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This article was nominated for merging with Logical constant in the past. The result of the discussion was keep. |
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)
@ Richard B. Frost: But is not a comparator that which takes two arguments and gives a boolean? Therefore, can a logical operator not be thought of as a kind of comparator? EditorPerson53 ( talk) 22:38, 6 February 2022 (UTC)
We have the following pairs of boolean/logical operators:
and the three-way equivalence:
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)
Why was this moved? Dysprosia 03:58, 28 May 2005 (UTC)
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:
Gregbard 05:31, 28 June 2007 (UTC)
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)
Interestingly, the same diagram (Image:Logictesseract.jpg) is already on wikipedia under Hasse diagram. Along with this information, I'm looking for articles by Zellweger, Shea. There is relevant info at Finite Geometry; Lindenbaum-Tarski algebra, and maybe someday at Geometry of logic. I will keep looking. Be well, Gregbard 11:08, 1 August 2007 (UTC)
I'm removing the "relative strength of operators" section. Based on this link provided by Gregbard, I figured out what is intended - that if you look at a particular 16 element sublattice of the Lindenbaum algebra of propositional logic, it gives you a way to rank the logical strength of the operators based on the partial ordering of the Lindenbaum algebra. But the link does not actually discuss that, I had to fill in the details myself. Moreover, I can't see any reason why the ratio of incoming to outgoing arrows is important - the Hasse diagram hides the transitivity of the partial order. Lacking any evidence that this method of ranking strengths is in the literature, or an important fact about the logical connectives, I'm moving the section to the talk page. — Carl ( CBM · talk) 15:11, 5 August 2007 (UTC)
{{ OR|section}}
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.
The relative strength of the 16 binary logical operators: T ↑ → ~p ← ~q ↓ ∨ q ⊄ p ⊅ & F 0 1/3 1/3 1 1/3 1 1 3 1/3 1 1 3 1 3 3 ∞
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)
The logical operators can be expressed in terms of sets (where ∅ represents the empty set):
Set Theoretic Definitions of Logical Operators ∅ - Contradiction () { ∅ , { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } - Tautology () { ∅ } - NOR (↓) { { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } - OR () { { ∅ } } - Material nonimplication (⊅) { ∅ , { { ∅ } } , { ∅ , { ∅ } } } - Material implication (⊃) { ∅, { ∅ } } - Not q { { { ∅ } } , { ∅ , { ∅ } } } - q { { { ∅ } } } - Converse nonimplication (⊄) { ∅ , { ∅ } , { ∅ , { ∅ } } } - Converse implication (⊂) { ∅ , { { ∅ } } } - Not p { { ∅ } , { ∅ , { ∅ } } } - p { { ∅ } , { { ∅ } } } - Exclusive disjunction () { ∅ , { ∅ , { ∅ } } } - Biconditional () { ∅ , { ∅ } , { { ∅ } } } - NAND (↑ or |) { { ∅ , { ∅ } } } - Conjunction ()
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, - Ste vertigo 02:19, 6 August 2007 (UTC)
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.
-- 75.15.135.58 06:45, 4 September 2007 (UTC)
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)
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)
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)
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)
How's that? I tried to fix it so that "one or two" is no longer present, and so that it all makes sense. I don't think I changed any of the meaning, just made it clearer and neater. Djk3 ( talk) 23:07, 24 March 2008 (UTC)
I changed the colors in the truth-table to alternating shades of white/light gray. I understand that the colors were there as an illustrative tool, but it really made the table muddy. Maybe there's another way we can present that information. Djk3 ( talk) 18:48, 29 March 2008 (UTC)
Alternative denial | |||||||||||||||
Notation | Truth table | Venn diagram | |||||||||||||
P NAND Q P | Q P → ¬Q ¬P ← Q ¬P OR ¬Q |
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Alternative denial | ||||||||||||||||
Notation | Equivalent formulas |
Truth table | Venn diagram | |||||||||||||
P NAND Q P | Q |
P → ¬Q ¬P ← Q ¬P OR ¬Q |
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Alternative denial | ||||||||||||||||
Notation | Equivalent formulas |
Truth table | Venn diagram | |||||||||||||
P NAND Q P | Q |
P → ¬Q ¬P ← Q ¬P OR ¬Q |
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8 | 9 | A | B | C | D | E | F |
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)
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)
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EJ and I disagree about what the lede should contain. I would like to discuss that here.
A Wikipedia article, especially the first paragraph, should be readable by the average, intelligent person, who has no training in the area under discussion. Exceptions are allowed in the case of highly technical articles, Ascending chain condition for example. But logic, and logical connectives, are basic to math and computer science, and so this article should be aimed at the introductory level. For that reason, I think it is best to begin the article with the five most commonly used logical connectives (I can site a dozen books that begin that way if you want me to, but I imagine anyone else reading this could do the same), instead of leaping into the question of the infinitely many n-ary logical connectives.
Here, line by line, are the problems I had with the other introduction:
This sentence could only be read by a mathematician or upper division math major, who would already know what a logical connective was. The beginner will not understand "logical constant" or "syntactic operation", and may also stumble over "well-formed formula", all concepts usually introduced after "logical connective". Also, there is no need to put all the synonyms into the first sentence, where they are stumbling blocks for the beginner. They can come later.
This is simply untrue, at least without considerably more discussion. What is true is that if A is a well-formed formula and B is a well-formed formula and # is a binary logical connective, then (A)#(B) is a well-formed formula. But this is too technical for the lede.
Before this discussion should come a discussion of truth values. Also "applied to" is vague, and easily misunderstood.
This will strike a lay reader as meaningless and a mathematician as wrong. (A mathematician would want something like "An n-ary logical connective can be seen as a function which maps n-tuples of truth values to truth values.")
Again, a comment unnecessary for a mathematician and opaque to a non-mathematician. Since the most common logical connectives are either unary or binary, it is hardly necessary to get into n-ary connectives in the lede.
I'm sure you can find a book that describe T and F as nullary connectives but that description does not appear in any of the textbooks or research papers I use regularly, and is in any case a construction that would only appeal to a research mathematician who already knows everything in this article. An article should be useful.
After being careful about arity above, you now omit the word "binary" which is essential here. Without "binary", the "finitely" is wrong. With "binary", the word "finitely" should be replace by the word "two".
And I have no problem with this sentence, if you would like to restore it to the article.
Rick Norwood ( talk) 13:14, 30 May 2008 (UTC)
In logic, the five standard logical connectives are the binary connectives, "AND", "OR", "IMPLIES", and "BICONDITIONAL", which connect two logical statements, and the unary connective "NOT", which modifies one logical statement.
Step back from this. Suppose you wondered what a "trig. function" was. You turn to Wiki and it says:
The three standard trig. functions ar sin, tan and cos.
Is a reader who does not know want "trig. function" means, likely to know what sin, tan and cos are? Then how would he be any the wiser. Explanation by example only works of the examples are more familiar than the term to be explained.
It is better to give give the examples after. Eg:
Mammal: the class of verterbrate animal that bears its young live and suckles them Eg. Dog, Cow, Kangaroo. Compare other vertebrebrates: Reptile, Fish, Bird.
--Philogo 13:36, 30 May 2008 (UTC) --Philogo 13:36, 30 May 2008 (UTC)
Rick, I have neither the time nor desire to getting involved in a lengthy discussion, especially given your attitude that you only show the willingness to discuss after reverting to your version of the lead. The previous lead has been there for many months, and people were happy with it. Instead, I have modified your text point by point where I've seen serious issues with it. — EJ ( talk) 14:15, 30 May 2008 (UTC)
I agree. Your recent edit is an improvement. Rick Norwood ( talk) 14:50, 30 May 2008 (UTC)
I have boldy added some content at the beginning rather than discussing here first. Feel free to edit or del it if you disagree with it.--Philogo 18:57, 30 May 2008 (UTC)
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)
The article is describing logical connectives (a) as they occur in natural language (as by words like and and or, and also (b) as they occur in logic and represented by our familiar symbols. I think that is a worthy aim, but I am just wondering if the article is clear on this and not confusing to the reader, assuming as we should that they are new to this subject.--Philogo 23:12, 30 May 2008 (UTC)
I agree with Lambiam. The lede uses and rather than & only to improve readability by the lay reader. Rick Norwood ( talk) 16:38, 31 May 2008 (UTC)
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:
I think it is always good to come with an example as soon as possible, and the next sentence might be:
Then I think we should list the five most common connectives, and finish off the lede with:
I don't see anything else that urgently needs to be put in the lede. -- Lambiam 03:16, 2 June 2008 (UTC)
Even though I wrote some of the new lede, I tend to agree with Lambiam. I was trying to preserve as much of the earlier lede as possible, and it identified the logical connective with its truth table, which is certainly one way to go. If nobody else has already fixed this, I'll take a shot later on today, working along the lines Lambiam suggests. Rick Norwood ( talk) 13:38, 2 June 2008 (UTC)
I've read that diagrams like the ones depicted in this article are actually called
Johnston diagrams rather than Venn diagrams. I'd change in on the article but I can't find the table template -- thoughts?
Jheiv (
talk)
09:20, 1 August 2008 (UTC) Nevermind. It seems very few people call these things Johnston diagrams, I have trouble finding mention of said diagram on the web or in logic books.
Jheiv (
talk)`
What happened to my article? Whoever deleted it obviously doesn't know the difference between philosophy and networking technology in search engines. I'm putting it back up, and if someone has an issue with it, I'd like a thorough explaination. Colonel Marksman ( talk) 08:55, 16 November 2008 (UTC)
I don't favor the giant imagemap, for the following reasons:
— Carl ( CBM · talk) 21:01, 18 November 2008 (UTC)
Hi,
what I like about the representation above is the following:
Concerning accessibility:
It is true, that articles should also be accessible to blind people, and for plain text uses, may it be for wapedia or whatever. I take that very serious. But in these cases a table containing wikipedia math symbols would be not useful as well. Thus a good solution for all kinds of users is to keep the imagemap template in the article, and to add a note like this: " Here you find this information in plain text."
The lines in this table should simply look like this:
The information displayed in the Hasse diagram can be shown by a simple list of conclusions like these:
I can create this subpage Logical connectives text table, if you agree that it makes sense. I think it does.
Greetings, Boolean hexadecimal ( talk) 12:19, 26 November 2008 (UTC)
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)
The summary says it all. To someone who knows what they are doing -- please fix.
DLA ( talk) 22:58, 24 March 2009 (UTC)
I respectfully disagree. See the Wikipedia entries for Karnaugh Map and Truth Table, both of which treat them as distinctly different concepts. I think that this Logical Connective Wikipedia entry should be consistant with the Karnaugh Map and Truth Table Wikipedia entries. Otherwise, I think that this entry is helpful.
DLA ( talk) 22:23, 31 March 2009 (UTC)
Would some kind ed look at and make work my non-functioning ref in the first sentence of this new section.-- Philogo ( talk) 22:35, 1 April 2009 (UTC)
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)
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)
This article was originally very limited, covering only truth-functional connectives in formal languages. At some point, I believe User:Philogo began to add some text about natural-language connectives. This is a good thing to add, but unfortunately it is outside the knowledge of many mathematics editors, including myself, so we can't really help with that. I believe there is a significant amount of additional material that could be added, modal connectives and other non-truth-functional connectives included. — Carl ( CBM · talk) 12:32, 25 June 2009 (UTC)
Hi, I would like to offer this table for inclusion in the properties section. Any comments or modifications are welcome. Thanks Zulu Papa 5 ☆ ( talk) 05:18, 1 November 2009 (UTC)
Preservation properties | Logical connective sentences |
---|---|
True and false preserving: | Logical conjunction (AND, ) • Logical disjunction (OR, ) |
True preserving only: | Tautology ( ) • Biconditional (XNOR, ) • Implication ( ) • Converse implication ( ) |
False preserving only: | Contradiction ( ) • Exclusive disjunction (XOR, ) • Nonimplication ( ) • Converse nonimplication ( ) |
Non-preserving: | Proposition • Negation ( ) • Alternative denial (NAND, ) • Joint denial (NOR, ) |
Where is this talked about in the literature please? What is its application? Thanks Dmcq ( talk) 09:49, 1 November 2009 (UTC)
What's so special about these two properties, as opposed to monotonicity, affineness, self-duality, or any other properties defining a clone in Post's lattice for that matter? To me the table looks like a random selection of trivial information. — Emil J. 11:18, 4 November 2009 (UTC)
Ok, I talked myself into placing this on the validity page with a short (see: validity) in this article. Thanks for the feedback. Zulu Papa 5 ☆ ( talk) 16:16, 5 November 2009 (UTC)
I've slightly changed the table [6] [7], 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)
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)
Shouldn't this article talk about those too? Are those not called logical? See [8] for instance. I have the impression the definitions in the lead are not really sourced. Tijfo098 ( talk) 14:57, 30 March 2011 (UTC)
Another way to say it is that this article is about the truth-functional connectives relevant to propositional logic. We can't write an article about every possible type of logical connective including modal operators, infinitary quantifiers, the operators from linear logic, and everything else, because that's not a topic that anyone actually writes about in the literature. Each logical system has its own syntax that includes particular connectives, so an article that tried to come up with a general definition of "logical connective" would be original research. On the other hand, many books (including Enderton's book in the references) cover the topic of arbitrary truth-functional logical connectives. That is an important topic for us to cover, and it's what this article is intended to discuss. — Carl ( CBM · talk) 16:34, 30 March 2011 (UTC)
“ | McGee's strategy is to invoke semantic notions instead of modal ones: he suggests that “[a] connective is a logical connective if and only if it follows from the meaning of the connective that it is invariant under arbitrary bijections” (McGee 1996, 578) | ” |
[12]. So, I see no option but to split this page. It's ridiculous to include two different notions in the same article and revert sourced attempts to distinguish them. Tijfo098 ( talk) 23:00, 4 April 2011 (UTC)
I am happy with the hatnote that clarifies this page is about logical connectives in classical (propositional) logic. There is no general concept of "logical connective" in an arbitrary logic that we could write about; the syntax varies so much, all we would be able to do is make a list of connectives in this logic, and this logic, and this logic. On the other hand there is a lot of philosophy discussion on arbitrary logical constants that is not really related to them being connectives (quantifiers are also important) but which should be covered in that article rather than this one. Phrases such as "whereupon" and "that is" are not really "logical" connectives, unless you think natural language is a sort of logic. — Carl ( CBM · talk) 11:51, 5 April 2011 (UTC)
I am not happy with the hatnote that indeed clarifies that this page is about logical connectives in (two-valued) classical propositional logic, but that leaves no room for non two-valued interpretations of logical connectives. In particular, that leaves no room neither for discussing the use of this very same concept of logical connective in intuitionistic logic or in non-necessarily two-valued interpretations of classical logic. I can understand that many readers expects "logical connective" to be a rough synonymous of "logical operator over 0 and 1" as they maybe just learned in their digital logic course, but this is not the only way to refer to the "digital logic" meaning since for instance "two-valued logical operators" would be as relevant if not more. On the other side, I don't know other common names for what logicians call "logical connective" (i.e. a formal symbol to build new formulas by composition). What can be done to solve the problem? For instance, logical operator is a redirect to logical connective. Could it be possible to exploit the difference of meaning between operator (the connective interpreted on some domain) and connective (the symbol properly speaking) to satisfy all needs at best? -- Hugo Herbelin ( talk) 20:47, 17 April 2011 (UTC)
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)
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)
I propose to replace red-coloured diagrams such as with green-coloured ones. Also I think that the border should be removed from SVGs: we can use table borders. Incnis Mrsi ( talk) 12:38, 9 March 2012 (UTC)
So, in absence of further objections, tomorrow I proceed to following steps:
I do not intend to make other changes to SVGs now. Incnis Mrsi ( talk) 12:13, 24 April 2012 (UTC)
I created the original images that served this purpose. They were replaced by these red ones. The original ones I made had circles which were labeled. So I would support any replacement, however the images themselves should be labeled with circles "A" and "B" (or preferably "P" and "Q"). Greg Bard ( talk) 20:37, 24 April 2012 (UTC)
Do what you want in the article, but please keep my red and white files out of this. If you want to upload something new you may overwrite the files in commons:Category:Blue and white Johnston diagrams, which are unused.
Red doesn't have any "negative" meaning when there is no green in the same context: This map doesn't show which territory is not the USA, and this one doesn't show the places to avoid when you are searching for Israel (compare this category). Here and here red is used to highlight the prime numbers. Here and here areas of Venn diagrams are highlighted. Red causes awareness, and that's also the reason for the use in anti-logos - not any symbolic meaning of this color.
Since a year there are the property sections like this one. Don't forget to delete the illustrations from them (I'm sure CBM will like that) or to upload some 3-circle diagrams in the new color. And don't forget to remove anything red from Logical biconditional. Lipedia ( talk) 15:54, 24 April 2012 (UTC)
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)
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)
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)
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).
The introduction states: "A logical connective is a logical constant used to connect two or more formulas" But only one sentence later, it states: "Common connectives include negation"
This is a contradiction.
Either negation is not a connective, or a connective need not join two or more formulas.
EditorPerson53 ( talk) 22:31, 6 February 2022 (UTC)
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This article was nominated for merging with Logical constant in the past. The result of the discussion was keep. |
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)
@ Richard B. Frost: But is not a comparator that which takes two arguments and gives a boolean? Therefore, can a logical operator not be thought of as a kind of comparator? EditorPerson53 ( talk) 22:38, 6 February 2022 (UTC)
We have the following pairs of boolean/logical operators:
and the three-way equivalence:
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)
Why was this moved? Dysprosia 03:58, 28 May 2005 (UTC)
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:
Gregbard 05:31, 28 June 2007 (UTC)
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)
Interestingly, the same diagram (Image:Logictesseract.jpg) is already on wikipedia under Hasse diagram. Along with this information, I'm looking for articles by Zellweger, Shea. There is relevant info at Finite Geometry; Lindenbaum-Tarski algebra, and maybe someday at Geometry of logic. I will keep looking. Be well, Gregbard 11:08, 1 August 2007 (UTC)
I'm removing the "relative strength of operators" section. Based on this link provided by Gregbard, I figured out what is intended - that if you look at a particular 16 element sublattice of the Lindenbaum algebra of propositional logic, it gives you a way to rank the logical strength of the operators based on the partial ordering of the Lindenbaum algebra. But the link does not actually discuss that, I had to fill in the details myself. Moreover, I can't see any reason why the ratio of incoming to outgoing arrows is important - the Hasse diagram hides the transitivity of the partial order. Lacking any evidence that this method of ranking strengths is in the literature, or an important fact about the logical connectives, I'm moving the section to the talk page. — Carl ( CBM · talk) 15:11, 5 August 2007 (UTC)
{{ OR|section}}
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.
The relative strength of the 16 binary logical operators: T ↑ → ~p ← ~q ↓ ∨ q ⊄ p ⊅ & F 0 1/3 1/3 1 1/3 1 1 3 1/3 1 1 3 1 3 3 ∞
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)
The logical operators can be expressed in terms of sets (where ∅ represents the empty set):
Set Theoretic Definitions of Logical Operators ∅ - Contradiction () { ∅ , { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } - Tautology () { ∅ } - NOR (↓) { { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } - OR () { { ∅ } } - Material nonimplication (⊅) { ∅ , { { ∅ } } , { ∅ , { ∅ } } } - Material implication (⊃) { ∅, { ∅ } } - Not q { { { ∅ } } , { ∅ , { ∅ } } } - q { { { ∅ } } } - Converse nonimplication (⊄) { ∅ , { ∅ } , { ∅ , { ∅ } } } - Converse implication (⊂) { ∅ , { { ∅ } } } - Not p { { ∅ } , { ∅ , { ∅ } } } - p { { ∅ } , { { ∅ } } } - Exclusive disjunction () { ∅ , { ∅ , { ∅ } } } - Biconditional () { ∅ , { ∅ } , { { ∅ } } } - NAND (↑ or |) { { ∅ , { ∅ } } } - Conjunction ()
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, - Ste vertigo 02:19, 6 August 2007 (UTC)
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.
-- 75.15.135.58 06:45, 4 September 2007 (UTC)
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)
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)
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)
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)
How's that? I tried to fix it so that "one or two" is no longer present, and so that it all makes sense. I don't think I changed any of the meaning, just made it clearer and neater. Djk3 ( talk) 23:07, 24 March 2008 (UTC)
I changed the colors in the truth-table to alternating shades of white/light gray. I understand that the colors were there as an illustrative tool, but it really made the table muddy. Maybe there's another way we can present that information. Djk3 ( talk) 18:48, 29 March 2008 (UTC)
Alternative denial | |||||||||||||||
Notation | Truth table | Venn diagram | |||||||||||||
P NAND Q P | Q P → ¬Q ¬P ← Q ¬P OR ¬Q |
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Alternative denial | ||||||||||||||||
Notation | Equivalent formulas |
Truth table | Venn diagram | |||||||||||||
P NAND Q P | Q |
P → ¬Q ¬P ← Q ¬P OR ¬Q |
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Alternative denial | ||||||||||||||||
Notation | Equivalent formulas |
Truth table | Venn diagram | |||||||||||||
P NAND Q P | Q |
P → ¬Q ¬P ← Q ¬P OR ¬Q |
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8 | 9 | A | B | C | D | E | F |
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)
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)
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EJ and I disagree about what the lede should contain. I would like to discuss that here.
A Wikipedia article, especially the first paragraph, should be readable by the average, intelligent person, who has no training in the area under discussion. Exceptions are allowed in the case of highly technical articles, Ascending chain condition for example. But logic, and logical connectives, are basic to math and computer science, and so this article should be aimed at the introductory level. For that reason, I think it is best to begin the article with the five most commonly used logical connectives (I can site a dozen books that begin that way if you want me to, but I imagine anyone else reading this could do the same), instead of leaping into the question of the infinitely many n-ary logical connectives.
Here, line by line, are the problems I had with the other introduction:
This sentence could only be read by a mathematician or upper division math major, who would already know what a logical connective was. The beginner will not understand "logical constant" or "syntactic operation", and may also stumble over "well-formed formula", all concepts usually introduced after "logical connective". Also, there is no need to put all the synonyms into the first sentence, where they are stumbling blocks for the beginner. They can come later.
This is simply untrue, at least without considerably more discussion. What is true is that if A is a well-formed formula and B is a well-formed formula and # is a binary logical connective, then (A)#(B) is a well-formed formula. But this is too technical for the lede.
Before this discussion should come a discussion of truth values. Also "applied to" is vague, and easily misunderstood.
This will strike a lay reader as meaningless and a mathematician as wrong. (A mathematician would want something like "An n-ary logical connective can be seen as a function which maps n-tuples of truth values to truth values.")
Again, a comment unnecessary for a mathematician and opaque to a non-mathematician. Since the most common logical connectives are either unary or binary, it is hardly necessary to get into n-ary connectives in the lede.
I'm sure you can find a book that describe T and F as nullary connectives but that description does not appear in any of the textbooks or research papers I use regularly, and is in any case a construction that would only appeal to a research mathematician who already knows everything in this article. An article should be useful.
After being careful about arity above, you now omit the word "binary" which is essential here. Without "binary", the "finitely" is wrong. With "binary", the word "finitely" should be replace by the word "two".
And I have no problem with this sentence, if you would like to restore it to the article.
Rick Norwood ( talk) 13:14, 30 May 2008 (UTC)
In logic, the five standard logical connectives are the binary connectives, "AND", "OR", "IMPLIES", and "BICONDITIONAL", which connect two logical statements, and the unary connective "NOT", which modifies one logical statement.
Step back from this. Suppose you wondered what a "trig. function" was. You turn to Wiki and it says:
The three standard trig. functions ar sin, tan and cos.
Is a reader who does not know want "trig. function" means, likely to know what sin, tan and cos are? Then how would he be any the wiser. Explanation by example only works of the examples are more familiar than the term to be explained.
It is better to give give the examples after. Eg:
Mammal: the class of verterbrate animal that bears its young live and suckles them Eg. Dog, Cow, Kangaroo. Compare other vertebrebrates: Reptile, Fish, Bird.
--Philogo 13:36, 30 May 2008 (UTC) --Philogo 13:36, 30 May 2008 (UTC)
Rick, I have neither the time nor desire to getting involved in a lengthy discussion, especially given your attitude that you only show the willingness to discuss after reverting to your version of the lead. The previous lead has been there for many months, and people were happy with it. Instead, I have modified your text point by point where I've seen serious issues with it. — EJ ( talk) 14:15, 30 May 2008 (UTC)
I agree. Your recent edit is an improvement. Rick Norwood ( talk) 14:50, 30 May 2008 (UTC)
I have boldy added some content at the beginning rather than discussing here first. Feel free to edit or del it if you disagree with it.--Philogo 18:57, 30 May 2008 (UTC)
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)
The article is describing logical connectives (a) as they occur in natural language (as by words like and and or, and also (b) as they occur in logic and represented by our familiar symbols. I think that is a worthy aim, but I am just wondering if the article is clear on this and not confusing to the reader, assuming as we should that they are new to this subject.--Philogo 23:12, 30 May 2008 (UTC)
I agree with Lambiam. The lede uses and rather than & only to improve readability by the lay reader. Rick Norwood ( talk) 16:38, 31 May 2008 (UTC)
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:
I think it is always good to come with an example as soon as possible, and the next sentence might be:
Then I think we should list the five most common connectives, and finish off the lede with:
I don't see anything else that urgently needs to be put in the lede. -- Lambiam 03:16, 2 June 2008 (UTC)
Even though I wrote some of the new lede, I tend to agree with Lambiam. I was trying to preserve as much of the earlier lede as possible, and it identified the logical connective with its truth table, which is certainly one way to go. If nobody else has already fixed this, I'll take a shot later on today, working along the lines Lambiam suggests. Rick Norwood ( talk) 13:38, 2 June 2008 (UTC)
I've read that diagrams like the ones depicted in this article are actually called
Johnston diagrams rather than Venn diagrams. I'd change in on the article but I can't find the table template -- thoughts?
Jheiv (
talk)
09:20, 1 August 2008 (UTC) Nevermind. It seems very few people call these things Johnston diagrams, I have trouble finding mention of said diagram on the web or in logic books.
Jheiv (
talk)`
What happened to my article? Whoever deleted it obviously doesn't know the difference between philosophy and networking technology in search engines. I'm putting it back up, and if someone has an issue with it, I'd like a thorough explaination. Colonel Marksman ( talk) 08:55, 16 November 2008 (UTC)
I don't favor the giant imagemap, for the following reasons:
— Carl ( CBM · talk) 21:01, 18 November 2008 (UTC)
Hi,
what I like about the representation above is the following:
Concerning accessibility:
It is true, that articles should also be accessible to blind people, and for plain text uses, may it be for wapedia or whatever. I take that very serious. But in these cases a table containing wikipedia math symbols would be not useful as well. Thus a good solution for all kinds of users is to keep the imagemap template in the article, and to add a note like this: " Here you find this information in plain text."
The lines in this table should simply look like this:
The information displayed in the Hasse diagram can be shown by a simple list of conclusions like these:
I can create this subpage Logical connectives text table, if you agree that it makes sense. I think it does.
Greetings, Boolean hexadecimal ( talk) 12:19, 26 November 2008 (UTC)
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)
The summary says it all. To someone who knows what they are doing -- please fix.
DLA ( talk) 22:58, 24 March 2009 (UTC)
I respectfully disagree. See the Wikipedia entries for Karnaugh Map and Truth Table, both of which treat them as distinctly different concepts. I think that this Logical Connective Wikipedia entry should be consistant with the Karnaugh Map and Truth Table Wikipedia entries. Otherwise, I think that this entry is helpful.
DLA ( talk) 22:23, 31 March 2009 (UTC)
Would some kind ed look at and make work my non-functioning ref in the first sentence of this new section.-- Philogo ( talk) 22:35, 1 April 2009 (UTC)
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)
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)
This article was originally very limited, covering only truth-functional connectives in formal languages. At some point, I believe User:Philogo began to add some text about natural-language connectives. This is a good thing to add, but unfortunately it is outside the knowledge of many mathematics editors, including myself, so we can't really help with that. I believe there is a significant amount of additional material that could be added, modal connectives and other non-truth-functional connectives included. — Carl ( CBM · talk) 12:32, 25 June 2009 (UTC)
Hi, I would like to offer this table for inclusion in the properties section. Any comments or modifications are welcome. Thanks Zulu Papa 5 ☆ ( talk) 05:18, 1 November 2009 (UTC)
Preservation properties | Logical connective sentences |
---|---|
True and false preserving: | Logical conjunction (AND, ) • Logical disjunction (OR, ) |
True preserving only: | Tautology ( ) • Biconditional (XNOR, ) • Implication ( ) • Converse implication ( ) |
False preserving only: | Contradiction ( ) • Exclusive disjunction (XOR, ) • Nonimplication ( ) • Converse nonimplication ( ) |
Non-preserving: | Proposition • Negation ( ) • Alternative denial (NAND, ) • Joint denial (NOR, ) |
Where is this talked about in the literature please? What is its application? Thanks Dmcq ( talk) 09:49, 1 November 2009 (UTC)
What's so special about these two properties, as opposed to monotonicity, affineness, self-duality, or any other properties defining a clone in Post's lattice for that matter? To me the table looks like a random selection of trivial information. — Emil J. 11:18, 4 November 2009 (UTC)
Ok, I talked myself into placing this on the validity page with a short (see: validity) in this article. Thanks for the feedback. Zulu Papa 5 ☆ ( talk) 16:16, 5 November 2009 (UTC)
I've slightly changed the table [6] [7], 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)
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)
Shouldn't this article talk about those too? Are those not called logical? See [8] for instance. I have the impression the definitions in the lead are not really sourced. Tijfo098 ( talk) 14:57, 30 March 2011 (UTC)
Another way to say it is that this article is about the truth-functional connectives relevant to propositional logic. We can't write an article about every possible type of logical connective including modal operators, infinitary quantifiers, the operators from linear logic, and everything else, because that's not a topic that anyone actually writes about in the literature. Each logical system has its own syntax that includes particular connectives, so an article that tried to come up with a general definition of "logical connective" would be original research. On the other hand, many books (including Enderton's book in the references) cover the topic of arbitrary truth-functional logical connectives. That is an important topic for us to cover, and it's what this article is intended to discuss. — Carl ( CBM · talk) 16:34, 30 March 2011 (UTC)
“ | McGee's strategy is to invoke semantic notions instead of modal ones: he suggests that “[a] connective is a logical connective if and only if it follows from the meaning of the connective that it is invariant under arbitrary bijections” (McGee 1996, 578) | ” |
[12]. So, I see no option but to split this page. It's ridiculous to include two different notions in the same article and revert sourced attempts to distinguish them. Tijfo098 ( talk) 23:00, 4 April 2011 (UTC)
I am happy with the hatnote that clarifies this page is about logical connectives in classical (propositional) logic. There is no general concept of "logical connective" in an arbitrary logic that we could write about; the syntax varies so much, all we would be able to do is make a list of connectives in this logic, and this logic, and this logic. On the other hand there is a lot of philosophy discussion on arbitrary logical constants that is not really related to them being connectives (quantifiers are also important) but which should be covered in that article rather than this one. Phrases such as "whereupon" and "that is" are not really "logical" connectives, unless you think natural language is a sort of logic. — Carl ( CBM · talk) 11:51, 5 April 2011 (UTC)
I am not happy with the hatnote that indeed clarifies that this page is about logical connectives in (two-valued) classical propositional logic, but that leaves no room for non two-valued interpretations of logical connectives. In particular, that leaves no room neither for discussing the use of this very same concept of logical connective in intuitionistic logic or in non-necessarily two-valued interpretations of classical logic. I can understand that many readers expects "logical connective" to be a rough synonymous of "logical operator over 0 and 1" as they maybe just learned in their digital logic course, but this is not the only way to refer to the "digital logic" meaning since for instance "two-valued logical operators" would be as relevant if not more. On the other side, I don't know other common names for what logicians call "logical connective" (i.e. a formal symbol to build new formulas by composition). What can be done to solve the problem? For instance, logical operator is a redirect to logical connective. Could it be possible to exploit the difference of meaning between operator (the connective interpreted on some domain) and connective (the symbol properly speaking) to satisfy all needs at best? -- Hugo Herbelin ( talk) 20:47, 17 April 2011 (UTC)
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)
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)
I propose to replace red-coloured diagrams such as with green-coloured ones. Also I think that the border should be removed from SVGs: we can use table borders. Incnis Mrsi ( talk) 12:38, 9 March 2012 (UTC)
So, in absence of further objections, tomorrow I proceed to following steps:
I do not intend to make other changes to SVGs now. Incnis Mrsi ( talk) 12:13, 24 April 2012 (UTC)
I created the original images that served this purpose. They were replaced by these red ones. The original ones I made had circles which were labeled. So I would support any replacement, however the images themselves should be labeled with circles "A" and "B" (or preferably "P" and "Q"). Greg Bard ( talk) 20:37, 24 April 2012 (UTC)
Do what you want in the article, but please keep my red and white files out of this. If you want to upload something new you may overwrite the files in commons:Category:Blue and white Johnston diagrams, which are unused.
Red doesn't have any "negative" meaning when there is no green in the same context: This map doesn't show which territory is not the USA, and this one doesn't show the places to avoid when you are searching for Israel (compare this category). Here and here red is used to highlight the prime numbers. Here and here areas of Venn diagrams are highlighted. Red causes awareness, and that's also the reason for the use in anti-logos - not any symbolic meaning of this color.
Since a year there are the property sections like this one. Don't forget to delete the illustrations from them (I'm sure CBM will like that) or to upload some 3-circle diagrams in the new color. And don't forget to remove anything red from Logical biconditional. Lipedia ( talk) 15:54, 24 April 2012 (UTC)
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)
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)
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)
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).
The introduction states: "A logical connective is a logical constant used to connect two or more formulas" But only one sentence later, it states: "Common connectives include negation"
This is a contradiction.
Either negation is not a connective, or a connective need not join two or more formulas.
EditorPerson53 ( talk) 22:31, 6 February 2022 (UTC)