24.962 Page 1 4/13/05 Formalization of opacity in OT (this contains new stuff interspersed with old bits from last 2 handouts) 1. Summary of last 2 lectures: (a) the learner benefits from unraveling an opaque system: might discover structure in noise(b)the system benefits from being opaque, in certain ways: (i)more expressive contrasts available in certain opaque cases, compared to transparent (ii)less distance in perceptual space between UR and SR, in counterfeeding cases (c)but not all opaque interactions provide these benefits, compared to transparent ones Epenthesis counterbleeding VA Epenthesis bleeding VA (= Voice Assimilation)1 (i) dt -> tt -> tet dt -> det -> det (ii) tt -> tet tt -> tet (d) opaque interactions useful to the system are common, the others perhaps less so, suggesting that learners are not unaware of the benefits of the useful opaque systems. 2. Today: exploring recipes for formalizing opacity in OT (a) ordering does not distinguish good from bad opacity or opaque from transparent systems (b) standard OT (rankings of simple markedness and faithfulness constraints) does not characterize opacity (c) extensions: local conjunction, sympathy, comparative markedness. 3. Target-counterfeeding interaction (in so-called chain-shift situations): Rules Constraint Rankings A -> B /X_Y *XAY >> Corresp A/B (I-O) D -> A/ X_Y *XDY >> Corresp D/A (I-O) (i) e -> i/ __V *[-high]/ __V >> Ident [high] (ii) a -> e/ __V *[+low]/ __V >> Ident [low] this order yields these rankings yield /eV/ -> [iV] /eV/ -> [iV] /aV/ ->[eV] but /aV/ ->*[iV] Source: Basque problem in Kenstowicz and Kisseberth 1978 •counterfeeding rule interaction models a lesser departure from input than one might expect from maximal application of existing rules. •standard OT lacks the means to mimic the effect of counterfeeding order.4. Analyzing system-friendly counterfeeding opacity: local conjunction of correspondence •Kirchner (LI 1996): combining 2 Corresp. constraints Corresp A and Corresp B into one constraint Corresp AŸB2 (violated only if both A and B are violated in a local domain). Local domain below is the segment. Ident ([high]Ÿ [low]) >> *[+low]/ __V, *[-high]/ __V >> Ident [high], Ident [low] /aV/ Ÿ [low] *[-high]/ __V Ident [high] Ident [low] aV *! * +eV * * iV *! * * Effects of local domain restriction: allows scattered violations of both constraints conjoined in the same expression, provided they don’t all occur in the same domain. Compare (a), (b) with (c). Ident [high] *[+low]/ __V Carlo Geraci (p.c. 04/11/05) notes the parallel effect with V-V assimilation and C-epenthesis. 2 The name can also be (and sometimes is) “Corresp A⁄B” or “Corresp A&B”. 124.962 Page 2 4/13/05 /auteu/ Ident [high]Ÿ [low] *[-high]/ __V Ident [high] Ident [low] a iutiu *! ** * b iuteu *! * * * c + eutiu * * * *[+low]/ __V • Gnanadesikan's solution (UMass diss.1997) consists of identifying in some relevant cases a ternary featureF, & two strictly ranked types of Corresp. constraints (Ident 2F >>...Ident 1F). Ident 2F penalizes 2-interval deviations from UR value. E.g. [low] and [high] combined into one ternary feature [open]. Ident open penalizes any deviation from the UR value for [open]. By contrast, Ident 2[open] penalizes 2-interval departures from the UR [open] value: thus a-> i, but not e-> i or a -> e. open-2 open-1 open a e i Ident 2[open] >> *[-high]/ __V, *[+low]/ __V >> Ident [open] /aV/ *[-high]/ __V *[+low]/ __V Ident [open] a * b +eV * * c * ** Ident 2[open] aV *! iV *! Local conjunction or the mention of local domain are unnecessary in this case: /auteu/ Ident 2[open] *[-high]/ __V *[+low]/ __V Ident [open] a iutiu *! b iuteu *! * c + eutiu * ** 5. Recall that an unusually large number of the randomly selected cases of counterfeeding opacity surveyed by Moreton are amenable to an analysis involving a single dimension of contrast and 3 or more categories defined on it. This is exactly what Gnanadesikan’s solution can describe, if we appropriately extend her features & grant that some are not ternary but plus-quam-ternary. 6. Kirchner’s solution can describe these, but it can describe much more and cannot distinguish the plausible and frequent cases below from implausible or non-existent ones, discussed a bit further down. 7. Examples (selections from the survey in Monday’s handout): Language scenario Unified dimension, assuming some extension of F theory Local conjuction of Corresp., assuming standard F’s Nzebi a -> E -> e -> i O -> o -> u F1 (Ident [±high]& Ident [±low] & Ident [±ATR])segment B.Inupiaq ˆgl -> igl -> ig¥ Duration of [-back] (Ident [±back]&Ident [±anter])?3 Sea Dayak Nga -> Na -> Na) Duration of [+nas] (MAX C & Ident [±nas])SRs Mwera mp -> mb -> m Duration of cluster (MAX C & Ident [±voice])3 Finnish pp,tt,kk-> p,t,k-> v,d,Ø (Ident [±long]& Ident[±voice]) 3 An analysis of Mwera, in the spirit of Gnanadesikan: /mp/ Ident 2-long Use shortest4 Ident long mp (longest) **! mb (shorter) * * m (shortest) *! ** 3 LD is unclear here: can’t be s or segment. Local conjunction does not stipulate a minimal LD so this would not be viewed as problematic. 4 Use shortest assigns one * for every degree of length in a surface C above shortest.24.962 Page 1 4/14/05 An analysis of Barrow Inupiaq, in the spirit of modified Gnanadesikan: /Ègl/ Ident 2-long/palatal *È Palatalize =*[iC0[+back] Ident long/palatal Ègl (0) *! igl (short) * * iJ¥ (longer) *! ** What remains to be worked out: unlike G’s cases, the number of categories defined on each dimension cannot be pre-set at n (e.g. 3 for G). But to measure distance between UR and SR and penalize too large departures from UR, we need to know in advance how to divide the relevant dimension into steps. 8. Context-counterfeeding interaction. Rules Constraint Rankings A -> B /X_Y *XAY >> Corresp A (I-O) D -> A/ X_Y *XDY >> Corresp D (I-O) (i) n-> m/ _[+labial] *n[+labial] >> Ident [coronal] (ii) ´ -> Ø/VC_CV *´ >> MAX V This order yields: These rankings yield: /anba/ -> [amba] /anba/ -> [amba] /an´li/ -> [anli] /an´li/ -> [anli] /kan´bis/ ->[kanbis] but /kan´bis/ ->*[kambis] Source: Hindi problem in Kenstowicz and Kisseberth 1978 9. Similarly (i) n -> N/k *Heterorganic >> Ident place/nas (ii) t-> Ø/ C_C *CCC >> MAX C This order yields: These rankings yield: /ktn/