Talk:Logical connective

message: This article and some of its relatives suffer from the lumping of operators and comparators into one big category, unfortunately called operators.  You can blame computer languages on this if you wish.
In mathematical systems, there are operators and comparators.  For example, in the familiar algebra of real numbers we have +, -, divide, * and others as binary operators, along with "=", "<", etc. as comparators.
In logic systems, this distinction is also made.  Consider for example what comparator is used in the field ({T, F}, and, xor).  It is isomorphic to the field F2.
In short, this page needs a major overhaul.  —Preceding unsigned comment added by Richard B. Frost (talk • contribs) 00:32, 25 September 2007 (UTC)
thread_title: There are unary operators, binary operators, and comparators

message: We have the following pairs of boolean/logical operators:
*Logical and / Conjunction
*Logical or / Disjunction
and the three-way equivalence:
*XNOR, Logical equivalence / Iff
In all of these cases I propose that what's on the left be merged into the article
on the right, as is the case with Logical not and  Negation at present.
Since I'm on the topic, this article could do with a lot of improving, eg. remove presumption that logic = Boolean logic, introduce slightly more high-powered mathematical analysis, such as lattice of expressiveness of sets of logical operators, and so on. ---- Charles Stewart 21:04, 11 Mar 2005 (UTC)
thread_title: Merging boolean operators with logical operators

message: I have proposed that this page be the centerpiece of a series of articles on the operators.
Wikipedia:WikiProject_Council/Proposals#Logical_Operators 
I thought the project would be too small for a formal wikiproject. There's just 16 of them. However, co-operation is needed from several disparate areas. I'd like to see:
*A) the logical, grammatical, mathematic, and computer science applications all on the same page for the same concept. 
*B) similar sections including truth table, venn diagram, properties (including theorems that demonstrate the properties), symbols (preferably from all the above disciplines).
*C) several merges including If and only if, logical biconditional, and logical equality; different pages for implication; logical NOR and NOR gate; others 
*D) unifying main page and nav bar. 
Gregbard 05:31, 28 June 2007 (UTC)
replies: text: Hmmm.  Some of these in (C) are the same as binary operators, but not as ternary/poly-ary operaters.  — Arthur Rubin |  (talk) 20:29, 28 June 2007 (UTC)
replies: text: You are correct. The operators have different qualities in different n-ary logic. They could be interpreted as a totally different thing with a different set of pages for the ternary operators, for instance. Perhaps it would be better to just include a section on the different "versions" of n-ary xor, for instance. Gregbard 20:47, 28 June 2007 (UTC)
thread_title: wikiproject proposed

message: I deleted the "Logical strength" section because I couldn't figure out what it was trying to say.  I now realize that the Sets section is an arbitrary representation of the operators, which probably requires a reference, as well.  If you can explain what you (Greybard) had in mind, I'll work on polishing them.  — Arthur Rubin |  (talk) 02:34, 29 July 2007 (UTC)
replies: text: Thank you Arthur_Rubin, I'm sorry for my tone in my frustration. I think you can see that the diagram may have taken some time and effort. What I had in mind was that the diagram represents an interesting  four dimensional relationship. I think it is informative on the logical connective concept. I have to go for a moment, I'll have more later. Gregbard 04:04, 29 July 2007 (UTC)
replies: text: I have never seen this diagram before and have no idea how it measures logical strength, as it appears to be relatively arbitrarily labeled and oriented. Do you know a reference that discusses it? — Carl (CBM · talk) 10:52, 29 July 2007 (UTC)

text: I'm quite familiar with Lindenbaum-Tarski algebras. Why not just say what you mean in the article, that the "strength" is just the ordering of this algebra (oriented with F on top), or that the figure is a Hasse diagram of the lattice?  — Carl (CBM · talk) 03:41, 4 August 2007 (UTC)
thread_title: ''Sets'' and ''Logical strength'' sections 

message: The ratio of implications between operators is demonstrated by the directional lines in the tesseract The number of lines aiming away from the operator divided by the number of lines aimed toward is the ratio.
:Image:Logical-connectives.gif 
 The relative strength of the 16 binary logical operators:
T	↑  	→  	~p	←  	~q	\equiv	↓	∨  	\not\equiv	q	⊄	p	⊅	&	F
0	1/3	1/3	1 	1/3	1 	1     	3	1/3	1         	1	3	1	3	3	∞
</blockquote>
I'm also moving this section from the article. It's quite unclear to me what these sets are supposed to represent. It was tagged as possible OR for some time. — Carl (CBM · talk) 17:01, 28 August 2007 (UTC)
thread_title: Relative strength of operators

message: This was moved (renamed) a couple weeks ago from logical operation/operator. Wondering if this was done with consensus, if connective is the best word (relation?, operation?), etc. And I also want to know if this is to be the overview article, are all linkages based in use of the term "logical operation/operator" (the convention until now, apparently) are going to be addressed. Seems like this was done out of process, and needs to be moved back, with "connective" being an alternative boldface term. Regards, -Stevertigo 02:19, 6 August 2007 (UTC)
thread_title:  Move 

message: The "Arity" section currently begins:
In two-valued logic there are 4 unary operators, 16 binary operators, and 256 ternary operators. In three valued logic there are 9 unary operators, 19683 binary operators, and 7625597484987 ternary operators.
Call me crazy, but I think it should read as follows:
In two-valued logic, there are 4 unary operators, 16 binary operators, and 256 ternary operators. In three-valued logic, there are 27 unary operators, 19 683 binary operators, and 7 625 597 484 987 ternary operators.
* Mathematics: there are 27 unary operators for three-valued logic, not 9.  Will someone check my math?
* Grammar
** Punctuation: introductory phrases should end with commas.
** Consistency: "X-valued" should use always either use a hyphen or not.
** Number format:  SI recommends spaces to format numbers into groups of three digits.  Bless the SI, but this seems problematic in cases where the number reaches a line break.  Some kind of  thousands separator would be useful.
--75.15.135.58 06:45, 4 September 2007 (UTC)
thread_title:  Changes to "Arity" section (major and minor) 

message: I don't mean to be impertenent or anything, as it is very clear that you have all spent a lot of time over this article, and care about it deeply: however, do you not think that you have perhaps taken the subject too broadly? I mean that a clear and succinct definition of a logical connective given at the beginning with examples of the main truth functional connectives would be sufficient. Once you start going beyond that, going into detail, as to the (potentially infinite) possibilities that exist for something to be a "logical connective" within a given language, then the article will be doomed to be unfinished, and, I think, you confuse the reader. Apologies if I angered anyone, I can tell you've put a lot of work into it. Wireless99 12:29, 8 September 2007 (UTC)
thread_title:  Too long? 

message: I have added some more examples and renderings into symbols, intended to give a better overview for the reader before he/she dives into the depths of this article.  Also removed example of causal relation on the ground that such, though interesting,  is not a truth-functional connective.--Philogo 13:05, 20 September 2007 (UTC)
thread_title:  Intro 

message: I added a line beneath the Venn diagrams crediting the source for their arrangement, which Greg Bard mentioned above ("'Sets' and 'Logical strength' sections") in a link he titled Finite Geometry.
Cullinane 11:26, 28 September 2007 (UTC)
thread_title:  Venn diagrams arrangement 

message: There's no reason to restrict to two formulae, right?  Certainly, the common logical connectives are all unary or binary, but one could define a truth-functional connective to operate on three WFFs and it would still be a truth-functional connective.  Shouldn't it say "one or more well-formed formulae"? Djk3 (talk) 18:45, 24 March 2008 (UTC)
replies: text: Zero or more, if you want to pursue that in full generality. — Carl (CBM · talk) 19:09, 24 March 2008 (UTC)
replies: text: Right, right. Djk3 (talk) 22:47, 24 March 2008 (UTC)

text: It's true. However everything arity greater than 2 can be expressed in terms of just binary connectives. I also think there may be a name for some of them, for instance:If P then Q, otherwise R. Pontiff Greg Bard (talk) 21:13, 24 March 2008 (UTC)
thread_title:  "two or more well-formed formulae" 

message: I don't believe that pointing out that these can be expressed in different ways, for instance, as a relation, is needless complication, nor does it miss any point which is being communicated. Pontiff Greg Bard (talk) 23:01, 30 March 2008 (UTC)
replies: text: The value in pointing out that it is a function is that for any input, it returns one and only one truth-value.  That property isn't present in the more general relation. Djk3 (talk) 00:07, 31 March 2008 (UTC)
thread_title:  expressed as a relation 

message: I'm posting this here for a look-over before I put it into the main article.  I spent a lot of time squinting my eyes and tipping my head doing these one after another, so they may be ripe with errors.  Please check it with fresh eyes and edit as appropriate.  Djk3 (talk) 01:28, 1 April 2008 (UTC)
replies: text: I was afraid that might happen - I also made a version at User:CBM/Sandbox. I copied yours in. I also changed the template to fix some alignment problems. — Carl (CBM · talk) 02:14, 1 April 2008 (UTC)
replies: text: Sorry if I switched the template on you while you were working on them.  I thinking lining them up in two columns opposite their negations expresses what the colors in the table were expressing just as well, but it's be a little bit friendlier on the eyes.  Djk3 (talk) 02:21, 1 April 2008 (UTC)
thread_title:  List of connectives with truth tables and Venn diagrams 

message: I see that Arthur has deleted the fact that logical connectives are a type of logical constant. Does that make any sense at all? Pontiff Greg Bard (talk) 21:34, 30 May 2008 (UTC)
replies: text: They're only logical constants in formal logic, which this article is not necessarily about.  In any case, it's stated further down within the lead.  (IMHO, it should be moved still further down, probably into another article, but that's just my opinion.)  — Arthur Rubin  (talk) 22:04, 30 May 2008 (UTC)
replies: text: Logical constant seems to me to be seminal to the concept. I was surprised to find it buried lower down. I find the distinction you make fascinating, but I'm wondering if it isn't pretty trivial or should be an early lead distinction to cover. In formal logic a logical connective is a logical constant, in informal logic there is a sense in which logical connectives aren't logical constants? Be well, Pontiff Greg Bard (talk) 22:45, 30 May 2008 (UTC)

text: If this article is intended to be read by somebody who wants to know something or more about Logical connectives,  then telling them that it is (if it is) a logical constant would only be informative if the term logical constant were more familiar to them than the term Logical connectives.  Thus e.g. suppose a person did not know what a kangaroo was (maybe a child, or person with limited English.)  Would  you tell them (a) it is a marsupual? (b) an animal that hops about carrying its young in a pouch? The purpose of writing is to communicate. --Philogo 23:01, 30 May 2008 (UTC)
replies: text: Then we have a basic difference of opinion on how articles should be organized. I think that we should always attempt to identify the next level of abstraction early in the lead. "A set is an abstract object." "An algorithm is a type of effective method." This is especially justified on Wikipedia since people can easily look up marsupial, for instance. Invariably, I would like to see a canonically worded account which gives some idea where in the big scheme of things the topic resides, beginning with the immediately next level of abstraction. X is a type of Y. "Oh, what's a 'Y'?" "Well just click on 'Y'."  Explanations are sufficiently easy to get that we are able to go ahead and use the proper terminology, even if it stands in need of explanation itself. Pontiff Greg Bard (talk) 00:14, 31 May 2008 (UTC)
replies: text: The problem with "logical constant" is that it is bad terminology in the first place. Calling quantifiers and connectives "constants" in a context where constants in a much more normal sense also play a role is incredibly bizarre, unpractical, and only serves to confuse people who are not initiated into this arcane terminology. In mathematics it's generally accepted that the subject is already hard enough and that we should do whatever we can to make it easier to understand. The term "logical constant" is obsolete; it does not contribute to making anything easier, and it can be easily replaced by "logical symbol", which has the same meaning except that it also includes the variables. There is no need to spread bad terminology all over the encyclopedia. --Hans Adler (talk) 21:00, 31 May 2008 (UTC)
thread_title:  Logical constant 

message: I don't like the new lede, which appears to conflate the connectives (which are symbols, living in the world of syntax) with truth functions (which are values, living in the semantic world). This may not be the intention, but the wording is very unclear. What is the antecedent to which the word "it" refers in "it is called a truth-function"? In any case, the formulation chosen is very convoluted and hard to understand, and such a heavy emphasis on truth functions is not needed or desirable. I think we should go back to earlier approaches and propose the following for the very first sentence:
:In logic, a logical connective is a symbol (usually denoted as a word or a special logical symbol) that connects a number of statements to form a compound statement, whose truth value is then determined by the truth values of the individual component statements.
I think it is always good to come with an example as soon as possible, and the next sentence might be:
:For example, in "x = 0 AND y = 1", "AND" is a logical connective that combines the two statements "x = 0" and "y = 1" to a single compound statement. The same connective can also be denoted by the symbols "&" and "∧", as in "x = 0 ∧ y = 1". For this example, the compound statement is true only if both component statements are.
Then I think we should list the five most common connectives, and finish off the lede with:
:Other terms in use for "logical connective" are Boolean operator, logical connector, logical operation, logical operator, propositional operator, sentential connective, and truth-functional connective.
I don't see anything else that urgently needs to be put in the lede.  --Lambiam 03:16, 2 June 2008 (UTC)
thread_title:  New lede 

message: One of the external links is to a Hasse diagram similar to  the one above except that it uses a strange (to me) notation in place of OR and NAND and so on.  What are the curlicues and rotated question marks etc in that diagram?  —Preceding unsigned comment added by 69.227.129.30 (talk) 10:33, 11 December 2008 (UTC)
replies: text: These are secret free-masonic symbols. Your head will explode if you read them aloud. — Emil J. 13:29, 11 December 2008 (UTC)

text: It looks like a very bad case of "original research" to me. This was added by the same editor who earlier tried to push a huge table containing a similar graphic (without the "masonic" symbols) into the article . This was discussed here, and I think it's safe to assume that there is a consensus that the link should be removed. Thanks. --Hans Adler (talk) 17:47, 11 December 2008 (UTC)
thread_title:  External link to obscure notation 

message: The summary says it all. To someone who knows what they are doing -- please fix. 
DLA (talk) 22:58, 24 March 2009 (UTC)
replies: text: They are commonly called truth tables in the literature. — Carl (CBM · talk) 00:24, 25 March 2009 (UTC)

text: Could you explain exactly why the tables in this article should be called Karnaugh maps and not truth tables? — Carl (CBM · talk) 05:19, 1 April 2009 (UTC)

text: The diagrams happen to be Karnaugh maps, but that does not mean that they are not truth tables. Truth table is simply an assignment of truth values of a Boolean function to all possible combinations of truth values of its input, the layout of the table is completely irrelevant if you are going to visualize it. In particular, see truth table#Condensed truth tables for binary operators for the layout used here. As Carl pointed out, these diagrams are usually called truth tables in the literature, whereas Karnaugh maps are only referred to in very specialized contexts (integrated circuit design). — Emil J. 12:59, 1 April 2009 (UTC)
replies: text: The tables in this article look like truth tables (a) to me (b) and as exampled in the article Karnaugh Map. I propose we agree any preferred terminology in the (as yet empty) section of [Wikipedia:WikiProject Logic/Standards for notation]--Philogo (talk) 13:02, 1 April 2009 (UTC)
thread_title:  Karnaugh maps (2-variable k-map) are incorrectly referred to as Truth Tables 

message: The article appears to me to be somewhat ambigous in its use of the term "logical connective"/"truth-functional connective" A logical conenective/truth-functional connective appears to mean variously (a) a symbol such as ,  &c which is a truth-function (b) a symbol such as ,  &c when used as to represent a truth-function (c) a truth-function that can be represented by a a symbol such as ,  &c.   (The ambiguity is perhaps akin to confusing/confounding numbers and numerals, or the plus-sign with the fucntion sum.)  Eg. we should be clear when we are talking about (i) a negation sign or symbol, like  (ii) the negation function.  We should be clear whether it is the symbols or the functions whcih are propery called logical connectives/truth-functional connectives.--Philogo (talk) 14:06, 2 April 2009 (UTC)
thread_title:  ambiguity 

message: As someone coming from constructive logic and computer science, I am used to a much broader definition of "logical connective" than what is implied by this article.  Although there is a brief mention of finite-valued logic in the section on arity, most of the article is heavily biased towards boolean logic.  I'm especially disturbed that this bias even sneaks into the section on natural language.  Of course so is a logical connective!  It combines two sentences to form a new sentence, and its meaning is uniquely determined by the meaning of those subsentences—you just can't model the meaning of those sentences by boolean truth values.  Perhaps much of the material in this article should be moved to a separate article on Boolean operators, and the Logical connective article could be streamlined to only discuss logical connectives in general terms? Noamz (talk) 16:21, 24 June 2009 (UTC)
replies: text: Well, no.  "So" depends on the extrinsic meaning of the sentences, not just their truth values, boolean or not.  I don't know of an example from a constructive logic where it makes sense.  Perhaps you could elaborate?  — Arthur Rubin  (talk) 20:25, 24 June 2009 (UTC)
replies: text: Yes, that's exactly what I said: the meaning of "so" depends on the meaning of its subsentences.  I did not know how broadly we are construing "truth value", which is why I used the term meaning.  Backing up a bit, perhaps what I should have first suggested is that we modify the lede.  Instead of, The truth value of the compound is uniquely determined by the truth values of the simpler sentences, I would just write something like, A connective is compositional when the meaning of the compound is determined by the meaning of the simpler sentences.  In the usage I've been exposed to, a "logical connective" can basically be any way of combining propositions, so long as its meaning can be defined compositionally.  Note that I count modal operators as logical connectives (and there are a gazillion papers on linear logic that do likewise). Noamz (talk) 03:25, 25 June 2009 (UTC)

text: Perhaps the article should have a small section saying there are other logics which don't follow the rules but I think this article is right to be at the straightforward propositional logic level. No need to muddle it up with things like quantum logic. Dmcq (talk) 10:30, 25 June 2009 (UTC)

text: I agree with Noam's suggestion.  A more dramatic bias towards classical propositional logic has happened in the case of satisfiability, which used to house an article that at least tangentially mentioned the general model-theoretic definition of when a model is satisfiable , but now is a redirect to Boolean satisfiability problem.  Fortunately, model theory does define unsatisfiable. — Charles Stewart (talk) 19:29, 26 June 2009 (UTC)

text: Postscript — I've created Satisfiability and validity, which is a stub that is meant to be a more informal introduction to the concepts than found in model theory.  I've just realised that interpretation (logic) is meant to be just that, so I have to think about merging it. — Charles Stewart (talk) 20:35, 26 June 2009 (UTC)
thread_title:  Boolean bias 

message: I've  slightly changed the table  , because the index elements of a matrix should be ordered lexicographically, as it is done e.g. in Karnaugh maps. So 0/false should be next to the matrice's orgin, not 1/true. 
Venn diagrams in white and red are more usual, because books with two ink colors were done rather in black and red than in black and light blue. Some examples: University of Leicester; University of Illinois; The Geometry of Logic by S. H. Cullinane 
These Venns (without the unnecesseary blue margin) are already used in the single articles like Logical conjunction.
Lipedia (talk) 17:15, 19 May 2010 (UTC)
thread_title: Small changes in the table

message: see Wikipedia:WikiProject Logic/Standards for notation#Symbols
It is raining if I am indoors (Q  P) <- fail fix it  —Preceding unsigned comment added by 85.231.122.178 (talk) 19:17, 16 February 2011 (UTC)
thread_title:  Standard Notation 

message: It is possible to define logical operators in terms of only conjunction (and) and negation (not). I have added this for disjunction (or) as it is common, well known and occasionally useful to be able to do this for disjunction in particular, and shows how each operator can be formed in its most basic alphabet. Would it be useful to add it to others? 86.0.254.239 (talk) 16:15, 5 May 2011 (UTC)
thread_title:  Logical operators in terms of conjunction and negation 

message: The following excerpt from the article is completely incoherent.
"Is some new technology (such as reversible computing, clockless logic, or quantum dots computing) "functionally complete", in that it can be used to build computers that can do all the sorts of computation that CMOS-based computers can do? If it can implement the NAND operator, only then is it functionally complete."
I would correct it, but I honestly cannot make sense of this. 75.72.7.108 (talk) 18:04, 28 July 2011 (UTC)
replies: text: I removed the paragraph.  It didn't make sense, and it didn't appear to add anything to the article. Justin W Smith talk/stalk 18:49, 28 July 2011 (UTC)
thread_title: Writing

message: So, in absence of further objections, tomorrow I proceed to following steps:
# Download all images from commons:Category:0 and 1 circle Johnston diagrams and commons:Category:Red and white Johnston diagrams;
# Change red to violet     by script and upload updated versions with links to this discussion;
# Replace "Category:Red and white Johnston diagrams" with commons:Category:Violet and white Johnston diagrams;
# Replace mentioning of red with violet in wikis, if necessary.
I do not intend to make other changes to SVGs now. Incnis Mrsi (talk) 12:13, 24 April 2012 (UTC)
replies: text: This image has the color I was talking about - a light violet. The darker violet, for me, doesn't have much contrast with the black border. — Carl (CBM · talk) 13:02, 24 April 2012 (UTC)

text: Now I lean to creation of completely new design. Please, propose colors and proportions. My proposal is to retain orthogonally intersecting circles from Lipedia's design, with not so thick outline, filled with a color m.b. slightly lighter than proposed earlier (say, #9000FF    ) but darker than in , and without any foreign elements such as borders or margins. Incnis Mrsi (talk) 18:58, 24 April 2012 (UTC)
thread_title:  Resolution 

message: In the section "natural language",
I removed from the table a line incorrectly stating that "only if" is the converse implication.  To the contrary, "P only if Q" means the implication, P implies Q.
As I am in a hurry - this implies error prone - I have not introduced a corrected version.
Wlodr (talk) 14:54, 20 July 2019 (UTC)
replies: text: This depends on how to write it down. “Only if P, then Q” – the converse implication P ← Q, certainly. Incnis Mrsi (talk) 15:05, 20 July 2019 (UTC)
thread_title:  only if 

message: 2 slightly different symbols are used: with the slash either *after* the arrow or in the *middle* of it (this second, IMO preferable symbol appears in the "redundancy - 2 symbols" section) Confused me for a minute, anyway
2A00:23C6:B211:D100:2598:1B13:2DDC:B828 (talk) 07:52, 5 October 2020 (UTC)
thread_title:  NIMPLY / Material implication 

message: The reference to software compilers in the Order of precedence section seems abrupt and out of context.
Maybe the section should be expanded?
Abd.nh (talk) 19:54, 28 October 2020 (UTC)
thread_title:  About the Order of precedence section 

message: I have a few doubts in the 5th row, i.e. the word "either...or...".
1, The interpretation of the word "either...or..." may be subjective. To me, this word applies to two exclusive terms which belong to the same system to categorize things. On the other hand, it is not uncommon that people use "inclusive disjunction" interpretations (esp. when it is convenient and short in natural languages), for example, "the solution is either x>0 or y>0", althou it is equivalent to "either (x>0 AND y>0), or (x>0 AND y<=0), or (x<=0 AND y>0)" if we use a categorization system using both x and y variables. Is "exclusive disjunction" more applicable than "inclusive disjunction", or vice versa? Or shall we delete this row completely since this depends on subjective interpretations of the natural language word "either...or..."?
2. The symbol "⊕" seems the logical connective "exclusive disjunction", or the logic gate "XOR". Shall it be "∨" if we go with the interpret of "either...or" as "inclusive disjunction"? Or shall we change the other columns for this row, since they ("inclusive disjuction", "⊕") are not consistent if I understand this issue correctly.
3. The 4th column, i.e. "Logical gate", shall use a term for logical gate. So the term for this row shall be "OR" (a logic gate term) if "inclusive disjunction" (a logical / boolean connective term), or "XOR" if "exclusive disjunction". It seems the term issue only occurs in the 5th row ("either...or..."), all other rows are fine.
4, This row went through a couple of revisions in history. I believe it might be due to the issue of different subjective interpretations of the word "either...or..." as described in the first doubt. This suggests that we might be better off removing the row completely. Or we shall put an extra footnote for readers about the possible subjective interpretations from the unprecise natural language word "either...or" to a precise mathematical logic concept (i.e. a logical connective). At least, we shall make the column elements in this row consistent with each other and error free. IMHO, the current edition (with the inconsistency between "inclusive disjuction" and "⊕" introduced by the revision "06:56, 16 December 2020‎", and the none logic gate term "Logical disjunction" introduced by the revision "11:54, 26 February 2021‎") may cause confusions for readers unfamiliar with this topic.
Need some help from knowledgeable Wikipedia fellows since I'm far from an expert in this topic (or I won't read this article).
:Thanks for pointing this out. I've trimmed the list and added some information above it. As for exclusive disjunction, it's not so much that it's subjective in the sense of different people having different opinions. It's more that disjunction can get different interpretations in different syntactic configurations and discourse contexts. I recommend this or this if you wanna read more. Botterweg14 (talk) 23:49, 11 March 2021 (UTC)
thread_title:  Doubts of the table in Section "In language", Subsection "Natural language"