Re: wrong name for exactly one

On Feb 14, 2017, at 12:14 PM, Peter F. Patel-Schneider <pfpschneider@gmail.com> wrote:
> 
> If there has to be an explanation that the name chosen for
> something means something else everywhere else, then the
> wrong name has been chosen.
> 
> From 4.6.4 sh:xor
>> "Note that despite the name, the semantics of sh:xor for
>> cases with 3 or more shapes are different from an exclusive
>> or in the mathematical sense. The general definition of
>> exclusive or makes it true only when an odd number of inputs
>> are true, while the SHACL definition of sh:xor relies on 
>> exactly one semantics."


All --

I've done a bit of research on this one.

First I found --

https://en.wikipedia.org/wiki/Exclusive_or 

> Exclusive or or exclusive disjunction is a logical operation 
> that outputs true only when inputs differ (one is true, the
> other is false).[1]

That article also discusses the "exclusive or" in English,
but focuses on the two-choice question ("french fried or 
mashed potatoes") but does not delve into the more complex 
question at hand ("french fries, baked, mashed, boiled, 
hash browns, or home fries").

That brought me to --

https://en.wikipedia.org/wiki/Uniqueness_quantification

> In mathematics and logic, the phrase "there is one and
> only one" is used to indicate that exactly one object
> with a certain property exists.


And these in turn led me to Stack Exchange --

http://math.stackexchange.com/questions/1183702/is-there-a-word-similar-to-iff-meaning-one-and-only-one

-- and Wolfram MathWorld --

http://mathworld.wolfram.com/ExactlyOne.html

-- both of which suggest --

> "onee" (one and only one) by analogy with iff (if and only if),
> "twoo" (two and only two), and "threee" (three and only three).
> This refinement is sometimes needed in formal mathematical 
> discourse because, for example, if you have two apples, you
> also have one apple, but you do not have exactly one apple.


-- credited to one John H. Conway --

   http://en.wikipedia.org/wiki/John_Horton_Conway

(I think the logic of the term is "one, exclusively.")

(I do note that the MathWorld page also states -- "In 2-valued 
logic, exactly one is equivalent to the exclusive or operator 
XOR". It is unfortunate that this apparently does not translate 
to multi-valued logic, and that failure-to-translate has never 
been mentioned in any of my previous encounters with either 
the linguistic "exclusive or" nor the operator "XOR".)


I'd be OK with switching from sh:xor to sh:onee on that basis, 
or perhaps to sh:oaoo, as I can find several pages that define
that letter sequence as meaning one-and-only-one or once-and-
only-once -- which is just about exactly what we intended in 
the first place.

Both sh:onee and sh:oaoo will of course be prone to typos, 
damned-auto-correct, and other errors, but I guess that's the 
price one pays for precise logical nomenclature...

Regards,

Ted






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