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Date: Thu, 4 Sep 2014 18:26:40 -0400
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] unquantified sumti with restrictive relative clauses in xorlo
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* Thursday, 2014-09-04 at 12:22 +0200 - selpa'i <seladwa@gmx.de>:

> la'o me. Martin Bays .me cusku
> > Recall the following production:
> >
> > sumti5 <- quantifier? sumti6 [relative-clauses]
> >
> > I want to understand the semantics of this in the case that there is no
> > quantifier, and there is a restrictive clause among the relative clause=
s.
> > {ko'a poi broda}, in other words.
> > [...]
> > I can see six broad approaches to interpreting such expressions, i.e. t=
hose of
> > the form {ko'a poi broda}.
> >
> > (i) Consider it an error, or just ignore any restrictives.
>=20
> I don't like this option, because it would be an exception. I believe=20
> {poi} can be defined in such a way that the same rule handles both=20
> quantified and unquantified sumti.
>=20
> > (ii) Declare that in this case (and this case alone), there is an impli=
cit
> >      quantifier after all.
>=20
> This is certainly how if feels at times, but it's probably not necessary=
=20
> for it to actually be the case at a formal level.
>=20
> By the way, the case of {lo broda poi brode ku'o ku} needs to be looked=
=20
> at as well. An outer quantifier wouldn't affect the {poi} clause here,=20
> but it still needs to be defined what it means and how it differs from=20
> {noi}.

Yes, true.

Relatedly: any option other than (i) or (ii) or (iv) has a limitation: if
{ko'a poi broda} is a referring expression in itself, one might expect
{ro ko'a poi broda} to mean
    (1)  {ro da poi me ko'a poi broda},
but instead we have a separate rule which makes it
    (2)  {ro da poi me ko'a gi'e broda},
and (1) and (2) agree only in case (iv).

They almost agree in case (v), and I'm tempted to amend case (v)
to have it give {ro ko'a poi broda} meaning (1) rather than meaning (2).

> > (iii) Have it pick out some referents such that they satisfy the restri=
ctives:
> >      ko'a poi broda -> zo'e noi me ko'a gi'e broda
>=20
> This is pretty much my take on it. I like the general definition of {poi=
=20
> broda} =3D=3D {je poi'i* broda} because it works in all cases, both with=
=20
> sumti and with selbri, and it doesn't matter if there are quantifiers=20
> present. (it is equivalent to your definition, but works better in real=
=20
> life as an afterthought, not that that's very relevant here)

Yes, this is definitely attractive in its simplicity. It's much looser
than restrictive relatives in english, though; if I point at some
assorted fruit and say {ti poi plise}, with (iii) there's no reason to
think that I'm referring to all the apples rather than only one.

> > (iv) Have it pick out those referents which each satisfy broda:
> >      ko'a poi broda ->
> >          zo'e noi ro da zo'u go da me ke'a go ge da me ko'a gi broda
>=20
> I think this doesn't fit with the current system where the argument=20
> places of predicates aren't defined as distributive or collective

Agreed.

> (they should be in my opinion).
>=20
> If you want distributive satisfaction, {ko'a poi ro ke'a broda} works.

Almost - but assuming we work with (iii), that doesn't get the idea that
*every* individual among ko'a which satisfies broda is a referent of
ko'a poi broda, as (iv) states.

> > (v) Something along the lines of (iv), but more in line with plural log=
ic /
> >      mereology, perhaps by requiring the obvious maximality condition, =
i.e.
> >      ko'a poi broda ->
> >          zo'e noi ge ge me ko'a gi broda gi ro da poi ge ge ke'a xi re =
me ke'a gi
> >          ke'a me ko'a gi ke'a broda cu du ke'a
> >      , perhaps making it an error if there is no unique such maximum, or
> >      perhaps taking all the maxima together (i.e. taking the join).
>=20
> This is also a bit too specific, like (iv).
>=20
> > (vi) Something along the lines of (v), but with no formal rule - just a=
n idea
> >      that the intended referents of {ko'a poi broda} are picked out amo=
ng the
> >      referents of {ko'a} by virtue of their brodaing.
>=20
> Isn't this similar to (iii) as well?

Not the way I meant it. I meant it as a translation of the english
"those of ko'a which broda" - which is rather more specific than (iii),
which is more like "some of ko'a, that broda,". (v) was also an attempt
at translating that english phrase.

This just reminded me of [Chierchia98]; using his notation, (v) (with
error when there's no unique maximum) can be expressed:
    {ko'a poi broda} ->
	\iota { x | x <=3D ko'a /\ broda(x) }.
It seems a reasonable translation of english restricted relatives.

I just had a quick look at some semantics papers, and I have the
impression that this is indeed a standard way to handle them - but I'm
not confident I'm reading the literature right.

> > The usage I've seen could fit any of (iii)-(vi), I think. So, taking va=
rious
> > degrees of liberty, could CLL's use of restrictives - although of cours=
e they
> > had implicit quantifiers, so are not really relevant.
>=20
> There is definitely a lot of contrasting usage between {ko'a poi} and=20
> {ko'a noi}, with meaningful distinctions being felt by the speakers.=20
> That, and the fact that I think the general definition of {poi} in terms=
=20
> of {je} (or gi'e) works made me believe that something like (iii) is the=
=20
> most practical solution.
>=20
> We could try to write up a table of all the cases:
>=20
> [snip]
>=20
> lo broda poi brode
> 	lo broda je poi'i broda / zo'e noi broda gi'e brode
>=20
> [snip]
>
> So a lot of these are equivalent as long as no quantifier is added, but=
=20
> they all use the same expansions which work whether or not there is a=20
> quantifier (or so I hope, let's look for mistakes!).

They look reasonable to me. Taking {lo broda poi brode} to be have the
same referents as {lo broda ku poi brode} would also be an option.

> PA broda noi brode
> 	PA da (to ri broda toi) poi ke'a broda
>=20
> Some of this depends on {ri}'s ability to repeat {da} and quantified=20
> terms. Writing {PA da (to da broda toi)} would be weird, as the {da}=20
> could just as well be a new variable.

Yeah, I don't think that's really legitimate. Pretending that {ri} can
pick up the {da} at all (and actually I believe it just skips over it to
the previous sumti), I'd say the bracketed phrase there has an unbound
("donkey") variable, and we should either consider it an error or
universally quantify it out to give
    {PA broda noi brode} -> {PA da poi broda zi'e noi brode}
    -> {to da brode toi PA da poi broda} *
    -> {to ro da brode toi PA da poi broda}
or, perhaps, remembering the domain of the variable and only universally
quantifying over that, giving
    {to ro da poi broda brode toi PA da poi broda} ;
but that's a bit of a pain in practice, since the clause giving the
domain could itself mention unbound variables, and you have to recurse.

Martin

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