Knowledge and Learning in Natural Language (review)

The principle and parameters (P&P) theory has been touted as a solution to the logical problem of language acquisition, which I take to be the problem of how a computationally bounded information agent could arrive at a workable grammar of a natural language after finite exposure to a text consisting of simple grammatical sentences of that language, devoid of any indication of an explicit grammatical analysis. If variation between languages could be reduced to a finite set of properties, then a learner could simply scan the input text for decisive evidence for or against each variable property, or so it seems.

In practice, the problem is not so simple. A real learnability proof for any P&P style system has been elusive. The space of possible grammars is probably too large for a brute enumeration to be either plausible or useful. Furthermore, the relationship between the parameters and the evidence in the text appears quite complex, which adds to the computational complexity of the problem. Finally, concrete parameterized systems have been rare.

The above does not imply that the learnability of P&P systems cannot be studied rigorously, although one must be willing to apply generous doses of common sense to the enterprise. One line of attack has been to take the mathematics of population biology and apply it to P&P systems in the hope that a learnability proof could be developed from a familiar set of mathematical tools; examples include Clark 1992, Clark & Roberts 1993, and now Charles Yang’s Knowledge and learning in natural language. The idea rests on an analogy between genes as units of biological variation on the one hand, and parameters as units of linguistic variation on the other. One thinks of the so-called ‘I-language’ as a genotype and ‘E-language’ as its phenotypic expression. One can then imagine a linguistic text as a kind of environment. Just as a population of organisms, each with a different genetic stock, would show differential fitness in a physical environment, so a population of grammars, whose variation is represented by variation at the level of parameters, would show differential fitness in the linguistic environment of the text. One could study how fit linguistic ‘genomes’ propagate in a particular environment, converging on the best grammars relative to a text. Out of this study, so it is hoped, a method of proof of learnability for P&P systems could be developed.

Y’s book provides a summary of recent work on the learnability of P&P systems. It introduces work inspired by population biology, competition models where grammars compete on sentences, with successful grammars being rewarded and unsuccessful ones being punished. In this kind of model the learner is presented with an input datum in the form of a sentence. It then selects a grammar from a pool of competing grammars. If the grammar successfully analyzes the datum, it is rewarded by increasing the probability of using that grammar. If the grammar fails to analyze the datum, it is punished by decreasing its probability of use. The pool of grammars can be specified by a vector of parameters, each associated with a probability.

The basic theorem of such a system is that, as the size of the text increases to infinity in the limit, grammars more compatible with the input text will come to dominate while incompatible grammars will disappear. This means that the learner will come to favor successful grammars—ones that strongly resemble the target—with high probability. Nothing about the system requires that the data be unambiguous. Any individual datum could be analyzed by a wide array of admissible grammars. For example, a simple transitive sentence of English might be analyzed by a grammar that generates strict SVO order, a verb-second grammar using SOV as the underlying word order, or a grammar that allows scrambling. What is required is that grammars have differential error rates. As more of the text is observed, these other...