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Date: Tue, 25 Jan 2005 05:52:24 -0800 (PST)
From: Jorge "Llambías" <jjllambias2000@yahoo.com.ar>
Subject: [lojban] Re: outer and inner quantifiers on "le"
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--- And:
> xorxes:
> > The move from restricted to unrestricted quantificaton for
> > fractional quantifiers, under any interpretation, won't work
> > like for regular quantifiers.
> 
> True. But partitive fractional quantifiers will not make sense with
> any {da}, whereas 'frequency'/'incidence' fractional quantifiers
> will at least make sense with restricted da.

It depends on how we define them.

For normal quantifiers, we have:

  PA <sumti> = PA da poi ke'a me <sumti>

For partitive fractionals, we have:

  pi PA <sumti> = lo pi PA si'e be pa <sumti>

so for restricted da we would have:

  pi PA da poi broda = lo pi PA si'e be pa da poi broda
 
> >> Likewise, if {mi citka pi mu plise}, is the cardinality of {lo'i se citka
> >> plise} 0.5? Hardly.
> >
> > That doesn't bother me so much, it is a reasonable extension of the
> > idea of cardinality.
> 
> To my unmathematical mind, cardinalities must be positive integers (or
> 0); nothing else makes sense.

That's true for pure cardinalities. But if you allow for things
to be partitioned, then fractional cardinalities make some sense.

> > It seems to me that any convention we adopt will have its unintuitive
> > side, so it's just a question of what is more useful.
> 
> In that case, I suppose {pi mu lo'i broda} might serve for "one in every
> two broda".

Well, the way we have it now, it is a set containing one in every
two broda:

pi mu lo'i broda 
= lo pi mu si'e be pa lo selcmi be lo broda

and a fraction of a set is conventionally a subset.

mu'o mi'e xorxes



		
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