Tier-Based Strictly 2-Local Phonotactics
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Kevin McMullin and Gunnar Ólafur Hansson. Oral presentation given at the 2014 Annual Meeting on Phonology. September 19-21, 2014 at MIT.
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Tier-Based Strictly 2-Local Phonotactics
- 1. Long-‐distance phonotactics as Tier-‐based Strictly 2-‐Local languages Kevin McMullin and Gunnar Ólafur Hansson Department of Linguis:cs University of Bri:sh Columbia Annual Mee:ngs on Phonology MassachuseCs Ins:tute of Technology September 19-‐21, 2014 1
- 2. Formal language theory • Phonotac:c paCerns: stringsets modeled as miniature languages • The Chomsky Hierarchy (Chomsky 1956) • Classifica:on for the computa:onal complexity of a language based on the type of grammar required to generate it 2 (non-‐computable languages) Type 0: recursively enumerable languages (recursive languages) Type 1: context-‐sensi:ve languages Type 2: context-‐free languages (finite languages) Yoruba copying (Kobele 2006) Bambara noun construc:on (Culy 1985) Swiss German crossing dependencies (Shieber 1985) English center embedding (Chomsky 1957) Type 3: regular languages
- 3. Phonology is regular • Virtually all phonological mappings are regular rela:ons (Johnson 1972; Kaplan and Kay 1994) • Any stringsets generated by these rela:ons are also regular (Rabin and ScoC 1959) • Surface phonotac:cs are regular 3 … … Type 3: regular languages AND PHONOTACTICS (finite languages) Yoruba copying (Kobele 2006) Bambara noun construc:on (Culy 1985) Swiss German crossing dependencies (Shieber 1985) Consonant dissimilaEon (Payne in press) Unbounded consonant harmony (Heinz 2010) … English center embedding (Chomsky 1957) ALL PHONOLOGY
- 4. Subregular hierarchy • Not all regular languages are aCested as phonotac:c paCerns • Instead, consider a proper subset of the regular region • We know a lot about the formal proper:es of some subregular classes (See e.g., Heinz 2010; Heinz, Rawal, and Tanner 2011; Rogers and Pullum 2011) • Can we define a demand for (dis)agreement within the Tier-‐based Strictly Local class of formal languages? 4 subregular A class Learnable?) (ACested? Regular languages Finite languages Regular Locally Testable Tier-‐based Strictly Local Strictly Piecewise Star-‐Free Locally Threshold Testable Strictly Local Piecewise Testable (Adapted from Heinz et al. 2011)
- 5. Research questions • What are the limits on the complexity of phonotac:c paCerns? • Long-‐distance + Blocking = Complex? 5 ACested languages Possible languages Long-‐distance consonant agreement with blocking Long-‐distance consonant disagreement Accidental gaps
- 6. Research questions • Can this boundary be defined as a class of formal languages? • All segmental phonotac:c paCerns are members of the class of Tier-‐based Strictly 2-‐Local languages (HYPOTHESIS) 6
- 7. Research questions • How does such a class differ from the predic:ons of other theore:cal approaches to long-‐distance phonotac:cs? • Specifically, Agreement by Correspondence 7
- 8. Long-‐distance dependencies • Non-‐adjacent co-‐occurrence restric:ons (focus on consonants) • Poten:ally unlimited number of intervening segments • Ex: La:n liquid dissimila:on (Jensen 1974, Roberts 2014) nav-‐alis ‘naval’ reg-‐alis ‘royal’ popul-‐aris ‘popular’ lun-‐aris ‘lunar’ milit-‐aris ‘military’ • Ex: Unbounded sibilant harmony in Aari (Omo:c; Hayward 1990) baʔ-‐s-‐e ‘bring-‐PFV-‐3SG’ ʔuʃ-‐ʃ-‐it ‘cook-‐PFV-‐1SG’ ʧʼa̤ːq-‐ʃ-‐it ‘swear-‐PFV-‐1SG’ ʃed-‐er-‐ʃ-‐it ‘see-‐PASS-‐PFV-‐1SG’ ʒa̤ːg-‐er-‐ʃ-‐e ‘sew-‐PASS-‐PFV-‐3SG’ 8
- 9. Tier-‐based Strictly 2-‐Local languages • Intui:vely (illustrated with liquid dissimila:on) • Co-‐occurrence restric:ons against con:guous pairs of segments… • Prohibited: *ll and *rr • PermiCed: lr and rl • …where adjacency is assessed only among a subset of segments • Liquids: {l,r} ⟵ this is the “Tier” • Back to La:n nav-‐alis ‘naval’ reg-‐alis ‘royal’ popul-‐aris ‘popular’ lun-‐aris ‘lunar’ flor-‐alis ‘floral’ plur-‐alis ‘plural’ 9 blocking by [r] (Heinz, Rawal, and Tanner 2011)
- 10. Tier-‐based Strictly 2-‐Local languages 10 (Heinz, Rawal, and Tanner 2011) • The parts • Some alphabet Σ (a segment inventory) of permiCed 2-‐factors (bigrams), labeled S • • Set is the set of prohibited 2-‐factors • A :er T that is a subset of Σ • Tiers can be defined with: • Features, natural classes, arbitrary subsets of the inventory • Example strings for :ers in a hypothe:cal word ‘piɹeʃaʃolu’: • Vowel :er – ieaou piɹeʃaʃolu • Consonant :er – pɹʃʃl piɹeʃaʃolu • Sibilant :er – ʃʃ piɹeʃaʃolu • Liquid :er – ɹl piɹeʃaʃolu • {ʃ,p,i,u} :er – piʃʃu piɹeʃaʃolu S
- 11. Locality/blocking as a consequence of the T • Illustra:ve harmony languages • Σ = {s,ʃ,p,t,a} • = {*sʃ, *ʃs} *[+ant][-‐ant] • ACested proper:es of long-‐distance phonotac:cs arise as a byproduct of the segments included in “T” • These languages will ban sequences of sibilants in some way • “Locality” will depend on the contents of Τ • i.e. Which segments are considered when assessing adjacency? 11 [+consonantal] | [+coronal –sonorant] | [+strident] S {s,ʃ,p,t} {s,ʃ,t} {s,ʃ} Τ = {??}
- 12. Attested properties of locality • Unbounded sibilant harmony • Σ = {s,ʃ,p,t,a} • = {*sʃ, *ʃs} • Τ = {s,ʃ} (all sibilants) • Members of L: {sasa, satasa, sasasasa, ʃaʃa, ʃataʃa, ʃapapaʃa, …} • Not in L: {saʃa, sataʃa, sasaʃaʃa, ʃasa, ʃatasa, ʃapapasa, …} • Example: Aari (Omo:c; Hayward 1990) baʔ-‐s-‐e ‘bring-‐PFV-‐3SG’ ʧʼa̤ːq-‐ʃ-‐it ‘swear-‐PFV-‐1SG’ *ʧʼa̤ːq-‐s-‐it ʃed-‐er-‐ʃ-‐it ‘see-‐PASS-‐PFV-‐1SG’ *ʃed-‐er-‐s-‐it ʒa̤ːg-‐er-‐ʃ-‐e ‘sew-‐PASS-‐PFV-‐3SG’ *ʒa̤ːg-‐er-‐s-‐e • Tier contains only the segments included in • Σ = {b,a,ʔ,s,e,u,ʃ,i,t,ʧʼ,a̤ː,q,d,r,ʒ,g} 12 S S [+cons] | [+cor –son] | [+strid]
- 13. Attested properties of locality • Transvocalic sibilant harmony • Σ = {s,ʃ,p,t,a} • = {*sʃ, *ʃs} • Τ = {s,ʃ,p,t} (all consonants; assumes CV syllables) • Members of L: {sasa, satasa, sapaʃa, ʃaʃa, sataʃa, sasapaʃaʃa, …} • Not in L: {saʃa, taʃasa, ʃasaʃa, …} • Example: Koorete/Koyra (Omo:c; Hayward 1982) baːr-‐us-‐ ‘lie.down-‐CAUS’ goːʧ-‐uʃ-‐ ‘pull-‐CAUS’ ʃod-‐us-‐ ‘uproot-‐CAUS’ • Tier contains everything in , and several addi:onal segments • Σ = {b,aː,r,u,s,g,oː,ʧ,ʃ,o,d} 13 S S [+cons] | [+cor –son] | [+strid]
- 14. Attested properties of locality • Sibilant harmony with blocking • Σ = {s,ʃ,p,t,a} • = {*sʃ, *ʃs} • Τ = {s,ʃ,t} (all coronal obstruents) • Members of L: {sasa, sapasa, ʃaʃa, ʃataʃa, sataʃa, ʃatapasa…} • Not in L: {saʃa, sapaʃa, sasaʃaʃa, taʃasa, ʃapapasa, …} • Example: Slovenian (Jurgec 2011) ʃpi-‐ʃ ‘(you) sleep’ *spi-‐ʃ ʒa-‐klɔn-‐iʃʧe ‘bomb shelter’ *za-‐klɔn-‐iʃʧe na-‐sit-‐iʃ ‘(you) feed’ *na-‐ʃit-‐iʃ zida-‐ʃ ‘(you) build’ *ʒida-‐ʃ • Tier contains everything in , and a few addi:onal segments • Σ = {ʃ,p,i,ʒ,a,k,l,ɔ,n,ʧ,e,n,s,t,z,d} 14 S [+cons] | [+cor –son] | [+strid] S
- 15. Summary of TSL2 patterns 15 • Long-‐distance consonant agreement (harmony) • Long-‐distance consonant disagreement (dissimila:on) • Unbounded dependencies • Transvocalic dependencies • Dependencies with blocking • No other variants of locality (e.g. “separated by up to two vowels”) • Transvocalic dependencies can be thought of as blocking by any consonant • The rela:onship between T and determines which of these proper:es the language exhibits These proper:es all come for free by allowing varia:ons in T S
- 16. Agreement by Correspondence • Faithfulness constraints • IDENT[ant]-‐IO • Correspondence constraints • Require certain sets of segments to be in correspondence • Correspondence is facilitated by trigger-‐target similarity • CORR[X⟷Y], CORR[G], or CORR[αG] (e.g., CORR[+strid]) • ‘CC·∙Limiter’ constraints (BenneC 2013) that impose restric:ons on correspondents • IDENT-‐CC constraints • Require correspondents to agree in some feature • IDENT[F]-‐CC (e.g. IDENT[-‐ant]-‐CC) 16 (Hansson 2001, 2010; Rose and Walker 2004)
- 17. Locality in Agreement by Correspondence • Locality constraints (CC·∙Limiters) • PROXIMITY (Rose and Walker 2004) • If X and Y are in correspondence… • …then X and Y must be in adjacent syllables • cf. Transvocalic (Hansson 2010) • Makes some strange predic:ons • Harmony that fails to apply to a sequence of targets • /ʃasa/➝[ʃaʃa], but /ʃasasa/➝[ʃasasa] • Harmony that applies only when target segment is preceded by an even number of segments in the harmonizing class • /ʃasa/➝[ʃaʃa], /sasaʃasa/➝[sasaʃaʃa], /sasasasaʃasa/➝[sasasasaʃaʃa], but • /saʃasa/➝[saʃasa], /sasasaʃasa/➝[sasasaʃasa] 17
- 18. Pathological ABC harmony systems • Harmony that fails to apply to a sequence of targets • This is not a TSL2 paCern • A word with ‘ʃs’ on the sibilant :er is only gramma:cal if ‘ss’ is also present on the sibilant :er • Belongs to the (Tier-‐based) ‘Locally Testable’ class at best 18 ! /paʃasasa/! PROXIMITY! CORR! [+strid]! IDENT! [:ant]: CLCR! IDENT! [ant]:IO! ! a.!paʃasasa! ! ***!! ! ! ! b.!paʃxasxasxa! *!! ! **! ! ! c.!paʃxaʃxaʃxa! *!! ! ! **! ! d.!paʃxaʃxasa! ! **! ! *!! ☞! e.!paʃasxasxa! ! **! ! ! !
- 19. Pathological ABC harmony systems • Harmony that does not apply when the trigger is preceded by an odd number of segments in the harmonizing class… 19 ! /pasaʃasa/! PROXIMITY! CORR! [+strid]! IDENT! [:ant]: CLCR! IDENT! [ant]:IO! ! a.!pasaʃasa! ! ***!! ! ! ! b.!pasxaʃxasxa! *!! ! **! ! ! c.!pasxaʃxaʃxa! *!! ! ! **! ☞! d.!pasxaʃxasa! ! **! ! ! ! e.!pasaʃxaʃxa! ! **! ! *!! !
- 20. Pathological ABC harmony systems • Harmony that does not apply when the trigger is preceded by an odd number of segments in the harmonizing class… • …but does when there is an even number • Such a paCern is computa:onally complex • Gramma:cality is determined by (unlimited) coun:ng of sibilants 20 ! /sasaʃasa/! PROXIMITY! CORR! [+strid]! IDENT! [9ant]9 CLCR! IDENT! [ant]9IO! ! a.!sasaʃasa! ! *****!*! ! ! ! b.!sxasxaʃxasxa! *!**! ! *! ! ! c.!sxasxaʃxaʃxa! *!**! ! ! *! ! d.!sxasxaʃxasa! *!! ***! ! ! ☞! e.!sxasxaʃyaʃya! ! ****! ! *! !
- 21. Another approach to locality in ABC • PROXIMITY (Rose and Walker 2004) • If X and Y are in correspondence… • …then X and Y must be in adjacent syllables • CC·∙SYLLADJ (BenneC 2013) • If X and Y are in correspondence… • …and there is no segment Z in the output such that X < Z < Y and X,Z are in correspondence… • …then X and Y must be in adjacent syllables • This effec:vely undoes the transi:ve property of the correspondence rela:on… • Xx…Zx…Yx would not violate CC·∙SYLLADJ (more like :ers) • …but s:ll makes problema:c predic:ons when using ABC constraints to derive dissimila:on 21
- 22. Problems with dissimilation in ABC • Surface Correspondence Theory of Dissimila:on (BenneC 2013) • Effec:vely, dissimila:on is the avoidance of correspondence • “Mismatch predic:on” for typology of harmony vs. dissimila:on • Dissimila:on should occur in exactly the opposite contexts • Predicts paCerns with liCle empirical support… • Beyond-‐transvocalic dissimila:on • …and raises complica:ons for descrip:vely simple paCerns • Transvocalic dissimila:on • Dissimila:on of iden:cal segments 22
- 23. How it works: Unbounded dissimilation • Unbounded dissimila:on with low-‐ranked [son] faithfulness • /p…b/ ➝ [p…m] (*p…b) 23 (…CvC…)& /lapaba/& CORR& [/son]& CC∙SYLL ADJ& IDENT& [voi]/CC& IDENT& [voi]/IO& IDENT& [son]/IO& Faithful& a.&lapxabya& *!& & & & & Faithful& b.&lapxabxa& & & *!& & & Harmony c.&lapxapxa& & & & *!& & Dissimilation& ☞d.&lapxamya& & & & & *& & (…CvcvC…)' /palaba/' CORR' [0son]' CC∙SYLL ADJ' IDENT' [voi]0CC' IDENT' [voi]0IO' IDENT' [son]0IO' Faithful' a.'pxalabya' *!' ' ' ' ' Faithful' b.'pxalabxa' ' *!' *(!)' ' ' Harmony c.'pxalapxa' ' *!' ' *(!)' ' Dissimilation' ☞d.'pxalamya' ' ' ' ' *' '
- 24. Dissimilation: Beyond-‐transvocalic • …Cv…vC… dissimila:on, but faithfulness/harmony at …CvC… 24 (…CvC…)& /lapaba/& CORR& [/son]& CC∙SYLL ADJ& IDENT& [son]/IO& IDENT& [voi]/CC& IDENT& [voi]/IO& Faithful& a.&lapxabya& *!& & & & & Faithful& ☞b.&lapxabxa& & & & *& & Harmony ☞c.&lapxapxa& & & & & *& Dissimilation& d.&lapxamya& & & *!& & & & (…CvcvC…)' /palaba/' CORR' [0son]' CC∙SYLL ADJ' IDENT' [son]0IO' IDENT' [voi]0CC' IDENT' [voi]0IO' Faithful' a.'pxalabya' *!' ' ' ' ' Faithful' b.'pxalabxa' ' *!' ' *' ' Harmony c.'pxalapxa' ' *!' ' ' *' Dissimilation' ☞d.'pxalamya' ' ' *' ' ' '
- 25. Beyond-‐transvocalic dissimilation • Beyond-‐transvocalic dissimila:on is not a TSL2 paCern • Gramma:cality cannot be determined based only on the :er-‐based 2-‐factors in the word • Transvocalic: CVpVbV, CVbVpV are gramma:cal • Beyond-‐: *CVpVCVbV, *CVbVCVpV are not • This is a (Tier-‐based) Locally Testable language • Gramma:cality is assessed based on the en:re set of 2-‐factors on a :er of consonants • No words with both ‘Cp’ and ‘Cb’ 25
- 26. Summary of argument • Comparison of two approaches to defining the space of possible long-‐distance phonotac:c paCerns: • as Tier-‐based Strictly 2-‐Local languages • as a factorial typology of Agreement by Correspondence constraints • The ‘formally grounded’ TSL2 approach seems to do a beCer job of capturing the aCested typology than ABC • except when the CC·∙Limiter constraints are made to treat correspondence sets more like :ers • Even then, other pathologies s:ll remain (Hansson 2014) 26
- 27. Further issues -‐ Similarity • In principle, any arbitrary class of segments can be a :er T • Does not entail any no:on of similarity • The vast majority of long-‐distance dependencies seem to be facilitated by some sort of similarity • Though some seem to involve unnatural classes • La:n liquid dissimila:on can also be blocked by labials and velars (Roberts 2014) • Tier of coronal non-‐nasal sonorants, labials, and velars • Poten:al solu:ons • Hard restric:ons on the sets of segments that can be a :er • Learning bias influencing how the learner navigates the space of possible :ers 27
- 28. Further issues -‐ Multiple TSL2 patterns • Transvocalic harmony + beyond-‐transvocalic dissimila:on • Transvocalic: lVl, rVr are gramma:cal, *lVr, *rVl are not • Beyond-‐: lV…Vr, rV…Vl are gramma:cal *lV…Vl, *rV…Vr are not • One possible case is aCested (Sundanese; BenneC 2013) • Details are complicated (infixa:on, syllable structure, etc) • Would this be a problem? • The surface phonotac:cs would not be TSL2 • …but could be modeled as two TSL2 paCerns (constraints), where harmony overrides dissimila:on in transvocalic contexts 28
- 29. Acknowledgements • Jeff Heinz and Adam Jardine (University of Delaware) • Douglas Pulleyblank and Blake Allen (UBC) • Audience at the ABC Conference, UC Berkeley 2014 • SSHRC Insight Grant 435–2013–0455: “Long-‐distance phonotac:cs: learning bias, change, and typology” (PI: Gunnar Ólafur Hansson) 29
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