Talk:List of logic symbols/Archive 1

Explanation of Material Implication: Overkill?
"A ⇒ B is true only in the case that either A is false or B is true, or both."

I wonder about the "or both" clause. It's true, but it's not needed, is it?

Doesn't "A is false or B is true" cover the three true cases, without need for the "or both" clause?

JimStearns206 (talk) 02:30, 27 February 2015 (UTC)

Note (correct) explanation under list of mathematical symbols. Len loker (talk) 07:39, 18 January 2017 (UTC)

Missing: First Order Logic 'Equality between terms'
In "Deduction Systems", Rolf-Socher-Ambrosius, Patricia Johann, Springer 1997:

The symbol "≈" (wavy equal, Equals_sign) is used to detnote euqality between terms (in some unspecified domain) in First Order Logic with Equality.

Incomplete
What is the meaning of (for example) L with subscript "omega one omega"? Logics (languages) with subscripts and superscripts are missing; thank you. — Preceding unsigned comment added by Uwacm (talk • contribs) 16:29, 21 February 2011 (UTC)

Re. to math table
This page is a trimmed version of Table of mathematical symbols. -Chira 15:46, 20 August 2005 (UTC)
 * We should add a few more operators here, in particular modalities, strict implication, and maybe the operators from linear logic. --- Charles Stewart 20:10, 23 August 2005 (UTC)


 * Do you see this table developing independently of Table of mathematical symbols? Paul August &#9742; 21:59, August 31, 2005 (UTC)
 * What are the origin of the THEREFORE and BECAUSE signs? The three-dot triangles I mean. Evertype 15:41, 14 September 2005 (UTC)


 * I hope somebody can answer that last point. I was trying to find out which character sets support the "therefore" symbol, and found it doesn't seem to be mentioned anywhere in Wikipedia – at least not anywhere obvious or findable by using the search tool on "therefore symbol". – Kieran T  ( talk  14:18, 23 July 2006 (UTC)


 * P.S. The W3C has come to my rescue revealing that &there4; is &amp;there4;. Would still like to see its etymology documented in WP somewhere though. – Kieran T  ( talk  14:23, 23 July 2006 (UTC)

The turnstile ("|-") symbols should be included here.

Regarding the Logic Symbols
To take care of the problem with the symbol fonts displaying differently on different browsers, why not make the symbols into image files? This would ensure that everyone (regardless of their browser) can view the symbols. I find it difficult to understand the logic of having a logic table that you may or may not be viewing properly. 64.95.214.18 17:46, 20 December 2005 (UTC)Anonymous

Agreed; they should be made into image files (where appropriate). It is a bit funny that for the modal symbols the article says "If you wish to use these in a web page, you should always embed the necessary fonts so the page viewer can see the web page without having the necessary fonts installed in their computer" and then the symbols directly below show up as boxes because they are unsupported by my browser. —Preceding unsigned comment added by 96.246.176.86 (talk) 05:03, 5 February 2009 (UTC)
 * The LaTeX symbol column renders the examples as PNG files. Perhaps this could be incorporated into the main Symbol column.Paulmiko (talk) 23:51, 22 February 2011 (UTC)

Overscore
'Twould be nice to include the overscore as a way of indicating logical negation/complementation. —12.72.71.7 12:50, 27 July 2006 (UTC)

Incomplete
This article's listing of logic symbols is incomplete. I noticed that a while back, but I was too lazy to fix it. I'll fix it now. Robocracy 11:46, 22 October 2006 (UTC)


 * There are still plenty of things to add/change. The triple bar is far more commonly used to indicate material equivalence than to indicate definition (if it does the latter ever).  The equals sign is commonly used for strict equivalence.  Double turnstile is missing.  It should be noted that – is sometimes used as negation, and . is sometimes used as conjunction (but also periods are used to serve the same purpose as parentheses sometimes).  Then there are, of course, the modal operators including the box (necessary, obligatory) and the diamond (possible, permissible) and the fishhook (strict implication).  Philosophers also often use the set membership, intersection, and union symbols.  Also the slashed equals sign, turnstile, double turnstile and set membership symbols are used to indicate the negation of those relations.  Then if we really wanted to get crazy, we could include even rarer things like the Sheffer stroke, corner quotes or the substitutional quantifier.  (I'd fix most of this right now, but tables annoy me and I don't have the patience to figure this one out at the present moment.) KSchutte 21:20, 3 April 2007 (UTC)


 * Also, the therefore symbol mentioned above on this very talk page still isn't included on the table. KSchutte 21:21, 3 April 2007 (UTC)

Why is the conjunction sign "ʌ" left out? This is a lot more common than "°". —Preceding unsigned comment added by 129.177.155.226 (talk) 09:10, 9 May 2011 (UTC)

Ordinary name for each sign
Two things. First, why not add each symbol ordinary name, the only one I know is the tilde "~", but I am sure they have ordinary names. Second, how about including the schefferstroke? Or should we change the article to be about the logical symbols only in propositional and quantified logic? RickardV 06:58, 30 April 2007 (UTC)

inference section... mistake?
"x ⊢ y means y is derived from x." According to the definition on the page, shouldn't it be x is derived from y? Springbreak04 23:45, 26 June 2007 (UTC)
 * x ⊢ y means "y is a syntactic consequence of x," or "from x we can derive y"

Gregbard 12:22, 23 July 2007 (UTC)

Symbols should appear in mathtype format
I cannot read many symbols, and I giess I'm not the only one. I think it's better to write them in mathtype format: $$Insert non-formatted text here$$. Please anyone who CAN read the symbols, do it. Dan Gluck 19:45, 23 August 2007 (UTC)

"And"
I don't know how to edit the table, but someone might note that the dot is often used for "and" (e.g in Copi). Carolynparrishfan (talk) 22:04, 24 November 2007 (UTC)

Table doesn't include Unicode U+22BC NAND and U+22BD NOR
See http://www.unicode.org/charts/PDF/U2200.pdf, page 207.

Note: Table does include U+22BB XOR.

DLA (talk) 23:17, 24 March 2009 (UTC)

Generalizing Multiple Quantifiers
Is there any symbol that can express theorems about statements of predicate calculus involving an arbitrary number of quantified variables. Like an operator akin to the operators for union and intersection over a set of sets. I realize it'd be tricky because the interesting theorems would involve alternating universal and and existential quantification, and would have to have a function specifiying the quantification for the nth variable. Has anyone found any use for this? 75.50.173.105 (talk) 20:55, 25 May 2010 (UTC)
 * Various ad hoc notations are used. For a block of quantifiers of the same kind, one would normally use the usual quantifier with whatever notation is employed for sequences of variables (typically an arrow or overbar), such as $$\exists\vec x\,\phi(\vec x)$$. When the quantifiers alternate, people write things like $$Q_0x_0\,Q_1x_1\,Q_2x_2\dots Q_nx_n\,\phi(x_0,\dots,x_n)$$ where every Qi stands for a universal or existential quantifier (so that your function is $$i\mapsto Q_i$$). I've never seen anything $$\bigcup$$-ish for this purpose, the triple dots notation is clear enough, and unlike unions and friends, there can't be infinitely many alternations anyway (unless you do serious business with some sort of game semantics, I don't know what notation these employ; the only example of this I recall seeing involved a countable sequence of alternating quantifiers that was again written with dots).—Emil J. 16:29, 26 May 2010 (UTC)

Wikipedia policies
Am I the only one who notices a dearth of citations to secondary sources? GcT (talk) 19:05, 19 June 2010 (UTC)

Seconded! I am trying to use this as a quick reference to incorporate logic symbols into a paper on literature, but I can't trust that these are accurate or even conventional w/o any citation. This page is thus useless to me... —Preceding unsigned comment added by 75.73.51.221 (talk) 06:18, 8 May 2011 (UTC)

Third! It would be nice to have citations for the last section on Poland and Germany, where did this information come from is it valid? Also why are some of the citations only to the authors wiki page not to an article itself? I was also very distracted by the white concave sided diamond. What is the use for this symbol in mathematics? Currently, there is no explanation given. Krutschc (talk) 22:25, 18 September 2016 (UTC)

Separating grouped symbols
I'm wondering what the advantages and limitations of lumping symbols together. For example, take the first set with the double-bar right arrow, single-bar right arrow and left-opened U. The entry visually suggests the three are synonyms, but the explanation suggests they all sometimes share a equivalent meaning but are different symbols.

I would like to suggest splitting the grouped symbols up into individual entries, unless they are truly and utterly synonymous. With particular deference to the example, while some content would be duplicated, the efficiency gained from the combination is lost to the potential confusion caused by the explanation.

Thoughts? Wolfraem (talk) 15:29, 27 July 2010 (UTC)
 * Agree, each symbol should have its own record. -DePiep (talk) 18:00, 20 March 2011 (UTC)
 * Agree. I think people usually use different sets of symbols in logic and engineer. We should give a list of symbols which are used in logic and a list of symbols which are used in engineer. — Preceding unsigned comment added by Qijiang ok (talk • contribs) 03:42, 10 March 2014 (UTC)

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: not moved. Andrewa (talk) 06:39, 25 March 2011 (UTC)

List of logic symbols → Table of logic symbols — Currently this title is just serving as a redirect; "Table of.." is both more accurate, and renaming it would make it consistent with Table of mathematical symbols. –Cosmopolitan (talk) 22:13, 17 March 2011 (UTC)


 * Support: It is indeed a table and this would improve consistency. I think everybody will understand that table is a subset of list in terms of Wikipedia article titles. –CWenger (talk) 19:27, 19 March 2011 (UTC)
 * Oppose: it is a list, so that's the name. Is there a specific reason to use 'table' for a list? -DePiep (talk) 23:49, 19 March 2011 (UTC)
 * That is, is there a reason to deviate from WP:LISTNAME? -DePiep (talk) 21:17, 23 March 2011 (UTC)
 * Oh, you're right, that is the standard convention, even for tables. In this case, we should rename Table of mathematical symbols, not this one. I'll request a move for that when this one closes. –Cosmopolitan (talk) 08:06, 24 March 2011 (UTC)
 * We agree. It is not to nitpic, but if a user looks for such a thing, it's good when they get it right first try in every situation by typing "list of such a thing". Again: we agree. -DePiep (talk) 17:39, 24 March 2011 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Standard Numeral
"U+0305 ̅ ​ combining overline, used as abbreviation for standard numerals. For example, using HTML style "4̅" is a shorthand for the standard numeral "SSSS0".

It was always my understanding that "standard numeral" referred to a standard decimal representation. The linked page for "Overline" does not contain this term, and wikipedia has no page for "Standard Numeral." A Google search returned nothing but decimal numerals. What is mean here by "Standard Numeral," and also by "SSSS0?" 67.194.27.28 (talk) 16:23, 17 April 2011 (UTC)

closing paragraph
The introduction to the main article ends:

Be aware that, outside of logic, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings.

Godel’s famous Incompleteness explicitly treats the formalism of Principia Mathematica, so one might expect he would use the same logical notation, which he does not — in particular, the notation for formal definition, a.=.b Df., not an entry on our List. Instead he uses Hilbert’s notation of the triple-bar ≡ which for propositional logic does appear on the List, twice.

I proposed the closing paragraph be changed to:

Be aware that, inside logic, different symbols sometimes have the same meaning, and a single symbol different meanings. — Preceding unsigned comment added by 75.82.51.192 (talk) 16:46, 17 May 2012 (UTC)

should contain "visually similar" or "legacy (eg. ascii) approximate notation" column
some characters are often rendered like "|=" or "^" in texts that use legacy character sets either for all symbols or just for some of them.

This may be due to either technical difficulties or lack of better knowledge or ease of simplicity.

Also the readers who are unfamiliar with how to enter these characters wouldn't be able to do a quick find on page search, when looking for a symbol that they saw on a (real) paper.

Especially if someone is looking for them cause he doesn't know its name.

The important thing is that I think it would be very useful for the readers who need this article the most (ie. unexperienced) to be able to search conveniently for the symbols with these "legacy" notations (for the lack of better expression).

I suppose the most logical and useful way to include them is via listing them in each row by an extra column.

Note that I call them legacy notation but they may be part of some anonymous notation, ie. "|=" it is easy to see why it is written like this, even if there is no known name for this "system" or no system at all. The keyboard is still a codepage based instrument in most countries and if a symbol can be written with ascii characters due to visual similarity, it's worth to include that notation here. edit maybe the column should be called visually similar instead

— Preceding unsigned comment added by 80.99.93.173 (talk) 22:57, 6 June 2012 (UTC)

Semantic variations of symbols should be listed
I just added $$\implies$$ and $$\iff$$ to the table, only to be removed minutes later by someone else stating "rm irrelevant opinions. It certainly isn’t common or recommended for the actual connectives in logic literature, though it is commonly used in other parts of mathematics as shorthand notation.".

I don't believe these semantic variations of symbols are "irrelevant", rather very useful. It is very common for LaTeX users to use the "wrong semantic variations" of symbols (e.g. the wrong dash, etc...). Seen as this is such a common problem, I think it's extremely useful to list the semantic variations too. Examples are:


 * $$\vDash$$ and $$\models$$
 * $$\iff$$ and $$\Leftrightarrow$$
 * $$\implies$$ and $$\Rightarrow$$

Kelley.vanevert (talk) 11:07, 13 June 2013 (UTC)
 * First, I didn’t remove the symbols. I only removed your comments about them looking “ugly here”, and that they are “recommended”. Second, like it or not, these symbols are not the recommended notation for the two connectives in question, and they are not used as such. This does not have much to do with their semantics, they just have the wrong shape. LaTeX symbol naming has never been “semantic” in this sense, but in any case the two sets of symbols have different semantics, and it is wrong to mix them up just because some of them have acquired misleading suggestive names, and others did not. \iff and \implies can only be used as informal shorthands in displayed equations like
 * $$ax^2+bx+c\text{ has two real roots} \iff b^2-4ac>0,$$
 * but it is completely wrong to use them as formal logical symbols for the implication and biimplication connectives in formulas: depending on the author’s conventions, $$(A\to(B\to C))\to((A\to B)\to(A\to C))$$, $$(A\supset(B\supset C))\supset((A\supset B)\supset(A\supset C))$$, or $$(A\Rightarrow(B\Rightarrow C))\Rightarrow((A\Rightarrow B)\Rightarrow(A\Rightarrow C))$$ are all OK (though the last one is a bit uncommon), but $$(A\implies(B\implies C))\implies((A\implies B)\implies(A\implies C))$$ is just terrible typography.—Emil J. 11:44, 13 June 2013 (UTC)
 * This is a very old talk post, but as some of these “semantic variations” have been added to the main article without any usage warning, it would be good if someone could find a citation on the common usage for the variants and add it to the article.―Bhbuehler (talk) 14:56, 21 February 2022 (UTC)
 * For someone reading this who doesn't know TeX well and who doesn't want to have to open the “edit source” to see what is being talked about, $$\implies$$ is written as  while $$\Rightarrow$$ is written as  . Similarly,

$$\Leftrightarrow$$ $$\models$$ $$\vDash$$ ―Bhbuehler (talk) 14:56, 21 February 2022 (UTC) Edited:Bhbuehler (talk) 15:00, 21 February 2022 (UTC)

Symbols not picured
Note that some of the symbols are not being translated into Wikipedia-ese. I don't know how to make it so. Volunteers? U+27E1 ⟡ white concave-sided diamond U+27E2 ⟢ white concave-sided diamond with leftwards tick: modal operator for was never U+27E3 ⟣ white concave-sided diamond with rightwards tick: modal operator for will never be U+27E4 ⟤ white square with leftwards tick: modal operator for was always U+27E5 ⟥ white square with rightwards tick: modal operator for will always be U+297D ⥽ right fish tail: sometimes used for "relation", also used for denoting various ad hoc. ..

Thank you, Wordreader (talk) 16:13, 24 January 2014 (UTC)

Quantifiers and Poland
I've seen $$\wedge$$ used for a universal quantifier in English papers and books, occasionally, also. They are often intentionally confused in algebraic logic and universal algebra. Unfortunately, I don't have any texts in those subjects, so I cannot verify my recollection. — Arthur Rubin (talk) 18:25, 25 November 2014 (UTC)

ℸ
Hi! Over on Wiktionary, we're trying to figure out if ℸ has ever actually been used as a symbol for the "fourth transfinite cardinal". (See wikt:WT:RFV.) Our resident mathematicians haven't seen it used that way, but one of them suggested asking logicians such as yourselves. Have you ever heard of it? I've also posted this query to Talk:List of mathematical symbols. -sche (talk) 21:45, 22 February 2015 (UTC)

Conditional and Biconditional
Is there any reason this table does not use those terms? Cake (talk) 02:06, 6 February 2016 (UTC)

Material implication symbol
Explanation different from that listed under list of mathematical symbols. Len loker (talk) 07:35, 18 January 2017 (UTC)

Simplify table by splitting second column
I did not recognize the that the second column of the "Basic logic symbols" table was split into three different parts until I saw the column header. I propose that the "Name / Read as / Category" column be split up into three separate columns to simplify the table. Somerandomuser (talk) 19:34, 28 April 2017 (UTC)

Last symbol example use
The last example used is "A → B ⊨ ¬B → ¬A" which, unless I'm sleep deprived, means "A implies B, which semantically entails that !A implies !B", which is not actually correct. The example just above it is very similar and I also think that it is wrong as well. Please tell me I'm not insane

Explanation of material implication is horrible
It's hard to think of a less intuitive (and indeed misleading) way to explain the concept than "$$A \Rightarrow B$$ is true if and only if $$B$$ can be true and $$A$$ can be false but not vice versa."

Why not define the symbol as "whenever $$A$$ is true, $$B$$ is also true"? That'a at least as precise as the current wording, and also matches the intuitive notion of implication. Grover cleveland (talk) 00:09, 17 April 2020 (UTC)

Table looks "corrupted"
Okay, whoa! Does the table look "messed up by a computer" to you or is it just me? Maybe someone can figure out the equivalent of "distribute columns" and then fix it? I don't want to ruin anything, but I will see if I can do it. YoSoyUnHamster (talk) 22:39, 29 April 2020 (UTC)

Turns out they're trying to smoosh three columns into one, and the result is awfully confusing. Can we work together to restructure this table so that it's a bit easier to read? YoSoyUnHamster (talk) 22:41, 29 April 2020 (UTC)
 * Yeah, that confused me as well. I moved each into its own column. Is this better? – Frood (talk) 21:09, 26 July 2020 (UTC)


 * Wow, that's excellent! Thank you! YoSoyUnHamster (talk) 21:48, 26 July 2020 (UTC)

Advanced and rarely used logical symbols
Is there any reason to not make this section a table, just like the above section? This bullet list barely gives any overview. JochemvanHees (talk) 11:48, 4 September 2020 (UTC)

Boolean Logic
Doesn't assuming (P AND not(P)) is "always" False assume two-valued (i.e.Classical, Boolean, Binary) Logic? I'm not sufficiently knowledgeable, but it seems some of the table's contents rely on there only being True or False values possible. (?) Also, multi-valued logic has many symbols not listed here (see the Wikipedia article on Many-valued logic for examples.) If this table is going to be restricted to Classical Logic, it should be noted so.174.131.48.89 (talk) 12:29, 23 August 2022 (UTC)