Brownian thought space

Cognitive science, mostly, but more a sometimes structured random walk about things.

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Chronically curious モ..

Thursday, November 18, 2010

A rule by another name...

Is this a rule or is this a little portion of an HMM?
Imagine some rule-based system, that has the following:
x -> {x | y}
It's in a made-up notation, but the meaning should be clear enough: 'x' can go to either of 'x' or 'y'. The first part (x->x) is just what this colorful picture represents (minus some probabilities of how likely is it that x->x). In fact, the above figure requires some kind of an identity function (x goes to itself).
Here are some more rules:
However, for some strange reason, people who think human language doesn't require rules, only mean rules like (4) - rules 1-3 (and, arguably, infinitely many more) are not just ok, they're often required.
Of course, there is a bigger question: can (4) be re-stated in a different system of rules? Probably. But, to take an example from physics, the Newtonian
does a fantastic job for most of our daily purposes; although we now "know" that the correct (relativistic) form is:
So, till those computationalists who deny rules like (4) can give us a better rule system with the kind of intra- and inter-language advances made by assuming variants of (4), it just remains a promissory note with limited substance.

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