Talk:Functional completeness

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[edit] truth-functional completeness

What is here called "functional completeness" is more usually called "truth-functional completeness".

The connectives described on this page are truth-functional meaning that the truth of a sentence built using these operators is a function of the truths of the component sentences, E.g. the truth of a negation is the negation of the truth of its (sole) sub-formula. There are (natural, E.g. English) connectives that are not truth functional, E.g. "because", which cannot therefore modeled by truth-functional connectives in logic. A because B might be true if A and B are both true, but it might equally well be false under those conditions, causality depends on more than truth.

A collection of connectives is then called truth functionally complete if every possible truth function (of every possible arity) can be constructed using those connectives. It really is not clear what "functionally complete" might mean.

This distinction should be incorporated into the article. Gregbard 05:51, 8 July 2007 (UTC)

Another synonym fashionable in college texts is "expressive adequacy."132.181.160.42 05:48, 7 November 2007 (UTC)

[edit] Functionally complete sets

I do not understand what is going on here. It is my understanding that there are 9 pairs of expressively adequate connectives, while this section shows 15. Also, universal algebra suggests a way of organizing the expressively adequate pairs, and I've introduced that into the entry. If you understand my intention, go ahead and modify what I've done.132.181.160.42 05:48, 7 November 2007 (UTC)

[edit] ampheck

I'm pretty sure this deserves some kind of mention, link, merge, etc with this article. It was taken out as a "distraction." That's not correct. Pontiff Greg Bard (talk) 22:34, 27 November 2007 (UTC)