Friday, March 5, 2010

Chapter 3 of Kornai's book

In chapter 3 of "Mathematical Linguistics" Kornai deals with phonology. It is very nice to see the mathematical theory of phonology laid out here, formalizing the autosegmental framework. I do have a few questions about this treatment, since it seems to rely heavily on the notion that there are phonemes and sound segments (consonants, vowels etc.) Autosegmental phonology is then formalized into a computational system using biautomata. It is emphasized that context-sensitive generating power is seemingly not needed for phonology, and that finite-state power is sufficient.

Kornai appears to state that we can solve the phonemicization problem for a language (meaning that the phonemic inventory is determined by the phonetic data). I thought Yuen-Ren Chao proved otherwise in 1934, and that this proof was formalized in Kracht 2003. For example, I fail to see how it is possible to prove that English affricates are actually single segments. Why aren't they sequences of two segments (a stop and a fricative)?

Another issue comes from speech perception research, where years of trying have failed to establish that people use consonants and vowels as perceptual units. Syllables appear to have much more traction in this regard. It is of course still desirable to transcribe syllables using segments, but this can be regarded as a convenient fiction, as was suggested already by Trager, I believe, in 1935. On the view just described, each syllable would then be formally treated as a sequence of distinctive features, with a certain ordering relation but without any timing slots.


  1. Hi Sean, sorry for the belated reply, it took me longer than I thought to recover the Joos reader where the Chao paper is reprinted. I read this as a student, and always thought that the problem of absolute neutralization was an issue only for a certain kind of surface phonemics, and not for generative phonology where underlying representations are available. Rereading the paper didn't change my mind, I still see no reason for the phonemic baby to be thrown out with the allophonic bathwater. The matter is covered quite cogently by Sandy Schane in his "On the Non-Uniqueness of Phonological Representations" Language, Vol. 44, No. 4 (Dec., 1968), pp. 709-716
    As for the monophonemic vs biphonemic analysis of affricates this is another problem that disappears once autosegmental representations are available, if my memory serves Clements-Keyser cover the gamut of pertinent cases in their "CV phonology" book. There was a paper a few years back in Lg by Port and Leary rehashing the same old arguments, as far as I could see they didn't even come close to casting serious doubt on the phoneme.

  2. OK now,

    though I must defer somewhat to your broader phonology knowledge (I still have a copy of your dissertation after all), I will try to go and read some of the references you cite. I have read the Port/Leary paper you mention, and yes, Bob Port is still crusading against "formal phonology." But just offhand for the moment, it does seem funny to use autosegmental phonology to rescue the phoneme as a useful concept. Doesn't it? Can't autosegmental phonology stand on its own with just features and no phonemes? I mean, you would have to replace phonemes with some other basic organization unit, such as syllables, but otherwise it seems to me a functionally equivalent scheme of autosegmental phonology could be devised that would never use phonemes. So given this, I don't see what phonemes are really for besides a (rather peculiar) methodological choice.

  3. Ah well,

    I got the classic Schane paper from Language, and it says right on the first page that he is only concerned with neutralization, and will have no solution for "the problems considered by Chao" for phonemicization. Schane takes a phonemic inventory as given to start with.

    This really steps over the main problem I'm concerned about with phonemes---namely the unlearnability of a phonemic inventory from data, because the problem is underdetermined.

  4. As far as autosegmental theory based purely on features, yes, for all intents and purposes this is what we have today. In such a theory the phoneme is no longer a primitive notion -- it is _derived_ as the total featural content associated to a timing unit (root node, CV unit, take your favorite theory of temporal organization). If some unit associates both to a stop and a fricative this is not a problem for the theory. The issue of learnability is greatly complicated by the fact that there seems to be a huge amount of innateness in the system. As is well known (which is a polite way of saying I don't have the time to dig out the reference) language learners start out with devoicing word-final stops even in languages that _have no_ voiceless stops! Whatever else our `language organ' does (and in general our goal would seem to be minimizing reliance on it) it's absolutely jam-packed with phonetic/phonological information that is hugely successful in accelerating phonetic/phonological development.

  5. Hi Andras,

    you certainly hit the nail on the head when you said "in general our goal would seem to be minimizing reliance on it." I am all for universal grammar, indeed my own work speaks to the necessity of many innate things for language learning, but I believe that the mainstream line of thought is rather to *maximize* reliance on innateness as a first methodological principle. Isn't this the essence of Principles and Parameters? It sort of trivializes the learning problem to one of finite combinatorics. This approach seems to be favored because of people being overawed by the so-called "poverty of the stimulus." I'm sympathetic to Pullum and Scholz (2002, The Linguistic Review), and quite sceptical of the stimulus poverty arguments.

  6. To correct myself, it wasn't Trager, it was Twaddell who, in a 1935 Language Monograph, famously suggested the phoneme should be a convenient fiction.