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    Phonological natural classes and set theory
Someone posted on Reddit about being in a phonology course that was being taught through set theory:


I’m in this course of Phonological Analysis this term and the classes so far have been pretty far from what I was expecting, but I’m wondering if I just didn’t know what to expect or if my prof is doing something very unusual.[…]
The first class was a course on set theory. It was naive set theory, it wasn’t super formal, and it wasn’t axiomatic, but it was still more mathematical than most students expected (as judged by the radical drop in the number of students from the first to the second class). When set theory was assumed to be understood, he used it to define n-tuples and from n-tuples he defined strings. He also used set theory to define relations un sets and from relations he defined functions. Only when he had those did he introduce functions on sets of strings, and from that the notion of phonological rules. It took about two weeks of class to reach a point where we’re doing anything resembling Phonology.
(via Generative-Grammar)


Which got me thinking that sets would actually be a pretty interesting way of representing phonological features or natural classes. And so I made this diagram (you may want to zoom in). 
I think it’s a cool representation, and it was fun to make. Each symbol is enclosed in its own unique intersection of sets/features, which is good from a rule-writing perspective. Interestingly, the most logical layout for the vowels seems to resemble the vowel trapezoid quite a bit, but the only layout I could get for the consonants doesn’t at all resemble the IPA consonant chart.
Caveats: I didn’t represent length, or nasality in vowels, because basically anything can be long and all vowels can be nasalized. I also didn’t represent devoiced sonorants, again because of space. I couldn’t figure out where to put diphthongs. I didn’t even try for non-English sounds. Coronal isn’t indicated as a feature because basically everything that isn’t labial or dorsal is coronal (except vowels). This should have all the phonemes of English and some of the allophones but by no means all. The features are probably closest to those in Bruce Hayes’s Introductory Phonology, but I’m aware that people differ on which features they adopt, especially with regard to having separate back/front features. Objects in mirror may be closer than they appear. 
Update: Rotated some sections to make diagram look better. Update 2: Added aspiration. It was bugging me. And fixed bad typo: I can’t believe no one called me on this one.

    Phonological natural classes and set theory

    Someone posted on Reddit about being in a phonology course that was being taught through set theory:

    I’m in this course of Phonological Analysis this term and the classes so far have been pretty far from what I was expecting, but I’m wondering if I just didn’t know what to expect or if my prof is doing something very unusual.[…]

    The first class was a course on set theory. It was naive set theory, it wasn’t super formal, and it wasn’t axiomatic, but it was still more mathematical than most students expected (as judged by the radical drop in the number of students from the first to the second class). When set theory was assumed to be understood, he used it to define n-tuples and from n-tuples he defined strings. He also used set theory to define relations un sets and from relations he defined functions. Only when he had those did he introduce functions on sets of strings, and from that the notion of phonological rules. It took about two weeks of class to reach a point where we’re doing anything resembling Phonology.

    (via Generative-Grammar)

    Which got me thinking that sets would actually be a pretty interesting way of representing phonological features or natural classes. And so I made this diagram (you may want to zoom in). 

    I think it’s a cool representation, and it was fun to make. Each symbol is enclosed in its own unique intersection of sets/features, which is good from a rule-writing perspective. Interestingly, the most logical layout for the vowels seems to resemble the vowel trapezoid quite a bit, but the only layout I could get for the consonants doesn’t at all resemble the IPA consonant chart.

    Caveats: I didn’t represent length, or nasality in vowels, because basically anything can be long and all vowels can be nasalized. I also didn’t represent devoiced sonorants, again because of space. I couldn’t figure out where to put diphthongs. I didn’t even try for non-English sounds. Coronal isn’t indicated as a feature because basically everything that isn’t labial or dorsal is coronal (except vowels). This should have all the phonemes of English and some of the allophones but by no means all. The features are probably closest to those in Bruce Hayes’s Introductory Phonology, but I’m aware that people differ on which features they adopt, especially with regard to having separate back/front features. Objects in mirror may be closer than they appear. 

    Update: Rotated some sections to make diagram look better. 
    Update 2: Added aspiration. It was bugging me. And fixed bad typo: I can’t believe no one called me on this one.

     
    1. callmemizu reblogged this from allthingslinguistic and added:
      Aw yeah, this saved my day. And my thesis. There’s nothing better than a colorful diagram with all possible options....
    2. mrisdal reblogged this from rattiepuff and added:
      Distinctive features are a major mindfuck to me after my directed readings this semester. Should have known … since...
    3. irresponsiblyaffectionate reblogged this from rattiepuff
    4. rattiepuff reblogged this from allthingslinguistic
    5. faust042 reblogged this from allthingslinguistic and added:
      Very interesting! :D
    6. artificialstops reblogged this from allthingslinguistic
    7. salazucar reblogged this from lingulate
    8. t33j reblogged this from dissimilate
    9. dissimilate reblogged this from allthingslinguistic
    10. empiricalcrescent reblogged this from donkeyhot
    11. donkeyhot reblogged this from lorygilmore
    12. lorygilmore reblogged this from allthingslinguistic
    13. lingulate reblogged this from allthingslinguistic and added:
      nicely done. might use this / something like this next time I teach any phonology
    14. trilobiter reblogged this from allthingslinguistic and added:
      didn’t bother with aspiration because the boxes were getting really small. I...Set theory...
    15. estelendur reblogged this from allthingslinguistic and added:
      this is nifty
    16. writingfish reblogged this from jackwhiter and added:
      ….I think you broke my brain…XD
    17. jackwhiter reblogged this from allthingslinguistic and added:
      didn’t bother with aspiration because the boxes were getting really small. I...coronal....
    18. grantk4 reblogged this from allthingslinguistic
    19. anightattheopera reblogged this from allthingslinguistic and added:
      didn’t bother with aspiration because the boxes were getting really small. I...coronal....
    20. brentammm reblogged this from allthingslinguistic and added:
      didn’t bother with aspiration because the boxes were getting really small. I...coronal....
    21. allthingslinguistic posted this