Re: Motion P1788/M0015.01: Definition_of_decorations: Up for discussion
P1788
Note an immediate consequence of passing Dan's motion:
We abolish the "bounded" property.
(Hurrah, say I.) Two reasons:
(a) It is not a pointwise property such as Motion 15 requires. That is, there is no predicate isBounded(f,x) or isBounded(f,x,y) that is defined for functions f, and points x (or x,y) in an interval, such that we ask if there exists x in xx such that isBounded(f,x) is true, etc.
"Bounded" can only be defined by a doubly quantified statement (there exists ...)(for all ...)... and hence its negation by (for all ...)(there exists ...)...
(b) It is a property of the current interval, not of history. Or should we set boundedSticky(xx)=false for xx=[-1,1] because it happens to have been computed as tanh(Entire) ?
Regards
John
On 23 Apr 2010, at 23:31, Ralph Baker Kearfott wrote:
> Since the motion has been presented by Dan Zuras and seconded
> by Chenyi Hu, it is now up for the three week discussion period
> ...
> ------------------------------------------------------
>
> To each interval there shall be a set of decorations that
> corresponds to that interval and carries information about
> how that interval was computed. Each decoration within
> that set shall carry 3 bits of information named
> 'thingy'True, 'thingy'False, and 'thingy'Sticky.
>
> ... Together with the predicate is'thingy' we define for all
> monadic interval functions f(xx):
>
> 'thingy'True = {there exists x in xx such that
> is'thingy'(f,x) is True}
>
> 'thingy'False = {there exists x in xx such that
> is'thingy'(f,x) is False}
>
> 'thingy'Sticky =
> 'thingy'False(xx) \or 'thingy'Sticky(xx)
>
> We define for all dyadic interval functions f(xx,yy):
>
> 'thingy'True = {there exists x in xx and y in yy
> such that is'thingy'(f,x,y) is True}
>
> 'thingy'False = {there exists x in xx and y in yy
> such that is'thingy'(f,x,y) is False}
>
> 'thingy'Sticky =
> 'thingy'False(xx) \or 'thingy'Sticky(xx) \or
> 'thingy'False(yy) \or 'thingy'Sticky(yy)
>
> There shall also exist predicates 'thingy'True(xx),
> 'thingy'False(xx), and 'thingy'Sticky(xx) and the
> extraction function
>
> get'thingy'(xx) = ('thingy'True(xx),'thingy'False(xx),
> 'thingy'Sticky(xx)).
>
> The initial (or default) value of 'thingy'True(xx), and
> 'thingy'False(xx) upon creation of a new xx shall be determined
> by the nature of 'thingy' (in a future motion). The initial
> value of 'thingy'Sticky(xx) shall be False.