Overview • A new formalism Efficient Generation in – What is Optimality Theory? (OT) Primitive Optimality Theory – Primitive Optimality Theory (OTP) • Some results for OTP Jason Eisner – Linguistic fit – Formal results University of Pennsylvania – Practical results on generation ACL - 1997 2 What Is Optimality Theory? Filtering, OT-style �� = candidate violates constraint twice • Prince & Smolensky (1993) • Alternative to stepwise derivation Constraint 1 Constraint 2 Constraint 3 Constraint 4 Candidate A • Stepwise winnowing of candidate set � � ��� Candidate B �� � such that different constraint Candidate C � � Gen . . . orders yield different languages Candidate D Constraint 1 ��� Candidate E Constraint 2 �� � � 3 Constraint Candidate F input �� ��� � output constraint would prefer A, but only allowed to break tie among B,D,E 3 4 Formalisms in phonology Unformalized OT isn’t a theory Computer Linguists Two communities with different needs ... Scientists OT (1993) OTFS ? ? Computer (finite-state) Linguists Scientists string rewrites finite-state (equivalent) SPE (1968) We need a formalism here, not informal English. (restricted) transducers Using English, can express any constraint Autosegmental tier-local rewrites finite-state (equivalent) ⇒ describe impossible languages phonology (1979) transducers ⇒ ⇒ ⇒ ⇒ specify any grammar with 1 big constraint OT (1993) informal OTFS ⇒ ⇒ ⇒ ? ? ? ? (undermines claim that typology = constraint reranking) English (finite-state) ⇒ no algorithms (generation, parsing, learning) ⇒ ⇒ ⇒ 5 6 1
OTFS: A finite-state formalization … but should linguists use OTFS? (used computationally: Ellison 1994, Frank & Satta 1996) Computer Linguists Scientists Let’s call this system OTFS , for “finite-state” : OT (1993) OTFS (finite- ? ? Q: What does a candidate look like? A: It’s a string. state) And a set of candidates is a regular set of strings. Linguists probably won’t use OTFS directly: Q: Where does the initial candidate set come from? A: Gen is a nondeterministic transducer. • Strings aren’t a perspicuous representation It turns an input into a regular set of candidate strings. • Again, can specify grammar with 1 big constraint Q: How powerful can a constraint be? • Too easy to express “unnatural” constraints A: Each constraint is an arc-weighted DFA. • Linguistically too strong? (e.g., it can count) A candidate that violates the constraint 3 times, ��� , too weak? (floating tones? GA?) is accepted on a path of weight 3. 7 8 Solution: Primitive OT (“OTP”) Representations in OTP Computer OTP’s “autosegmental timeline” specifies the relative timing Linguists Scientists of phonetic gestures and other constituents. (not absolute timing) OT (1993) OTP OTP (equivalent) OTFS OTP style (new) cf. Goldsmith style (old) voi voi • Formalizes current practice in linguistics nas nas nas nas (and easy for linguists to use) C C C C V C C V • Turns out to be equivalent to OTFS V V σ σ σ σ (new result! not in the paper) Stem • Simple enough for computational work Stem 9 10 Edges & Overlaps The Primitive Constraints voi α α α α → → → → β β β β Each α overlaps with some β . OTP’s constraints are simple & local: nas nas “implication” β β β β They merely check whether α α α α α α α α α α α C C C these gestures overlap in time, and whether their edges line up. V V 2 violations (all other α ’s attract β ’s) σ σ α α α α ⊥ ⊥ ⊥ ⊥ β β β β Stem Each α overlaps with no β . “clash” β β β β α α α α α α α α α α α α α α • Edges are explicit; no association lines • Associations are now captured by temporal overlap 3 violations (all other α ’s repel β ’s) 11 12 2
Examples from the literature Input, Output, and Gen in OTP voi } etc. nas → voi n every nasal segment bears some voicing feature Gen proposes all e G underlying candidates that include tiers [ σ → [C C V C C every syllable starts with some consonant (onset) this input. voi } voi F → [ µ surface every foot crosses some mora boundary (non- C V C C tiers degenerate) C V C C V ATR ⊥ low no ATR feature on any low vowel ]F ⊥ ]word voi voi no foot at the end of any word (extrametricality) C V C C C V C C [ σ ⊥ C no σ boundary during any consonant (no geminates) V velar voi C C σ → H or L every syllable bears some tone ( ) conj → disj C C C C C C C V 13 14 Example (Korean Final Devoicing) Example (Korean Final Devoicing) Input Output son → voi ]word ⊥ ]voi voi → voi bi-bim bab bi-bim bap voi word-final, devoiced word bibim bab �� b a b word-final, NOT devoiced (because it’s sonorant) bibim ba p � � voi winner! word Relevant constraints bibi m ba p � � �� son → voi “sonorants attract voicing” b a p ] word ⊥ ] voi “ends of words repel voicing” p i p im p a p voi � ���� voi → voi “input voicing attracts surface voicing” word (and many p a p more) 15 16 INTERMISSION Linguistic appropriateness • I’ve sketched: • Tested OTP against the literature – Why (something like) OTP is needed • Powerful enough? – How OTP works – Nearly all constraints turn out primitive • Not too powerful? • What’s left: – All degrees of freedom are exercised … – Results about OTP and OTFS x → y x → [ y [ x → [ y [ x → ] y • e.g., – How can we build a tool for linguists? – … in each of several domains: • features, prosody, featural prosody, I-O, morph. 17 18 3
Generative power: OTP = OTFS Is OTP = OTFS strong enough? -F +F • OTP less powerful than McCarthy & Prince’s [F Generalized Alignment, which sums distances • Encode OTP grammar in OTFS? ]F • Proof : – Cheaply - OTP constraints are tiny automata! – Align-Left( σ , Hi) prefers a floating tone to – Encode multi-tier candidates as strings dock centrally; this essentially gives a n b n • Encode OTFS grammar with just OTP? H H H σσσσσσσ σσσσσσσ σσσσσσσ – Yes, if we’re allowed some liberties: 0+1+2+3+4+5+6 6+5+4+3+2+1+0 3+2+1+0+1+2+3 • to invent new kinds of OTP constituents = 21 violations = 21 violations = 12 violations (beyond nas, voi, σ …) • to replace big OTFS constraint with many small – Pumping ⇒ ⇒ OTFS can’t capture this case ⇒ ⇒ primitive constraints that shouldn’t be reordered 19 20 On the other hand ... Eliminating Generalized Alignment • OTFS known more powerful than rational transductions (Frank & Satta 1997) rat. transductions < OTP < OTP+GA Should we pare OTP back to this level? So is OTP too weak or too strong ?? Should we beef OT up to Hard to imagine this level, by allowing GA? making it any simpler. rat. transductions < OTP < OTP+GA Ugly mechanisms like GA weren’t needed before OT. GA is non-local, arithmetic, and too powerful. past linguistic practice current linguistic practice (serial derivations) (OT as she is often spoke) Does OT really need it, or would OTP be enough? 21 22 Stress typology without GA Building a tool for generation • OTP forbids A LIGN and other stress constraints • If linguists use OTP (or OTFS), can we – But complete reanalysis within OTP is possible help them filter the infinite candidate set? – The new analysis captures the data, and does a better job at explaining tricky typological facts! OTP grammar Gen . . . • In OTP analysis, constraint reranking explains: Constraint 1 – several iambic-trochaic asymmetries Constraint 2 3 – coexistence of metrical & non-metrical systems Constraint input – restricted distribution of degenerate feet output – a new typological fact not previously spotted 23 24 4
Recommend
More recommend
