Talk:Boolean function

Plus and its vicissitudes

• JA: In mathematical contexts, let me recommend using " " for the field operation in GF(2), and thus for the boolean operation also known as "XOR", "NEQ", etc. This is the way that Boole originally used it, so it's a misnomer to describe inclusive disjunction by that name. When Peirce and Jevons later made OR a main squeeze, they respected prior algebraic use and coined new symbols for it, Peirce using " ," at first. It seems to have been Schröder who initiated the perversion of using " " for OR, and that became more commmon in engineering applications, but it has caused almost as much miscommunication and consequent wasted resources as English and Metric units on the same spacecraft. Jon Awbrey 19:42, 12 March 2006 (UTC)

Done. I had been in two minds as to whether I should use " ". My knowledge of boolean functions is pretty much limited to their uses in crypto, so feel free to edit as you see fit. …Ner102 21:26, 12 March 2006 (UTC)

Why is "logical operator" directed to this page?

There is also the article "logical connective" with direct reference regarding "logical operator" as the preferred term in algebraic logic. An explanation of the concept follows (that explanation cannot be found here under "Boolean function").

At least I as a layman in that filed could not find a good piece of reference for a "logical operator" under the present article. This existing redirect seems to be somewhat vague. Maybe "logical operator" should be redirected to "logical connective" instead of here? —Preceding unsigned comment added by 213.219.91.114 (talk • contribs) 15 May 2006

JA: This whole complex of articles is currently in the process of being cleaned up. Right at the moment, though, the best target for logical operator and logical operation both is boolean function. The reason is this: Strictly speaking, a logical operator is an operation on logical values, values like true and false, while a logical connective is really an operator on syntactic strings, say, sentences. Some of these distinctions have gotted mushed over in recent years for various historical and philosophical POV reasons. The relevant articles will eventually be rewritten to make all of this more clear, so stay tuned. Jon Awbrey 03:44, 15 May 2006 (UTC)

Note that logic operation, instead, redirects to Boolean logic (which, strangely, isn't ever linked to in this article). I haven't changed this yet, since it all looks like a mess, but this definitely needs attention. LjL 20:00, 16 May 2006 (UTC)

In that case, it would probably be best to create a separate article "logical operator" and explain the differences as well as different relations of the concept. 23:54, 16 May 2006 (UTC) —Preceding unsigned comment added by 213.219.91.114 (talk • contribs)

JA: I redirected "logic operation" to boolean function for now. One of the confusions that developed over the years is that most mathematicians consider "operation" and "operator" to be synonyms, while some folks in philosophy and also engineering use "operator" to mean something morally equivalent to the "symbol" that denotes the corresponding operation. Jon Awbrey 02:58, 17 May 2006 (UTC)

I strongly support user:213.219.91.114. The claim that Logical operation is some part of the boolean functions theory is not valid. There are some differences deeply in mathematical logics, some of which are visible in programming. For exapmle, in C a statement like if ( check_condition && some_condition() ) { do_somephing; }; has nothing to do with boolean function $\land$. гык 11:30, 24 June 2007 (UTC)

• I know its been a long time since somebody has looked in here, but a Boolean Operator is also a word or symbol helped to refine searches in a search engine, and while related, is not one of the described topics. I made a brief entry about it, but if it cannot be expanded, merging is suggested. Colonel Marksman (talk) 07:27, 22 September 2008 (UTC)

Boolean function

There is a typo on the Boolean function page.

There are 2 to the 2 to the k functions from f:B to the k -> B.

But the count appears AFTER the introduction of general boolean-valued functions:

• "More generally, a function of the form f : X → B, where X is an arbitrary set, is a boolean-valued function. If X = M = {1, 2, 3, …}, then f is a binary sequence, that is, an infinite sequence of 0's and 1's. If X = [k] = {1, 2, 3, …, k}, then f is a binary sequence of length k.

There are 2 to the 2 to the k such functions."

For the prior functions with domain X = [k], there are only 2 to the k functions. I suggest moving the 2 to the 2 to the k before the prior paragraph..

All Greek to me

I thought I knew a bit about Boolean functions, and looked up this page to learn more. I couldn't understand enough of it to work out what Boolean functions are. I studied 2 years of university level maths (pure and applied), though admittedly a few years ago.

Could we have an intro that regular people understand? --Chriswaterguy talk 23:40, 16 March 2010 (UTC)

== ditto on the all Greek==

I've completed Calculus III and I have no idea what any of this article is talking about either. I could be wrong but I believe only mathemeticians will understand it. I wish these articles could be more helpful to the general population. The authors are probably more concerned with being scrutinized by their equals than with being helpful to the learners. I know this is supposed to be an 'encyclopedia' but who is it helping if that position is taken?

I think people who surf Wikipedia and scrutinize and criticize the minutia of the technical details of the authors really are doing more harm than good. I think Wikipedia should be for everybody, not just the elite. —Preceding unsigned comment added by 99.147.240.11 (talk) 14:38, 3 September 2010 (UTC)

Boolean function vs. truth function

What is the difference between boolean function and truth function? --Abdull (talk) 17:23, 5 September 2010 (UTC)

What is the difference between English verbs and verb? Perhaps several millions of people feel no difference. Incnis Mrsi (talk) 06:30, 6 September 2010 (UTC)

There is certainly much less difference between them (if any) than between many other pairs of topics that have been merged. Unfortunately we have an incredible amount of useless duplication in our elementary logic articles. The problem is often made worse by sloppy language in one or more of the articles. In this case, if you take the definitions seriously as mathematical definitions:

• Boolean functions are always about standard binary logic (i.e. there are exactly two truth values), while truth functions can be more general. – This is arguably true, but not something that should be stressed by creating two completely separate articles.
• Boolean functions always take finitely many arguments while truth functions can also take infinitely many. I don't think this is true. – My educated guess is that "including an infinity of them" was added by a certain banned former editor who is obsessed with inventing terminological differences.)
• For Boolean functions the order of the arguments matters. For truth functions it only matters which values are present for the arguments. E.g. for classical logic the domain of a truth function is [a subset of ] the set consisting of the following four elements: the empty set, the set {true}, the set {false}, the set {true, false}. – The last sentence is of course completely false.

The only legitimate difference that I can see is that when you want to generalise to arbitrary "truth values" you can call it a [generalised] truth function but not a Boolean function because the word "Boolean" carries a strong connotation of "binary".

If you want to see more examples of this problem, take a look at WP:WikiProject Logic/Boolean algebra task force. Unfortunately the task force for cleaning up these articles has given up. (I hope only temporarily.) Hans Adler 11:17, 6 September 2010 (UTC)

PS: Real function redirects to real analysis, and complex function redirects to complex analysis. I think Boolean function should redirect to Boolean algebra (logic). (That article should really be at Boolean logic, but the title is "owned" by a user who has taught Boolean logic at some kind of school although he doesn't even seem to have reached the level of conscious incompetence yet.) Hans Adler 11:32, 6 September 2010 (UTC)

I agree, there is a lot of clueless duplication, for example there are articles Boolean algebra (logic), Boolean logic, Boolean domain and Two-element Boolean algebra almost about the same; I think we need two or three articles instead of four. But analogy with real and complex values functions is incorrect. Words "real" or "complex" functions are ambiguous: real/complex-valued? From real/complex numbers to the same field? But a "Boolean function" is something well defined. Of course, truth functions are yet another topic, because e.g. « x → y » and « ¬x ⋁ y » are equivalent as Boolean functions, but may differ in another logical systems. Incnis Mrsi (talk) 15:28, 6 September 2010 (UTC)

Your point is a good one. I didn't consider that real/complex function are not standard mathematical terms. I am not sure that I agree about your last sentence. When you take a different set of truth values, these expressions are a priori undefined. I think you are intending a more syntactical approach, as in logical connective. I didn't mention that article because of this legitimate distinction from Boolean function / truth function. Hans Adler 19:19, 6 September 2010 (UTC)

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