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Date: Thu, 12 Jul 2012 23:44:27 +0100
From: And Rosta <and.rosta@gmail.com>
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Subject: Re: [lojban] &Lang
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.arpis., On 12/07/2012 23:09:
> The common way (speaking as a computer scientist) of avoiding variable re=
petition (and variable naming issues) in formal methods is to use De Bruijn=
 indices (https://en.wikipedia.org/wiki/De_Bruijn_index), but this fails th=
e requirement of fitting in human memory.

Can you give an example of how it would work if applied to a predicate--arg=
ument structure? I can't follow the wikipedia article enough to see how it =
would work (-- setting aside the memory limitation problem you mention).

> On Thu, Jul 12, 2012 at 2:31 PM, And Rosta <and.rosta@gmail.com <mailto:a=
nd.rosta@gmail.com>> wrote:
>
>     Let me try harder to explain:
>
>
>     Take a variety of predicate logic consisting of predicates, quantifie=
rs and variables. In normal predicate logic notation, if a given variable i=
s an argument of more than one predicate, it gets repeated. And every bound=
 variable is notated at least twice, once where it is shown bound by quanti=
fier 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 line=
arize the string.
>
>     If the notation could be two dimensional, then you wouldn't need to w=
rite 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 argume=
nt place. Each argument place symbol is placed on the appropriate row for t=
he variable that fills the argument place.
>
>     That's the basic data structure for predicate--argument structure. A =
2-dimensional notation can notate it without redundancy. But spoken languag=
e is 1-dimensional. Is there a way of linearizing predicate-argument struct=
ure 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 unambiguousn=
ess are not outweighed?
>
>     --And.
>
>     John E Clifford, On 12/07/2012 17:17:
>
>         As far as I can figure from the limited information, &'s language=
 differs from Logjam in two significant respects.
>         1. Instead of a predicate with various arguments dripping from it=
, the core utterance is an argument (topic, say) with dangling predicates (=
comments -- not the standard usage quite but Logjam is not famous for follo=
wing precedents in terminology). This is a feasible structure, easily reali=
zed in two (and simply in three) dimensions, without anaphora. The case of =
existential graphs and general topological considerations, however, suggest=
 that anaphora will be needed in one-dimensional speech. The usual problems=
 with that are simplified by the canonical location of topics. Multiple top=
ics increase the complexity of this but not its basic simplicity. Comments =
come and go (naturally) while topics run on and on (and so are always avail=
able for connection).
>         2. Comments have no inherent places, which need to be filled impl=
icitly 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 topic 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 exi=
sting predicate or rearrange those places). The bareness of comments means =
that comment words can be raised to topics directly to do business as prope=
rties or events, without a lot of extra detail.
>         These points are too sketchy to give any notion of the relative s=
ize, ease or clarity of an &lang as here conceived, but at least it looks f=
easible so far.
>         **
>
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>
> --
> mu'o mi'e .arpis.
>
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