ONT Re: Effective Logical Formalism
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ELF. Literature Note 11
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
In the process of trying to place the LBase document within
a more common and comparative critical framework, we can see
that we have become engaged in another one of those exercises
in commensurability that we have come to know, if not to love
so well in this forum. By way of trying to summate the impacts
of the discussion so far I will set out my working synthesis of
the compromise language so far arrived at. It always help me to
draw some diagrams.
| 1. Model-Theoretic Semantics
|
| A model-theoretic semantics for a language assumes that the language refers
| to a 'world', and describes the minimal conditions that a world must satisfy
| in order to assign an appropriate meaning for every expression in the language.
| A particular world is called an interpretation, so that model theory might be
| better called 'interpretation theory'. The idea is to provide a mathematical
| account of the properties that any such interpretation must have, making as
| few assumptions as possible about its actual nature or intrinsic structure.
| Model theory tries to be metaphysically and ontologically neutral. It is
| typically couched in the language of set theory simply because that is the
| normal language of mathematics -- for example, this semantics assumes that
| names denote things in a set IR called the 'universe' -- but the use of
| set-theoretic language here is not supposed to imply that the things in
| the universe are set-theoretic in nature.
|
| R.V. Guha and Patrick Hayes,
|"LBase: Semantics for Languages of the Semantic Web",
| W3C Working Group Note, 10 Oct 2003.
|
| http://www.w3.org/TR/2003/NOTE-lbase-20031010/
The first ten times I read this paragraph, I'm sure
that I had the following sort of picture in my mind:
o Language
|
|
| Interpretation
|
v
o World
Reading things this way, I would recognize one of the conventional
uses of the word "interpretation", namely, the use that interprets
it as a mapping from a sign domain, more exactly a formal language,
to an object domain, a so-called world. I would also be cognizant
that what is really going on here is more exactly drawn like this:
Translation
Source Language o---------->o Target Language
\ /
\ /
\ /
\ /
v v
o
World
In this situation the source language is the formal language whose
meaningfulness, in all of the usual senses of the word, is under
ongoing investigation, while the target language is something
like the language of naive set theory, whose meaningfulness
is being assumed for the sake of the proceeding. There is,
then, as you can see when I show it in slo-mo, an element
of stage indirection in the model theoretic magic show,
the effect of whose hocus pocus makes you think that
the action of interpretation is passing mysteriously
from language to world, when the true facts are that
all the action is a level translation from language
to language. The illusion only works because the
target audience is likely to identify the target
language with worldly reality itself. Of course,
a practictioner of the art can get kicked out of
the profession for revealing how the trick works.
So watch out for that.
Next time I'll tell what I saw the
eleventh time I read the paragraph.
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o