J. E. Fenstad has a provocative little book called Grammar, Geometry, and Brain (CSLI 2010). It is speculative and is sort of like an annotated bibliography, but as such it is very valuable as a discussion of work in cognitive science and brain modeling at the interface with linguistics. Fenstad is a mathematical logician and occasional linguist. The book is filled with his own preferences and experience, but it is very forward thinking, perhaps venturing into the crackpot, but that's OK with me. It is inspiring.
Fenstad states "you can never be more than the mathematics you know," something I heartily agree with. Like him I will continue to seek out new mathematics to apply in linguistics. I'm tired of formal language theory and logic, these tools cannot be everything for linguistic theory. Fenstad's suggestion is that Geometry can provide a direct link between linguistic theory and cognitive modeling. He points to the Conceptual Spaces framework of Gärdenfors (MIT Press 2000) for a geometrical theory of semantics which he suggests could be connected to syntax using attribute-value grammar. He also discusses several works in cognitive neuroscience, suggesting how geometry could play a role in a bridging model connecting neuronal assemblies to conceptual spaces. It's an interesting book that pointed me to a lot of other readings.
Tuesday, June 28, 2011
Wednesday, June 1, 2011
What makes languages learnable?
A recent paper by Ed Stabler (in Language Universals, Christiansen et al. eds. 2009) puts the focus on an important question that is rarely formulated in the literature. What are the structural properties of natural languages which guarantee learnability? We know from a variety of negative results going back to the famous Gold theorem that such properties have to go far beyond the defining principles of the Chomsky hierarchy, since none of the traditional language classes except the finite languages are strictly learnable, in the sense of identifiability in the limit. Because we presume to model natural languages as some sort of infinite languages, something else must be going on. There must be some restrictions on the possible forms of natural language that permit learnability in some sense. Stabler says that to address this question, we need a proposal about how human learners generalize from finite data. There is as yet no complete answer to this problem, and indeed very little research seems to be currently motivated by such questions.
While I do not generally use this forum to highlight my own published work, in this case I believe that my 2010 paper in the Journal of Logic, Language and Information (together with an erratum published this year) does address Stabler's question directly. The title of my paper is Grammar Induction by Unification of Type-Logical Lexicons, and therein the basic proposal is given. Human learners are proposed to generalize from finite data by unification of the sets of syntactic categories that are discovered by an initial semantic bootstrapping procedure. The bootstrapping procedure extracts basic category information from semantically annotated sentence structures (this is highly enriched data, to be sure, but I argue for the plausibility of that in general terms). The basic system of categories is then unified by a two-step process that takes into account the distribution of the words (usage patterns, expressed structurally), and is able to generalize to "recursively redundant extensions" of the learning data. This is then a specific proposal of the sort invited by Stabler. The resulting learnable class of languages is highly restricted, including only those that are in some sense closed under recursively redundant extensions. This is in accord with general thinking about human languages, in that it is normally the case that a recognized recursive procedure (such as the appending of prepositional phrases to expand noun phrases, in rough terms) can always be applied indefinitely to yield grammatical sentences of increasing length.
I hope in the future to highlight my findings in a more general journal like Cognitive Science. It is helpful that Stabler conveniently provided the leading question to my purported answer.
While I do not generally use this forum to highlight my own published work, in this case I believe that my 2010 paper in the Journal of Logic, Language and Information (together with an erratum published this year) does address Stabler's question directly. The title of my paper is Grammar Induction by Unification of Type-Logical Lexicons, and therein the basic proposal is given. Human learners are proposed to generalize from finite data by unification of the sets of syntactic categories that are discovered by an initial semantic bootstrapping procedure. The bootstrapping procedure extracts basic category information from semantically annotated sentence structures (this is highly enriched data, to be sure, but I argue for the plausibility of that in general terms). The basic system of categories is then unified by a two-step process that takes into account the distribution of the words (usage patterns, expressed structurally), and is able to generalize to "recursively redundant extensions" of the learning data. This is then a specific proposal of the sort invited by Stabler. The resulting learnable class of languages is highly restricted, including only those that are in some sense closed under recursively redundant extensions. This is in accord with general thinking about human languages, in that it is normally the case that a recognized recursive procedure (such as the appending of prepositional phrases to expand noun phrases, in rough terms) can always be applied indefinitely to yield grammatical sentences of increasing length.
I hope in the future to highlight my findings in a more general journal like Cognitive Science. It is helpful that Stabler conveniently provided the leading question to my purported answer.
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