Re: Motion 18: The "domain" tetrit and bool_set semantics
Nate, P1788
On 21 May 2010, at 15:13, Nate Hayes wrote:
> I submit the updated position paper "Trits to Tetrits" as a formal motion.
> In particular, I move that P1788 shall:
>
> -- adopt the general Level 1 and Level 2 definitions of a tetrit --
> along with the propagation rules for tetrits in the P1788 exception handling
> mechanism -- as outlined in Sections 2.1 and 2.2, respectively.
>
> -- adopt the specific Level 1 and Level 2 defintions of a "domain"
> tetrit as outlined in Sections 2.1.1 and 2.2.1, respectively, and require
> that all P1788 decorations must include such a "domain" tetrit.
I support the general aim of this motion, but have some specific criticisms.
(1) I said on 19 May:
> Your basic table in 2.2, and similarly in your emails about this:
>> Rank Tetrit Description
>> 3 (T,F) Everywhere true
>> 2 (T,T) Somewhere true, somewhere false
>> 1 (F,T) Everywhere false
>> 0 (F,F) Nowhere true, nowhere false
> This is not correct because "Everywhere true/false" doesn't exclude the empty set.
Well (with some set X assumed, and P a predicate, and ~ meaning negation), in usual mathematics terminology
"everywhere P" simply means: (all x in X) P(x),
equivalent to "nowhere ~P",
which makes the (T,F) and (F,T) descriptions wrong. HOWEVER, I think Nate's usage is that
"everywhere P" means: (all x in X) P(x) & (exist x in X) P(x)
equivalent to (all x in X) P(x) & X is nonempty.
So it is not the same as "nowhere ~P".
I've nothing against this meaning of "everywhere". It adds expressive power, since it now does something that "nowhere" can't do. But you should *define* it, and point out it isn't standard - at least not in my experience.
(2)
> Please note, this motion specifically is NOT meant to take a position on:
> -- a decision to include or exclude any decoration attribute other than
> the required (by this motion) "domain" attribute
>
> -- a decision to allow or prevent any other decoration attribute to be
> defined in terms of something other than a tetrit
I agree to both these.
> The sole purpose of the present motion is to nail down Level 1 and Level 2
> definitions of a tetrit and to require these semantics are applied to a
> "domain" attribute that shall be part of the standard for all decorations.
However, I don't agree the semantics derived from your ranking, above, should be the ONLY semantics for tetrits. Can you define it, and say that (a) it is appropriate to the "domain" tetrit but (b) other attributes, for which a tetrit representation is appropriate, are free to use other semantics?
(3) In section 2.2, Definition 1, it defines the semantics more formally and uses the expression
inf(inf(P1,P2,...,Pn), inf(P(f,X1),P(f,X2),...,P(f,Xn))) (*)
The term inf(P(f,X1),P(f,X2),...,P(f,Xn)) doesn't make sense and should be
P(f,X1,X2,...,Xn)
which is an obvious extension, to the multivariate case, of the notation previously introduced and means the tetrit (P+, P-) = P(f,X) where X is the cartesian product of the X_i; that is,
P+ is (exist x1 in X1) ... (exist xn in Xn) P(f,x1,...,xn)
P- is (exist x1 in X1) ... (exist xn in Xn) ~P(f,x1,...,xn).
So, your (*) should be, I believe,
inf(P1,P2,...,Pn), P(f,X1,X2,...,Xn)).
I submit these as friendly amendments.
Regards
John Pryce