Talk:Functional completeness

message: 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)
replies: text: Another synonym fashionable in college texts is "expressive adequacy."132.181.160.42 05:48, 7 November 2007 (UTC)
thread_title: truth-functional completeness

message: 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)
thread_title: Functionally complete sets

message: 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)
thread_title:  [[ampheck]] 

message: Examples: 
* Computer theory: Turing completeness
* Hardware (computing instructions as functions): Minimal instruction set computer, Orthogonal instruction set.
* Topology: all possible topologic relations between two 2D geometries (see DE-9IM), and the interior / boundary /exterior completeness, about this dscription.
* Mathematical morphology and the completeness of the erosion / Dilation (morphology) operators.
* Expressive power: relation between "expressiveness" and "completeness".
* ...
--Krauss (talk) 09:50, 20 August 2012 (UTC)
replies: text: See the article Completeness (logic) -- however, you are right -- this article should include a section that at least mentions, compares and contrasts to other forms of completeness.  Right now, it seems very-boolean-logic influenced.  See also List of logic systems. 67.198.37.16 (talk) 02:06, 31 August 2016 (UTC)
thread_title:  Comparing another kinds of completeness 

message: To call a gate, or a truth table, nand, does 
not make nand something primitive. Nand can only be 
understood as the logical connection of the primitive
not and the primitive and operator.
Equivalently for nor.  — Preceding unsigned comment added by 146.52.31.210 (talk) 00:24, 15 August 2015 (UTC)
replies: text: Nand is also known to be the sheffer stroke which is known to be complete! So, yes, in fact, nand is primitive. 67.198.37.16 (talk) 02:09, 31 August 2016 (UTC)
thread_title:  minimal functional complete operator sets always consist of at least two primitive operators 

message: "changing the truth value of any connected variables from F to T without changing any from T to F never makes these connectives change their return value from T to F"2A00:23C4:AC83:CE00:59DD:19D1:DCA0:F91 (talk) 09:32, 29 December 2016 (UTC)
thread_title:  What does this mean?