Talk:Boolean function

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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)[reply]

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)[reply]

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) 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)[reply]

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)[reply]

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)

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)[reply]

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)[reply]

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..