Talk:Boolean logic

order of operations

Is there an official order of operations for boolean logic, like there is for standard mathematical operations? -Ravedave (talk) 23:13, 25 March 2008 (UTC)

Usually, when people have to manipulate expressions with multiple operations, they make up an order of operations. One common convention is that parentheses are done first, then negation, then conjunction and disjunction are done from left to right, then implication is done from left to right. Also, it's common to take $A\to B\to C$ to mean $A\to (B\to C)$, which is important because implication is not associative. But not all authors follow all these rules, and some authors might have other conventions (perhaps conjunction is done before disjunction) so you have to double-check each text. — Carl (CBM · talk) 00:26, 26 March 2008 (UTC)

I pretty much agree. The parens comes first, then NOT. The only debatable part is whether AND or OR has higher priority. I'd always use parens to make it clear. StuRat (talk) 03:06, 28 March 2008 (UTC)

That is totally insane. Everyone knows what 2 * 3 + 4 equals, I can't believe there isn't a standard rule for what "true and false or true" means. Hrm I guess you learn something every day. -Ravedave (talk) 03:54, 28 March 2008 (UTC)

"(true and false) or true" and "true and (false or true)" are both true, so the syntactic ambiguity doesn't make this semantically ambiguous. Truly ambiguous formulae of the form "P and Q or R" are only "false and false or true" and "false and true or true". In Boole's notation, conjunction was written as algebraic multiplication and disjunction as addition, and PQ+R meant, as in standard algebra, (PQ)+R. This is probably the reason why some people give "and" precedence over "or" – which means you need to exercise more care in order to apply De Morgan's laws faultlessly. Not everyone agrees what 1/2·3 means either; is it (1/2)·3 or 1/(2·3)?  --Lambiam 09:26, 28 March 2008 (UTC)

true or false and false is a better example. (true or false) and false = false; true or (false and false) = true. I thought "and before or" was a rule, but I can't find it anywhere... — Preceding unsigned comment added by 216.234.101.74 (talk) 13:38, 19 September 2013 (UTC)

Entire Article Rewrite

I suggest a rewrite for the entire article because of the manner in which it is written. This is supposed to be an encyclopediac entry containing pure fact, not a tutorial.--Trehansiddharth (talk) 00:11, 27 October 2009 (UTC)

This article is a known problem. A number of people tried to solve it at various times. Most notably, an expert (Vaughan Pratt) rewrote this very article several times. The problem is that the unencyclopedic idiosyncrasies and inaccuracies in this article are being defended by an uncooperative editor who believes he is an expert on teaching the topic. If you rewrite this article once more, the odds are that after a while this editor will notice that 'his' article has disappeared once again and will once more resurrect it by creating yet another fork. This will add yet another article to the disambiguation page Boolean algebra. Relevant policy links: WP:OWN, WP:POVFORK. Hans Adler 13:32, 28 October 2009 (UTC)

While I don't like bringing things up at non-article pages, I wonder if StuRat's dogged insistence that his article serves a purpose not served by the other articles on the subject should be brought up at an etiquette page as the violations listed by Hans. As an account of Boolean algebra the article is a disaster. I notice that the many reasons I gave for this a while back have been archived. Perhaps I should list the main ones here again. --Vaughan Pratt (talk) 09:13, 16 January 2010 (UTC)

Problematic article

This article serves no purpose. It has been superseded by more comprehensive articles and lives on in Wikipedia only because its owner User:StuRat revived the old version. The reason it was superseded is because it has the following problems, listed by section number.

Lede: Fails most requirements of WP:LEDE; vacuous definition of subject; covers only history and applications, nothing about main points of article.

1. (Set logic vs. Boolean logic) No definition of subject, just two sentences, content-free other than promising vaguely that there will be an explanation of "set logic" and Boolean logic, promise not subsequently fulfilled.

2. (Terms) First sentence: "Let X be a set." This explains nothing while assuming an understanding of "set." Furthermore the only subsequent appearance of X is "The universe is the set X." This is incoherent. The rest of the section lists the concepts of membership and nonmembership (which have nothing to do with Boolean logic), the empty set, NOT, OR, and AND (referred to as "set operations" which they are not, they are Boolean operations), and the subset and proper-subset relations and their converses (presumably part of "set logic"). Nothing is said about what these concepts are for: are they the promised material on "set logic" (whatever that is) or are they Boolean logic? They seem to be a random mix of the two.

3. (Example) Example of what? We still haven't been told whether this is set logic or Boolean logic. A Venn diagram is given but left undefined in the article. The section then switches abruptly to an incomplete and incoherent discussion of syntax applicable to algebra in general: compound terms are called "chaining," the role of parentheses is explained, and that's it for syntax. Finally "bits" are mentioned and several things that "could be done" with bits are listed.

4. (Properties) Symbols for Boolean operations are introduced here (why not in section 1 or the lede?), and 21 equations organized as ten properties are listed. (I couldn't bear to see nothing concrete said about them so I added "The first three properties define a lattice; the first five define a Boolean algebra. The remaining five are a consequence of the first five" some time ago to try to shore up that section.)

5. (Other notations) Alternative symbols for the Boolean operations. Too trivial to be a whole section.

6. (Basic mathematics use of Boolean terms) Trivial uses.

7. (English language use of Boolean terms) Section begins with an advisory: "Care should be taken when converting an English sentence into a formal Boolean statement." The rest of the section illustrates this with four sentences pointing up this need for care.

8. (Applications) Lists three applications: digital electronic circuit design, databases, search engine queries. This section is a mish-mash of disconnected and incomprehensible sentences ("Whether these gates are wired in series or parallel controls the precedence of the operations"), undefined concepts ("every possible input-output behavior can be modeled by a suitable Boolean expression" -- what is an IO behavior?), concepts already dealt with ("Multiple sets of nested parentheses may also be used, where needed"), false statements ("Any Boolean operation (or operations) which combines two (or more) tables together is referred to as a join"), etc.

Besides these problems intrinsic to the article it is also in violation of WP:OWN and WP:FORK. Absent any purpose for this article, is there any reason not to delete it? --Vaughan Pratt (talk) 10:18, 16 January 2010 (UTC)

Well, let's at least keep the terms of debate straight — there's certainly no reason to delete it; the search term Boolean logic needs to take you somewhere, and as far as I'm aware there's nothing in the article's history so problematic that it needs to be made unavailable except to administrators. The most that's on the table is a redirect-without-merge, which is different from a delete.

I'm not taking a position at the moment as to whether the article should be redirected, with or without a merge. There are, however, clearly too many overlapping articles in the area. I would look favorably on an outcome that wound up with only two articles, one for the structures and one for the calculus. --Trovatore (talk) 09:25, 17 January 2010 (UTC)

I think for a central topic such as this, which has so many facets, the number of articles isn't really the main problem. But all existing articles must be structured sensibly. E.g. we could move Introduction to Boolean algebra to Boolean algebra (over the disambiguation page). It already has some subarticles, but parts of it could perhaps be abbreviated, and then it could have the following subarticles per WP:SUMMARY:

• Boolean algebra (logic), moved over Boolean logic
• Propositional logic
• Boolean algebra (structure)
• Boolean algebras canonically defined

Hans Adler 12:46, 17 January 2010 (UTC)

I really don't think it's a good idea to have the intro article at simply Boolean algebra. I am not aware of any other case where an introduction to... article has been made the primary topic (and if they were, I would still think that was a bad idea and argue against it).

For Boolean algebras it's especially problematic, because many of the links are going to be intending the structure.

As for canonically defined, it needs to be merged into the structure article, as does Boolean ring (assuming that one's still separate; I haven't checked lately). --Trovatore (talk) 20:31, 17 January 2010 (UTC)

So Trovatore, you don't agree with me that each of this article's eight sections has one or more serious problems? Care to defend each section? And why don't the blatant violations of WP:OWN and WP:FORK bother you?

Even the old Relation algebra article was a lot better than this. I can't point to any mathematical article on Wikipedia with remotely near the number of problems this article has. --Vaughan Pratt (talk) 19:28, 18 January 2010 (UTC)

I didn't say I didn't agree with you. I neither agree nor disagree, because I haven't put in the time to look at the article lately.

That wasn't my point. My point was that, no matter how bad the content is, I don't see any reason to delete the article. Deletion of an article means that the name turns into a redlink. I don't think Boolean logic should be a redlink. Deletion followed by redirection would not make it a redlink, but would blank the history; I don't see any need to do that either. --Trovatore (talk) 21:11, 18 January 2010 (UTC)

I agree that this article is a mess, including issues with respect to WP:OWN and WP:FORK (and I'm sure so does Trovatore). But that doesn't mean it needs to be deleted, clearly we need to have at least a redirect if not an article under the title "Boolean logic". No? Paul August ☎ 19:50, 18 January 2010 (UTC)

By the way for notion that is meant to be covered by this article see the following Google search: http://books.google.com/books?q=%22Boolean+logic%22&btnG=Search+Books Paul August ☎ 20:10, 18 January 2010 (UTC)

Yes, sorry, "delete" was the wrong word. Certainly Boolean logic has to be catered for somewhere/how. --Vaughan Pratt (talk) 21:21, 18 January 2010 (UTC)

What about moving Boolean logic to a new place named e.g. Applications of binary logic (cf. this to similar usage with other topics). That article could then be trimmed in such a way that all theoretical content (rigor definitions etc.) gets moved to Boolean algebra (logic), therefore removing any unnecessary redundancy between articles. Applications of binary logic could focus on the use of binary logic in fields such as electronics and search engine queries. Having separate articles helps with keeping the articles slim and helps by providing a higher degree of accessibility for different target groups (mathematically/theoretically inclined vs. application inclined). --Abdull (talk) 22:48, 8 February 2010 (UTC)

At a first glance this sounds plausible. --Trovatore (talk) 02:20, 9 February 2010 (UTC)

Absent further objections then, I'll propose merging this article with Introduction to Boolean algebra, which is mostly Boolean logic anyway with a short bit at the end on Boolean algebras plural. --Vaughan Pratt (talk) 17:40, 9 July 2010 (UTC)

Meanwhile I see a merge was proposed back in February, albeit to Boolean algebra (logic) rather than Introduction to Boolean algebra. I think readers looking for "Boolean logic" would be better served by the introductory article.

But in that case I'm no longer sure the dab page Boolean algebra is really needed any more given that it isn't so much disambiguating the term as pointing to this hierarchy of articles. So perhaps Introduction to Boolean algebra should be merged into Boolean algebra so that the latter becomes essentially all the text of the former. The upshot would be to simplify the existing structure of Boolean algebra articles to one introductory one called simply Boolean algebra, which refers readers who want more depth to respectively Boolean algebra (logic) and Boolean algebra (structure), and Boolean logic would simply redirect to Boolean algebra. There would then be neither a dab page nor an article titled "Introduction to...". Comments? --Vaughan Pratt (talk) 18:14, 9 July 2010 (UTC)

Oh, I just realized Hans Adler proposed exactly that back in January, where he wrote (see above) "E.g. we could move Introduction to Boolean algebra to Boolean algebra (over the disambiguation page)." Well, that's two of us who see that as making sense. Any objections? Since the dab page Boolean algebra has no significant discussion of its own, the discussion of Introduction can just be moved manually to that of Boolean algebra, if that creates no problems. Trovatore's concern that the main article is introductory goes away because once that move is made it's simply an article on Boolean algebra, which covers both its logic and its structure (Trovatore's other objection was that some Boolean algebra links were assuming structure rather than logic) at a level sufficient at least to get people started, and who can follow up the links to Boolean algebra (logic) or Boolean algebra (structure) if they need more. --Vaughan Pratt (talk) 18:19, 9 July 2010 (UTC)

Well, not exactly. My objection is that the links are likely to be intending the count-noun sense, which refers to the structures. The intro article may talk about the structures, but the title clearly uses the term as a mass noun. I think that's not a good outcome when the link is used as a count noun. --Trovatore (talk) 09:00, 12 July 2010 (UTC)

Can it be determined (by someone familiar with the subject matter) from the context of the links which ones should go straight to Boolean algebra (structure)?

Incidentally this seems like a situation where an argument could be made for an exception to the usual plural rule, namely shortening "Boolean algebra (structure)" to "Boolean algebras." While I don't care much either way, maybe someone else has strong feelings? --Vaughan Pratt (talk) 03:26, 17 July 2010 (UTC)

I've learned that basic topics in Wikipedia are often a train wreck. What I find funny is that WP:WPM doesn't even try to "claim" this article anymore. Tijfo098 (talk) 20:35, 24 March 2011 (UTC)

Unlike most other WikiProjects, WPM doesn't "claim" articles. We only use the project template for rating articles. This article is so odd that it's probably better not to rate it. Hans Adler 21:27, 24 March 2011 (UTC)

A few edits of the "English language"

hi sorry i don't know where to write this - i edited the "English language" bit re m/f etc, then removed imperative, i think now it is good, i definitely did not hack the page with references to bodily parts. thanks. —Preceding unsigned comment added by 203.220.104.236 (talk) 08:55, 30 January 2011 (UTC)

cardinality and cartesian product

Aranoff (talk · contribs) is adding material which clearly doesn't belong in this article. As his last edit, in 2009, was adding material which clearly didn't belong in General relativity Black hole, something needs to be done. Now. — Arthur Rubin (talk) 16:03, 27 February 2011 (UTC)

Reported at WT:MATH. — Arthur Rubin (talk) 16:06, 27 February 2011 (UTC)

I agree with this edit. Cardinality and Cartesian product are not related to Boolean logic.

However, there is one other nonconstant unary operator, namely the one that returns whatever truth value it is given. — Carl (CBM · talk) 23:51, 27 February 2011 (UTC)

Establishing consensus whether this article is redundant

Is this article redundant to boolean algebra, thus should it be turned into a redirect there?

• Yes, redirect, because (1) it was clear after doing my research for the lead for Boolean algebra that it's the same topic, and (2) there wasn't much in boolean logic that isn't in boolean algebra; Venn diagrams are in, and even google queries. The only thing that is not in are SQL queries, but there aren't conceptually different (not when restrcited to discussion about boolean operators), and there are thousands of programming languages (PL) out there, why SQL in particular? There's a CS-ish article on boolean expression that could cover that, but as you can see from its stubby nature, nobody (except perhaps User:StuRat) thinks the syntactic difference in how boolean expressions are written in various PLs in an encyclopedic topic. Tijfo098 (talk) 02:34, 29 March 2011 (UTC)

What are "PLs" ? StuRat (talk) 02:48, 29 March 2011 (UTC)

A subject in Computer science along with ToC, AI, NLP, etc. Treats IPL, APL, PL/1, APL, BCPL, Fortran, etc. --Vaughan Pratt (talk) 06:50, 29 March 2011 (UTC)

I take it you are being intentionally difficult ? I've since figured out from the context that it means Programming Languages here. Thanks for nothing. StuRat (talk) 07:00, 29 March 2011 (UTC)

• No, this article is designed to be simple, with lots of examples, while that other article is not. Different audiences need different articles. StuRat (talk) 02:48, 29 March 2011 (UTC)

• Yes, redirect. I agree with StuRat that we need an article that can be understood at the beginning-college level, without a lot of higher math about Boolean algebra objects. Boolean algebra is that simpler article. Boolean logic is redundant. —David Eppstein (talk) 03:19, 29 March 2011 (UTC)

I'd go down to high-school level or even lower, where such topics are first used. Why should we make this topic opaque to that audience ? StuRat (talk) 03:22, 29 March 2011 (UTC)

Perhaps we should even teach toddlers how to read in this article? Oh, wait, there's a simple:Boolean logic for that. Tijfo098 (talk) 03:35, 29 March 2011 (UTC)

Don't you think any Wikipedia article should ever be written for anyone below college level ? Or is there just some reason why this topic shouldn't be ? StuRat (talk) 05:23, 29 March 2011 (UTC)

• Redirect. An article should be the authority on its subject, Wikipedia is not in the habit of creating multiple articles on the same fundamental subject - split articles generally take on different related subjects, which is not the case here. If Boolean Algebra is too technical, that is cause to rewrite it to provide delineated basic and in-depth treatments, not to create a 'Logic for Dummies' style fork. TechnoSymbiosis (talk) 03:31, 29 March 2011 (UTC)

That approach has been tried. Any attempt to make it more accessible is immediately reverted. StuRat (talk) 05:21, 29 March 2011 (UTC)

That seems more like an issue that should be taken up with editors involved and resolved rather than walking away from it to edit a fork article instead. TechnoSymbiosis (talk) 05:39, 29 March 2011 (UTC)

First, "immediately reverted" is something of an exaggeration given that three years elapsed between the first and second times your article was merged into another article. Second, accessibility is not the same thing as an attempt at accessibility. If editors point out a dozen reasons why your article is inaccessible to ordinary readers and you ignore them and leave the article in essentially the same incomprehensible form as when you first wrote it, you cannot claim to have succeeded in your attempt. Third, you are in violation of WP:OWN for starters: you're the only one who even understands what your article is trying to say, let alone wants it on Wikipedia. WP:POVFORK and the WP:3RR obstacle (you can't keep reverting this all by yourself) are also hanging over your head. --Vaughan Pratt (talk) 06:50, 29 March 2011 (UTC)

What are you talking about with "3 years" ? I'm talking about making changes to Boolean Algebra, not the deletion (which you call a "merge") of Boolean Logic. StuRat (talk) 07:00, 29 March 2011 (UTC)

Could you provide a diff? You never edited Introduction to Boolean algebra or Elementary Boolean algebra, and I found nothing relevant in any of the other Boolean algebra articles. Hans Adler 07:41, 29 March 2011 (UTC)

No articles have been deleted at any point. Your original article was merged into another three years ago, and parts of your article can still be found years later in Boolean algebra. You then revived the entire text of your original article, and since in the intervening three years you had not supplied any additional text needing merging, Boolean logic was simply redirected. If you're concerned that some of the text you wrote was edited out, you should be submitting your material to some other venue than Wikipedia. No one owns what they write here. --Vaughan Pratt (talk) 08:19, 29 March 2011 (UTC)

• Yes, redirect. So far only the original author and owner of this incomprehensible article says otherwise. --Vaughan Pratt (talk) 06:54, 29 March 2011 (UTC)

• Redirect. Actually, I agree with StuRat to the extent that we need an article whose basics can be understood by practically everybody, including children. However, I do not agree that the version owned by StuRat provides this, I do not agree that we need an article that does not eventually go beyond what every child can understand, and I consider this article severely misleading. Apparently StuRat taught this material on various levels over a number of years, and apparently during that time he has developed an idiosyncratic opinion on what does and what does not belong to it. The crash course in set theory, which has been marked as undue weight since September, violates WP:NOTTEXTBOOK, but in the past StuRat insisted vehemently on keeping it in precisely this form. The reader gets the impression that $\in$ is somehow related to Boolean logic. This problem is made worse by the fact that nothing is done with the relations of set theory once they have been introduced.

In the past StuRat has made it clear that he is not interested in fixing the defects. It's nothing but a POV fork for an idiosyncratic POV. Some readers may actually prefer this article because it's nice to read a mathematics article and understand all of it, up to the very end, without much effort. But in the present case this is achieved not by better explanation but by presenting only the most elementary aspects of the purported topic and some vaguely related topics, and then not even tying them together. There are wordy explanations for minor aspects that every reader will understand easily, such as "chaining operations together" and "using parentheses", while the relation between true/false, 1/0 and sets is left extremely obscure. StuRat may be able to help us make the other article more accessible, but not while he has a chance to cling to his article. Hans Adler 07:27, 29 March 2011 (UTC)

Agreed. 12-year-olds for whom Boolean algebra is suited might include the young Ramanujan or Terence Tao, but most of us at that age would be better served by something relatively simple. However whether Boolean logic is the best way to bring 12-year-olds up to speed on Boolean algebra is an interesting question, as is the question of how to tell whether they were up to speed. Ability to merely regurgitate sentences from an article is not the same thing as being able to put the article's contents to use.

Hans Adler's point as I understand it is that there is too little content in Boolean logic on which to base a graduated curriculum. It's like telling eighth-graders that they're competent merely because they've mastered material they were assumed to be on top of in fifth grade. --Vaughan Pratt (talk) 08:19, 29 March 2011 (UTC)

• Redirect I also believe that much of the stuff here should be chopped down to a paragraph with a 'main' pointer elsewhere, for instance the electronic stuff should point to logic gate. This article should just deal with its primary topic in detail and summarize things which are better covered elsewhere. There's also bits which sound a little too didactic to me. Dmcq (talk) 09:05, 29 March 2011 (UTC)
• I am in favor of having fewer, more comprehensive articles. Boolean algebra / boolean logic is not an advanced topic, in my opinion, so there is not a reason to have a more introductory fork. If the main article is not accessible enough, we should improve it rather than duplicate it. — Carl (CBM · talk) 10:32, 29 March 2011 (UTC)
• Comment I am very sympathetic with StuRat's intentions, but there are many problems with the present article. I think the best approach is to work to make Boolean algebra as accessible as possible. Hopefully StuRat will help in that. I would support him in that where I was able. Paul August ☎ 11:36, 29 March 2011 (UTC)
• Comment I basically agree with most comments above, but merging the articles should not hide that there are unresolved issues with the current version of Boolean algebra:

• Coverage: Does the article have to be semantics-oriented (i.e. fixing a domain and defining concrete operations on this domain) or, as the name algebra suggests, algebraically-oriented (i.e. about the study of abstract operations), or both? Does it have to extend into Boolean algebras (the structures) as much as it does? Does it need to extend so much in subjects that have their own page (e.g. Boolean algebra#Venn diagrams, Boolean algebra#Deductive systems for propositional logic, ...). Does it need to extend into subjects whose direct relation with Boolean algebra is unclear (e.g. the paragraph on natural languages in Boolean algebra#Boolean operations).
• Textbook vs news style vs summary style: Does the article have to extend so much about comparing Boolean algebra to ordinary elementary algebra (e.g. in Boolean algebra#laws). Efforts have to be made to make it less verbose, less repeating itself (e.g. "All of the laws treated so far have been for conjunction and disjunction."), less commenting itself (e.g. "There is nothing magic about the choice of symbols for the values of Boolean algebra").

So, in my opinion, since it seems there is these days a collective willing for reaching a Boolean algebra article worthy its name, what I strongly support, the merge of Boolean logic and Boolean algebra, which I ultimately support, should not go without also getting a relative consensus on what the Boolean algebra article should contain. --Hugo Herbelin (talk) 15:09, 29 March 2011 (UTC)

• Support redirect to Boolean algebra. If there are issues that Boolean algebra is not accessible enough, they should primarily be addressed by improving that article, in line with WP:TECHNICAL and WP:Manual of Style (mathematics)#Suggested structure of a mathematics article.  --Lambiam 22:11, 6 April 2011 (UTC)