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Date: Fri, 13 Jul 2012 15:31:42 +0100
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.arpis., On 13/07/2012 00:59:
> I'm not sure I understand the predicate-argument structure well
> enough to do so. Could you give an example of how it would look with
> normal variables and explain the meaning of the example?

An example (without wanting to be distracted by irrelevant details):

"Da djuno lo du'u de prami da gi'e de nelci da"
djuno(da, &(prami(de, da), nelci(de, da)))

Task 1: notate this (linearly) so that "da" and "de" each appear only once.

And then:

Task 2: Improve the system so that speakers don't have to hold in memory th=
e arbitrary correspondence between variable & phonological form.

Will De Bruijn indices deal with Task 1? If they do, I'd be thrilled to hav=
e learnt summat new.

--And.

>
> On Thu, Jul 12, 2012 at 6:44 PM, And Rosta <and.rosta@gmail.com <mailto:a=
nd.rosta@gmail.com>> wrote:
>
>     .arpis., On 12/07/2012 23:09:
>
>         The common way (speaking as a computer scientist) of avoiding var=
iable repetition (and variable naming issues) in formal methods is to use D=
e Bruijn indices (https://en.wikipedia.org/ wiki/De_Bruijn_index <https://e=
n.wikipedia.org/wiki/De_Bruijn_index>), but this fails the requirement of f=
itting in human memory.
>
>
>     Can you give an example of how it would work if applied to a predicat=
e--argument structure? I can't follow the wikipedia article enough to see h=
ow it would work (-- setting aside the memory limitation problem you mentio=
n).
>
>         On Thu, Jul 12, 2012 at 2:31 PM, And Rosta <and.rosta@gmail.com <=
mailto:and.rosta@gmail.com> <mailto:and.rosta@gmail.com <mailto:and.rosta@g=
mail.com>>> wrote:
>
>              Let me try harder to explain:
>
>
>              Take a variety of predicate logic consisting of predicates, =
quantifiers and variables. In normal predicate logic notation, if a given v=
ariable is an argument of more than one predicate, it gets repeated. And ev=
ery bound variable 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 necessar=
y to linearize the string.
>
>              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 nota=
tion 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 ea=
ch argument place. Each argument place symbol is placed on the appropriate =
row for the variable that fills the argument place.
>
>              That's the basic data structure for predicate--argument stru=
cture. A 2-dimensional notation can notate it without redundancy. But spoke=
n language is 1-dimensional. Is there a way of linearizing predicate-argume=
nt structure ergonomically, in such a way that it is not so verbose or so t=
axing on the memory that the advantages of its logical explicitness and una=
mbiguousness are not outweighed?

--=20
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