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Date: Fri, 13 Jul 2012 20:20:07 +0200
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Subject: Re: [lojban] &Lang
From: Escape Landsome <escaaape@gmail.com>
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De Bruijn indices, --- or, at least, some kind of indices ---, are
required in any semantic theory.

This is because of the constraints due to syntax.   Some syntactically
equivalent phrases need to be labelled as refering to the same object,
or to different objects.

Consider the following utterance :

"the black cat looks at the small cat"

Some syntactico-semantic coding would be something like :

lookat(black(cat),small(cat)).PRESENT

or maybe

lookat((cat.black.the),(cat.small.the)).PRESENT

But then, this is not satisfactory since we must also encode somewhere
that the two objects designed by the noun phrases are distinct (or are
the same)

So, =E0 la SOWA, you could code something like :

lookat((cat.black.the)[1],(cat.small.the)[2]).PRESENT

the [1] and [2] things being different.

Sometimes, you will have the same indices, when the objects are the same.

Yet, this is not so simple, because in "You are not you", which is a
philosophical statement about you, one could argue that in some sense
YOU are the same YOU, and in another sense, both YOU are different.

Another problem lies in the mass noun, because a set { a, b, c } is
different than a set { a, b, d }, so, will we say that {a, b, c} is a
[1] and {a, b, d} a [2], or encode it otherwise ?   If we opt for the
former solution, the indices notations [1] and [2] show us clearly
that {a, b, c} and {a, b, d} are not the same individuals, but they
fail to encode the common elements a and b which pertain to both sets.

Thus, a good semantic index ought to be some kind of semantic distance
within some semantic space, but this is too complex to be encoded in a
single word or a few ones.

--esc

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