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Subject: Re: [lojban] &Lang
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The 1-dimensional constraint of speech is a big one in terms of serializing=
 anything significant.  How about consider exploiting more than one 1-dimen=
sional stream to slightly alleviate the issue, perhaps conveyed through sem=
aphore or dance :-)

kozmikreis

On 12 Jul 2012, at 19:31, And Rosta wrote:

> Let me try harder to explain:
>=20
>=20
> Take a variety of predicate logic consisting of predicates, quantifiers a=
nd variables. In normal predicate logic notation, if a given variable is an=
 argument of more than one predicate, it gets repeated. And every bound var=
iable is notated at least twice, once where it is shown bound by quantifier=
 and once where it is argument of a predicate. But this is one and the same=
 variable; the repetition is a mere notational device necessary to lineariz=
e the string.
>=20
> If the notation could be two dimensional, then you wouldn't need to write=
 variables at all. For simplicity's sake, I'll describe a notation for only=
 predicates and variables:
> Use a 2 dimensional grid, infinite in both dimensions.
> Each 'row' corresponds to a variable.
> Each 'column' corresponds to a predicate.
> Predicates are notated by sets of symbols, one symbol for each argument p=
lace. Each argument place symbol is placed on the appropriate row for the v=
ariable that fills the argument place.
>=20
> That's the basic data structure for predicate--argument structure. A 2-di=
mensional notation can notate it without redundancy. But spoken language is=
 1-dimensional. Is there a way of linearizing predicate-argument structure =
ergonomically, in such a way that it is not so verbose or so taxing on the =
memory that the advantages of its logical explicitness and unambiguousness =
are not outweighed?
>=20
> --And.
>=20
> John E Clifford, On 12/07/2012 17:17:
>> As far as I can figure from the limited information, &'s language differ=
s from Logjam in two significant respects.
>> 1. Instead of a predicate with various arguments dripping from it, the c=
ore utterance is an argument (topic, say) with dangling predicates (comment=
s -- not the standard usage quite but Logjam is not famous for following pr=
ecedents in terminology). This is a feasible structure, easily realized in =
two (and simply in three) dimensions, without anaphora. The case of existen=
tial graphs and general topological considerations, however, suggest that a=
naphora will be needed in one-dimensional speech. The usual problems with t=
hat are simplified by the canonical location of topics. Multiple topics inc=
rease the complexity of this but not its basic simplicity. Comments come an=
d go (naturally) while topics run on and on (and so are always available fo=
r connection).
>> 2. Comments have no inherent places, which need to be filled implicitly =
when not explicitly, but have only those which are explicitly filled. This =
means, apparently, that the nature of the connection of a comment to its to=
pic has to be specified in (almost) every case, an added nuisance in speech=
 but probably a simplification in learning (and possible a reduction in the=
 need for compounds, many of which are just to add a place to an existing p=
redicate or rearrange those places). The bareness of comments means that co=
mment words can be raised to topics directly to do business as properties o=
r events, without a lot of extra detail.
>> These points are too sketchy to give any notion of the relative size, ea=
se or clarity of an &lang as here conceived, but at least it looks feasible=
 so far.

--=20
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