator would result in NXOR, and I don't consider that to be a personal thought/opinion but rather an objective fact.

So unless you despute what I consider a fact, I'm left wondering: where exactly lies the issue?2A01:799:965:9400:809C:C3B0:7357:4FE (talk)12:20, 27 April 2025 (UTC)[reply]

As has been explained above, the problem is in your introduction of editorializing. I'll link the relevant stuff again: SeeWP:OR andMOS:EDITORIAL. It doesn't matter if you consider it an 'objective fact', you still need a source, since Wikipedia is not an indiscriminate collection of facts or opinions that happen to occur to its users.MrOllie (talk)12:31, 27 April 2025 (UTC)[reply]

Surely, you must be joking MrOllie, if an encyclopedia is not a collection of facts, then what is it!? It's not like I created an article about some obscure fact I find interesting.

Wikipedia even goes beyond such a basic collection, and discusses disproven "facts" such as the Flat Earth theory; it even has entire articles devoted to things people commonly confuse (eg.Map–territory relation)...

And how does this have anything to do with OR, may I ask? It's a note about the name/acronym, intended to help understanding and avoid the confusion it can lead to; and it's evedently factual, as several requests to argue the opposite has produced nothing.

Moreover, the entire XNOR gate article has 3 refs, so don't tell me every little bit of information therein is backed by a reference.

My understanding of editorializing, is that the text should be impartial, and not try to persuade; how does a simple fact ala "the naming is inconsistent with the other gates" break this?2A01:799:965:9400:809C:C3B0:7357:4FE (talk)16:01, 27 April 2025 (UTC)[reply]

Read the provided links, your answers lie therein.MrOllie (talk)16:09, 27 April 2025 (UTC)[reply]

I have, repeatedly, but there must be something I'm missing as cannot see how it applies to my revised edits. Could you please be more concrete/specific?2A01:799:965:9400:809C:C3B0:7357:4FE (talk)17:40, 27 April 2025 (UTC)[reply]

You added your own personal commentary, based on no source, simply because you personally thought it was right. This is exactly what the policies say not to do. That's as clear as I can make it.MrOllie (talk)17:48, 27 April 2025 (UTC)[reply]

Thank you, I appreciate you being explicit.

---

However, I don't agree that pointing out a simple fact* is any more my personal commentary than if I were to imply that the Earth is ball-like in an article where that would be relevant. Would I really need a reference for that?

---

(*) The article clearly states the working of XNOR as "the logical complement of the Exclusive OR", and following the convention used for the other gates that are negations, ie. NOR and NAND, the "Not" goes in front, hence NXOR. This may seem like a very minor issue, but see my earlier posts for argumentation as to why I think this deviation is important to point out.2A01:799:965:9400:809C:C3B0:7357:4FE (talk)21:15, 27 April 2025 (UTC)[reply]

You're welcome to disagree with Wikipedia's policies, but we all have to follow them. You need a reference for anything somebody challenges, as is made very clear by Wikipedia's policies. Have another look, and if you still don't understand you can direct follow-up questions toWP:TEAHOUSE, which is a board set up to explain this kind of thing to new users.MrOllie (talk)22:05, 27 April 2025 (UTC)[reply]

As far as I can tell, the "challenge" is related to the wording/"form" and not the content per se (I've asked repeatedly if there is any disagreement over the content), so I would think the logical way forward was a suggestion for rewording etc. (I've asked multiple times about that as well).2A01:799:965:9400:809C:C3B0:7357:4FE (talk)13:10, 28 April 2025 (UTC)[reply]

I challenge it. It is challenged. You have asked multiple times and been answered multiple times - but I for one won't be repeating my answers here any more. The logical way forward is for you to either provide a reliable source or walk away.MrOllie (talk)13:50, 28 April 2025 (UTC)[reply]

I've been answered in terms of links to various pages explaining eg. writing style (which I agree was, and may still be, an issue) and OR (which I don't see the relevance), but I have still not seen a single argument challenging thefactual content of my edit (ref (*) in my next latest post); until such is provided, I consider it an undisputed fact.

Simply stating "I challenge", without providing any counter argument or other concrete critisism (of the underlying factual content), seems to me like abuse of role/power.

---

"Facts do by definition not require proof" is a sentence with 6 words, that is an undisputable fact, but I'd have a hard time finding a ref for it.2A01:799:965:9400:809C:C3B0:7357:4FE (talk)15:58, 28 April 2025 (UTC)[reply]

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