Extending binary NOR

Extending the concept of binary NOR so that is can operate on a column of values, rather than only two values, seems to me to be a useful generalization.

Marshall has called attention to the difference between his generalization which relies on folding, and Pamela's which does not. I have a problem with the result you get by folding NOR, in terms of the usefulness of such a generalized operation.
logical NOR is commutative, but not associative. e.g.

(T nor T) nor F) is not equal to (T nor (T nor F))

Thus the result of applying folded NOR to a column of values is dependent on the order of the values in the column, if the column has more than 2 values. This looks ugly to me, as I prefer to think of a column of values as representing a set.

I prefer the generalization made by the manufacturers of standard NOR gates. There are standard NOR gates with 3 or 4 inputs, and I believe their output is independent of the "order" of the inputs. I believe they yield false in any of the inputs are true, and yield true otherwise. I think this generalization models what Marshall has called n-ary NOR.

I think this generalization is more useful, if you are going to use generalized gates to model boolean logic. I also think that this generalization is more useful if you are going to build a computer out of gates. And I think either one of these assertions follows from the other. Notice I'm saying "more useful" not "more correct".

I want to provide some reference for this discussion, although I'm not suggesting that these references are necessarily definitive. If you start in the Wikipedia Article entitled "Zeroth order logic" and click on "Logical NOR" and then click on "NOR gate", you get a description of the NOR gate that generalizes to 4 inputs. Incidentally, I couldn't get to this article by a direct search in Wikipedia, but I may be doing something wrong in my use of Wikipedia.