Quantum Computational Linguistic Model (and then some)
- From: Ben <BenSprott@xxxxxxxxx>
- Date: 1 May 2007 07:23:42 -0700
I have developed a quantum computational linguistic model but
haven't found anyone interested in discussing it. Realizing that the
meaning of such a grandiose, if escoteric title is vague, let me be
somewhat more clear. Basically, I have found that one may represent
natural languages as groups and (Lambek uses pre groups which makes
more sense) these groups are essentially equivalent to formal
grammars. These groups have representations in the operators on a
Hilbert space. This is the basic idea of a quantum computational
linguistic model.
The model that one gets when allowing only Unitary transformations
is far too clean to be a model for natural language. You get groups,
and then grammars, but you don't get things like probabilistic phrase
structure grammars (PPSG). However, if one allows for a larger set of
operations, like say, the superoperators, then that is exactly what
one finds, PPSGs (that is my assertion). The basic idea is that of a
mixture over unitaries would allows for what I would call "weak
commutativity" whereing the rules of the language are somewhat
flexible.
The next step is somewhat more exciting.
Natural languages can be models as the solutions in a game theory.
By this, I mean the functor from the data set, the data set being the
list of generally accepted sentences which forms the language, cannot
be shifted (I suppose by means of a natural transformation), by any
one participant alone, to some algebraic theory, and by extension to a
theory and its imprecisely known category, which benefits only that
person.
That is a huge mouthful, and to put it more succinctly, a natural
language should be taken not just as the sentences, but as the theory
that one "functors up" to and that theory is a fixed point over
natural transformations. I could use some help on this categorical
stuff. Anyway, the magic is that one can find fixed points in the
superoperators and the spaces on which they act. They are just the
decoherence free subspaces.
Hopefully you are asking why I am posting this stuff here. As a guy
with a physics degree who now wants to start talking about language, I
know of very few people who want to get into this stuff. Basically, I
am just looking for a few good rifs on my ideas. I hope you enjoy the
post and it inspires you. If you know of any papers that really puts
together these kinds of ideas, please send them on.
I have a bunch more stuff to post and will do so in the next few
weeks.
Happy readings.
Ben
.
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