Introduction to Optimality Theory EGG 2011 Peter Jurgec ~ peter@jurgec.net What is Optimality Theory? Optimality Theory (OT) is a theory of constraint interaction. Constraints are requirements that forms must meet. Today s Plan OT vs. Previous Approaches OT Architecture: constraints OT grammar constraint ranking tableaux Why OT?
Two approaches Rules: a must turn into b most Generative Phonology, starting from A real-world example Two ways of describing locations Example: New York Public Library The Sound Pattern of English (1968) Constraints: no a OT, some previous approaches Option 1 Start Left Straight Straight Straight Straight Straight Straight Right Straight Straight End Option I1 NYC, Intersection of 40th Street and 5th Avenue
Two approaches A phonological example Operations Start Left Straight (x 6) Right Straight (x 2) End Target NYC, Intersection of 40th Street and 5th Avenue Tibetan consonant clusters Option I: C / # Option II: No initial CC A phonological example Tibetan consonant clusters Option I: C / # Option II: No initial CC A phonological example Tibetan consonant clusters Option I A rule: C / # Option II A constraint: No initial CC
Rules v. Constraints Are the two approaches equivalent or are they fundamentally different? Do the two approaches make different predictions? Optimality Theory Optimality Theory Prince and Smolensky (1993) OT is a theory of constraint interaction. The main idea is that grammars impose a set of restrictions on what are valid surface forms. These restrictions can be formalized in terms of constraints. What is this course about (and what not)? Introduction to Classic OT: Basic principles (Prince & Smolensky 1993/2004; McCarthy & Prince 1993b, 1994) Correspondence Theory (McCarthy & Prince 1995, 1999) Generalized Alignment (McCarthy & Prince 1993a;
Constraints Constraints Constraints make restrictions on forms (candidates) In a nutshell, they require that candidates satisfy some condition: be like that or don t be like that Constraints can be satisfied or violated. What kind of constraints are there? Pre-OT constraints Constraints are a new way of describing and analyzing phonological patterns Were there constraints before OT? Examples: Morpheme Structure Constraints Obligatory Contour Principle (OCP) Markedness constraints Languages generally prefer forms that: simple easy to pronounce easy to process common Some forms are better than others. Markedness is a way to formalize this situation.
Markedness an old concept (going back to structuralism) Phonology exhibits asymmetries: unmarked (common, frequent) marked (rare, exotic) Examples: Markedness all languages have voiceless obstruents, but only some have voiced obstruents all languages have front unrounded vowels, but only some front rounded vowels all languages have oral vowels, but only some have nasal vowels all languages have C-initial words, but only some have V-initial words Marked structures In OT, marked structures violate some constraint. Examples: Obstruents must be voiced. No front rounded vowels. No nasal vowels. Words must start on a consonant. Markedness constraints Constraints that impose restrictions on surface forms are called markedness constraints. Are markedness constraints enough?
Markedness constraints Faithfulness constraints If only markedness constraints existed, we would get only unmarked structures. Marked structures would never appear. No languages with voiced obstruents, front round vowels, nasal vowels, or C-initial words. We need another type of constraints that offset the effects markedness constraints. Faithfulness constraints mitigate the effects of markedness constraints. How? OT Grammar OT Grammar /input/ Gen candidate set Eval [output]
OT Grammar Gen(erator) Gen creates a candidate set Freedom of Analysis = Any amount of structure may be posited. Consistency of Exponence = No changes in the exponence of a phonologically-specified morpheme are permitted. (aka Input morphemes are output morphemes. ) OT Grammar Eval(uator) Eval selects a single winner from the set of candidates. Constraints are part of Eval.
Constraints Two types: markedness = impose restrictions on outputs faithfulness = mitigate the effect of markedness constraints Faithfulness constraints Faithfulness constraints prefer no change from input to output. Faithfulness constraints refer to both the input and the output. Faithfulness constraints require identity between input and output. Two types of constraints Faithfulness constraints Examples: No changes in nasality. No deletion. No insertion. No reordering.
Interim summary OT background OT grammar OT constraints Constraint Ranking OT Grammar OT Grammar
Constraints are... universal = all grammars have the same constraints violable = no candidate satisfies all constraints strictly ranked = a violation of a dominant constraint cannot be offset by non-violation of all other constraints How do constraints work? OT tableau OT tableau
OT tableau OT tableau OT tableau OT tableau
An example: Tibetan numerals Tibetan Numerals -teen (+10) -ty ( 10) dzu 10 < dzig 1 dzu-gdzig 11 < < < Si 4 dzu-bsi 14 Si-bdZu 40 < < Na 5 dzu-na 15 Na-bdZu 50 < < gu 9 dzu-rgu 19 gu-bdzu 90 < < Observation: Tibetan doesn t allow initial consonant clusters. (Note: Tibetan numerals /ŋa/ [ŋa] 5 /rgu/ [gu] 9 /bd ʒu/ [d ʒu] 10 /rgu-bd ʒu/ [gu-bd ʒu] 90 /bd ʒu-gd ʒig/ [d ʒu-gd ʒig] 11 Tibetan generalizations /ŋa/ [ŋa] 5 /bd ʒu/ [d ʒu] 10 /rgu-bd ʒu/ [gub.d ʒu] 90 /bd ʒu-gd ʒig/ [d ʒug.d ʒig] 11 No complex onsets! Tibetan generalizations /ŋa/ [ŋa] 5 /bd ʒu/ [d ʒu] 10 /rgu-bd ʒu/ [gub.d ʒu] 90 /bd ʒu-gd ʒig/ [d ʒug.d ʒig] 11 No complex onsets!
Tibetan generalizations No Complex Onset In Tibetan, complex onsets violate some markedness constraint. How do we know? Tibetan avoids complex onsets. All languages that allow complex onsets also allow simple onsets. *COMPLEXONSET (or NOCOMPLEXONSET) No complex onsets. Note: Syllables with simple onsets do note violate this constraint. Faithfulness Tibetan 99 The constraint *COMPLEXONSET outranks some faithfulness constraint. We will call this constraint simply Faith. FAITH No changes. (The input and the output must be identical.)
(b) wins (b) wins Evaluation of *COMPLEXONSET Evaluation of FAITH *COMPLEXONSET = No complex onsets. FAITH = No changes.
Violation marks (*) Violation marks (*) Violations are marked with stars (*). Violations are marked with stars (*). Violation marks (*) The ranking of constraints matters If the ranking of *COMPLEXONSET and FAITH were reversed, we would not get the right grammar. Fatal violations are marked with an exclamation mark (!).
Anti-Tibetan Rankings Anti-Tibetan preserves all segments rather than avoids complex onsets. Higher constraints are more important than lower constraints. A violation of a higher constraint cannot be offset by not violating all other constraints. What s next? Exercise: Winners Tuesday: Faithfulness, Intro to typologies Wednesday: Factorial Typology Thursday: More on rankings Friday: How to do an analysis?
Correspondence Theory EGG 2011 Peter Jurgec ~ peter@jurgec.net Summary so far OT = A theory of constraint interaction Constraints = universal, violable, strictly ranked Tableaux = a tool to represent input output mappings Principles of OT (McCarthy & Prince 1993) Tibetan 99 Universality Violability Ranking Inclusiveness (large candidate set) Parallelism
Some OT lingo Constraint = an element of Eval; a constraint can be satisfied or violated Strict Ranking of constraints = a violation of the highest ranked constraint cannot be offset by not violating all other constraints To outrank = A outranks B iff A is ranked above B (also: A B) OT lingo Violation marks (*) = designate violations of a constraint Candidate = an input output pair Optimal Candidate / Winner = the candidate tnjat incurs the least violation marks of the highest constraints compared to all other candidates (marked with ) OT lingo Loser = a candidate that is not optimal Fatal Violation (!) = a candidate fatally violates a constraint if (i) there is at least one other candidate that fares equally on all higher ranked constraints, and (ii) if another candidate does not violate the current constraint Recall Tibetan Tibetan doesn t allow complex onsets. In OT, this situation can be formalized using two constraints: a markedness constraint that penalizes complex onsets and is ranked above a faithfulness constraint that penalizes deletion markedness outranks faithfulness
Recall Tibetan Tibetan doesn t allow complex onsets. In OT, this situation can be formalized using two constraints: a markedness constraint that penalizes complex onsets and is ranked above a faithfulness constraint that penalizes deletion markedness outranks faithfulness Correspondence Theory (McCarthy & Prince 1995, 1999) Faithfulness constraints evaluate 2 different forms : the input and output. The main idea: Each segment, feature, constituent of the input is in correspondence with a segment, feature, constituent of the output. Input Output Correspondence Faithful candidates Input / p 1 a 2 t 3 a 4 / Output [ p 1 a 2 t 3 a 4 ] Each segment of the input has a corresponding segment in the output. A candidate is faithful, if it doesn t violate any faithfulness constraint. (This is slightly simplified.) Unfaithful candidates violate some faithfulness constraint.
Unfaithful candidate Example: Input / p 1 a 2 t 3 a 4 / Output [ p 1 a 2 t 3 ] /a4/ doesn t have an output correspondent. This violates some faithfulness constraint. Why are candidates not faithful? Two types of constraints Two types of constraints There are two types of constraints: markedness constraints impose restrictions on outputs faithfulness constraints favor no changes between input and output Faithfulness constraints Correspondence is evaluated by faithfulness constraints. There are many types of different faithfulness constraints.
Faithfulness constraints IDENT(ITY) An input segment and its output correspondent must be identical. (No changes.) MAX(IMALITY) Every input segment must have an output correspondent. (No deletion.) DEP(ENDENCE) Every output segment must have an input correspondent. (No epenthesis.) Deletion Input / p 1 a 2 t 3 a 4 / Output [ p 1 a 2 t 3 ] /a4/ doesn t have an output correspondent, violating MAX. MAX Every input segment must have an output correspondent. (No deletion.) Epenthesis Input // p 11 a 22 t 3 t 3 a 4 / / Correspondence Input / p 1 a 2 t 3 a 4 / Output [[ p 11 a 22 t 3 t 3 a 4 ]] [a4] doesn t have an input correspondent, violating DEP. DEP Every output segment must have an input correspondent. (No epenthesis.) Output [ p 1 a 2 t 3 a 4 ] Each segment of the input has a corresponding segment in the output.
Change Input / / p 1 a 2 t 3 a 4 // Back to Tibetan Output [ [ p 1 1 a 2 t 3 3 ai 4 ] ]] /a4/ and [i4] are in correspondence, but they are not identical. This violates IDENT. IDENT An input segment and its output correspondent must be identical. (No changes.) MAX The relevant constraint is MAX. Are we done? MAX Every input segment must have an output correspondent. (No deletion.)
More candidates? What other constraints are there? Problem: Candidate (c) wins! Solution: Candidate (c) violates another constraint that is not violated by (b). DEP But where? DEP Every output segment must have an input correspondent. (No epenthesis.) This ranking makes wrong predictions. Candidate (c) is not the actual winner. Solution: Candidate (c), but not (c), violates DEP. To rule out (c), we need to rank DEP higher.
DEP ranked higher DEP ranked even higher This ranking works! This ranking works, too! The ranking between DEP and *COMPLEXONSET doesn t matter. The data are ambiguous and can be explained but either ranking. Multiple rankings Even more candidates Important: The constraints are still strictly ranked wrt to one another, it s just that the ranking doesn t matter.
Even more candidates (with *s) Can (d), (e) ever win? (d), (e) are harmonically bounded Harmonic bounding A candidate is harmonically bounded when it cannot win under any ranking.
(d), (e) are harmonically bounded (a), (b), (c) can win under some ranking (a) wins when DEP, MAX *COMPLEXONSET (b) wins when DEP, *COMPLEXONSET MAX On no constraint do (d), (e) fare better than all other candidates. (c) wins when MAX, *COMPLEXONSET DEP Summary Exercise: Evaluation Faithfulness constrains are of different kinds. Constraints can have different rankings in different languages. There is no restriction on ranking. Crosslinguistic typologies come from possible rankings. Some candidates can never win in no language.
Summary so far Factorial Typology EGG 2011 Peter Jurgec ~ peter@jurgec.net OT grammar OT constraints Tableaux Correspondence Theory Today s Outline Factorial Typology Nasalization typology Syllable typology Constraints are universal, but their ranking is language specific. The differences among languages are due to different constraint rankings.
Factorial Typology Suppose there are n universal constraints. These constraints produce n! different rankings. Factorial Typology 10 constraints 10! = 3,628,800 rankings At first, this seems to be a very large number of grammars, a portion of which are actually attested. However, it turns out that not all rankings produce different grammars. Distribution of nasal vowels Four attested patterns V + oral C V + nasal C a. Highly Restricted Inventory pal pan b. Complimentary Distribution pal pãn c. Positional Neutralization pal pãl pãn d. Full Contrast pal pãl pãn pan Let s look at them in more detail... I. Highly restricted inventory Allows only oral vowels, but nasals (nasal sonorant stops) are possible. Attested: pal, pan Not attested: *pãl, *pañ
II. Full contrast Nasal vowels are possible in all positions. Attested: pal, pan, pãl, pañ III. Complimentary Distribution Nasal vowels are possible only before nasals, and oral vowels are possible only before oral consonants. Attested: pal, pañ Not attested: *pãl, *pan 1V. Positional Neutralization Only nasal vowels are possible before nasals. Attested: pal, pãl, pañ Not attested: *pan 1. Highly restricted inventory Allows only oral vowels, but nasals (nasal sonorant stops) are possible. Attested: pal, pan Not attested: *pãl, *pañ
Distribution of nasal vowels Four attested patterns V + oral C V + nasal C a. Highly Restricted Inventory pal pan b. Complimentary Distribution pal pãn c. Positional Neutralization pal pãl pãn d. Full Contrast pal pãl pãn pan OT analysis Let us think of what constraints are required to capture these patterns. Other patterns are not attested. Constraints Three different types of constraints: general markedness constraints contextual markedness constraints faithfulness constraints Two types of markedness constraints Why are they required? The general constraint penalizes one type of vowels regardless of their position. The context-specific constraint penalizes one type of vowels in a particular position.
General Markedness Constraints Similar sets of segments typically exhibit asymmetries in terms of markedness. More marked = less common crosslinguistically, subject to restrictions... These phonological facts often have to do with their phonetic properties (harder to articulate, perceive etc.). General Markedness Constraints Some examples: All languages have oral vowels, but some also have nasal vowels. All languages have front unrounded vowels, but not all languages have front rounded vowels. All languages have voiceless obstruents, but not all languages have voiced obstruents. Nasal v. oral vowels Which are more marked? All languages have oral vowels, but some may also have nasal vowels. Oral vowels are more frequent than nasal vowels. No language have more nasal vowels than oral vowels. Nasal vowels are marked... compared to oral vowels This generalization can be captured using a markedness constraint. This constraint is context-free, and applies to all nasal vowels. *NASALVOWEL No nasal vowels.
Contextual markedness constraints Not all segments are equally marked in all positions. Examples: In the position before voiceless obstruents, voiced obstruents are more marked than voiceless obstruents. Voiced obstruents are more marked in wordfinal position than voiceless obstruents. Contextual markedness constraints What about nasal and oral vowels? Recall: Nasal vowels are generally more marked than oral vowels. Is there a position in which the situation is reversed? Contextual markedness constraints Oral vowels are more marked than nasal vowels in the position before a nasal consonant. [an] is more marked than [ãn] Contextual markedness constraints Oral vowels are more marked than nasal vowels in the position before a nasal consonant. How do we know? Languages show neutralization before nasal consonants. Some languages only allow nasal vowels before nasal consonants.
Contextual markedness constraints Contextual markedness constraints penalize sequences of segments. *Vn No oral vowels followed by nasal consonants. Two markedness constraints General markedness constraint: *NASALVOWEL No nasal vowels. Contextual markedness constraint: *Vn No oral vowels followed by nasal consonants. Are these two constraints enough? Faithfulness constraints If only markedness constraints existed, we would expect only two types of languages: no nasal vowels only nasal vowels before nasals, only oral vowels elsewhere Solution: A faithfulness constraint is also involved!
Let s check that Faithfulness constraints Grammar 1: All vowels map to oral vowels. /ã/ *ã *an a. [ã] *! b. [a] (*) 2 constr = 2 rankings Grammar II: Nasal vowels before nasal C,...oral vowels elsewhere /ãl/ *an *ã a. [ãl] *! b. [al] /an/ *an *ã a. [an] *! b. [ãn] * If only markedness constraints existed, we would expect only two types of languages: no nasal vowels only nasal vowels before nasals, only oral vowels elsewhere Solution: A faithfulness constraint is also involved! Richness of the Base (Prince and Smolensky 1993:209) All inputs are possible in all languages, [and] distributional and inventory regularities follow from the way the universal input set is mapped onto an output set by the grammar, a languageparticular ranking of the constraints. No constraint holds at the level of the input. Every possible input must map to some output. Inputs wrt nasal vowels Four possible inputs must be considered: /pal/ = oral vowel + oral consonant /pan/ = oral vowel + nasal consonant /pãl/ = nasal vowel + oral consonant /pañ/ = nasal vowel + nasal consonant
Why? Challenge: Some languages don t even have nasal vowels. Question: Why do we need to consider inputs with nasal vowels? Answer: Richness of the Base = no constraint applies at the level of the input Why? Challenge: Some languages don t even have nasal vowels. Question: Why do we need to consider inputs with nasal vowels? Answer: Richness of the Base = no constraint applies at the level of the input. Mappings in a language without nasal vowels Inputs /pal/ /pan/ /pãl/ /pañ/... Outputs [pal] [pan] Mappings in a language without nasal vowels Inputs /pal/ /pan/ /pãl/ /pañ/... Outputs [pal] [pan]
Mappings in a language without nasal vowels Inputs /pal/ /pan/ /pãl/ /pañ/... Outputs [pal] [pan] Lexicon Optimization How do we know what inputs map to what outputs? Lexicon Optimization (Prince and Smolensky 1993:209) Lexicon Optimization Lexicon Optimization Suppose that several different inputs I 1,I 1,..., I n,whenparsedby agrammargleadtocorrespondingoutputso 1,O 1,..., O n,allof which are realized as the same phonetic form Φ these inputs are all phonetically equivalent with respect to G. Now one of these outputs must be the most harmonic, by virtue of incurring the least significant violation marks: suppose this optimal one is labelled O k.thenthe learner should choose, as the underlying form for M, the input I k. In a nutshell, if several phonetically equivalent inputs exist, we need to consider the one that that violates the lowest faithfulness constraints.
Faithfulness constraints Faithfulness constraints We will consider changing of nasality from the input to output. We will consider changing of nasality from the input to output. IDENT(nasal) Corresponding segments must be identical in terms of nasality. (No changes in nasality.) IDENT(nasal) Corresponding segments must be identical in terms of nasality. (No changes in nasality.) Constraints *NASALVOWEL No nasal vowels. *Vn No oral vowels followed by nasal consonants. IDENT(nasal) Corresponding segments must be identical in terms of nasality. (No changes in nasality.) Highly restricted inventory No nasal vowels: *NASALVOWEL is top ranked /pan/ *NASV *Vn IDENT(nas) a. [pan] * b. [pãn] *! * /pãn/ *NASV *Vn IDENT(nas) a. [pan] * * b. [pãn] *!
Highly restricted inventory a. [pal] /pal/ *NASV *Vn IDENT(nas) b. [pãl] *! * /pãl/ *NASV *Vn IDENT(nas) a. [pal] * b. [pãl] *! Full contrast No restrictions: *IDENT(nasal) is top ranked /pan/ IDENT(nas) *NASV *Vn a. [pan] * b. [pãn] *! * /pãn/ IDENT(nas) *NASV *Vn a. [pan] *! * b. [pãn] * Full contrast *Vn is high ranked a. [pal] /pal/ IDENT(nas) *NASV *Vn b. [pãl] *! * /pãl/ IDENT(nas) *NASV *Vn The ranking of the lower ranked constraints becomes relevant. a. [pal] *! b. [pãl] *
Exercise: Factorial Typology Two other grammars Complimentary distribution: *Vn *NASALVOWEL IDENT(nasal) Nasal vowels only before nasal consonants, oral vowels in all other positions. Positional neutralization: *Vn IDENT(nasal) *NASALVOWEL Only nasal vowels before nasal consonants, full contrast in all other positions. Four possible grammars Highly restrictive inventory: *NASALVOWEL IDENT(nasal), *Vn Full contrast: IDENT(nasal) *NASALVOWEL, *Vn Complimentary distribution: *Vn *NASALVOWEL IDENT(nasal) Positional neutralization: *Vn IDENT(nasal) *NASALVOWEL Rankings vs. grammars 3 constraints 3! = 6 rankings... but only 4 different grammars! Not all rankings will result in a distinct grammar. Some rankings produce the same grammar. Hence, 10 constraints won t produce 10! = 3,628,800 different grammars.
Interim summary Constraints are universal. Cross-linguistic differences stem from rankings. Not every ranking produces a unique grammar. Some rankings don t matters. Factorial typology produces the full range of attested grammars. Another example: Syllable typology The Syllable Onsets All languages have onsets. Some languages may also have syllables without onsets.
Codas Constraints Not all languages allow codas. If a language has syllables with codas, it will also have syllables without codas. ONSET Syllables must have onsets. *[σv *CODA No codas. *C]σ Syllable types Some universals Syllable type ONSET *CODA CV CVC * V * Universal syllabification CV.CV CVC.V ( more harmonic than ) VC * *
No language has [tat.a] How do we get syllables? /tata/ ONSET *CODA a. [ta.ta] b. [tat.a] *! *! They can be in the input or not. Richness of the Base allows for any kind of syllabification in the input. How do we get syllables? Usually, we assume that only the output is syllabified (prosodified): Freedom of Analysis = Any amount of structure may be posited. Syllabification is governed by markedness constraints. Summary Factorial typology predicts the range of attested languages. Some rankings produce the same grammar.
More on constraint ranking EGG 2011 Peter Jurgec ~ peter@jurgec.net Summary so far OT grammar OT constraints Factorial Typology Today s Outline The Emergence of the Unmarked (TETU) Homogeneity of Target/Heterogeneity of Process (HoTHoP) Generalized Alignment How does constraint ranking work? Dominant constraints are much more likely to be active compared to low-ranked constraints. Active = have fatal violations, exclude one or more candidates. Violations of lower ranked constraints many times do not matter.
The Emergence of the Unmarked aka TETU A phenomenon in which a lower-ranked constraint becomes active. Recall last time... Constraints on syllable structure: ONSET Syllables must have onsets. *[σv *CODA No codas. *C]σ A toy language Mappings Allows onsetless syllables Never prefers deletion or epenthesis DEP and MAX outrank ONSET /pata/ [pata] /pae/ [pae] /ata/ [ata]
Assign *s ONSET is not active /ata/ [ata] /ata/ Dep Max Onset a. a.ta b. Pa.ta /ata/ [ata] /ata/ Dep Max Onset a. a.ta * b. Pa.ta *! Constraint ranking More candidates Lower ranked constraints typically don t matter! /ata/ [ata] /ata/ Dep Max Onset a. a.ta * b. at.a **! c. Pa.ta *!
TETU Even though ONSET is frequently violated in this language (and thus ranked low), it is nevertheless still active, crucially deciding among some candidates. ONSET prefers outputs with onsets rather than codas. Homogeneity of Target/ Heterogeneity of Process (HoTHoP) HoTHoP OT is a target-oriented theory. Targets are enforced by markedness constraints. HoTHoP There are several ways of satisfying a markedness constraint. The way a markedness constraint is satisfied is determined by other constraints. Pre-OT term: conspiracy (Kisseberth 1970)
Example: *NC Example: *NC (Pater 1999) *NC No nasal + voiceless consonant sequences. Is *NC a good constraint? (Pater 1999) *NC No nasal + voiceless consonant sequences. Is *NC a good constraint? *NC *NC is formally not an ideal markedness constraint. The featural connection between a nasal and a voiceless consonant is unclear. *NC Phonetically grounded: nasalization correlates with voicing, and it is difficult to produce a sequence of consonants that differ in voicing. Typologically grounded: languages that allow NC clusters also allow NC clusters, but not vice versa.
Let s look at some data NC resolution Toba Batak: nasals become oral Kelantan Malay: nasals delete Japanese: voiceless C becomes voiced Ranking of other constraints matters! These grammars are predicted by different rankings of *NC and other constraints: IDENT(nasal) IDENT(voice) MAX Rankings a. Toba Batak *NC, Ident(voice), Max Ident(nasal) b. Kelantan Malay *NC, Ident(voice), Ident(nasal) Max c. Japanese *NC, Ident(nasal), Max Ident(voice) d. English Ident(voice), Ident(nasal), Max *NC
Interim summary OT is typological Constraints can be satisfied by different repairs. This is an advantage of the theory! The repair is determined by other constraints. OT constraints and rankings predict attested patterns. OT constraints and rankings exclude unattested patterns. What s our task? What s next? Figure out the data & generalizations Figure out constraints Figure out the factorial typology Recall *NC phonetically & typologically grounded formally somewhat problematic We will now look at a constraint (family) that satisfies both criteria.
Generalized Alignment Generalized Alignment (McCarthy & Prince 1993) The idea is that morphological and prosodic domains tend to be aligned with one another. Alignment constraints are a way to formalize this tendency. Evidence for alignment Prosody: many languages have initial or final stress no language has stress on the syllable that is further from both edges feet are often alignment with one or another edge Evidence for alignment Assimilation: directional, targets an edge of a domain often fails to apply across a domain boundary
The template (McCarthy & Prince 1993:2) ALIGN(Cat1, Edge1, Cat2, Edge2) Cat1 Cat2 such that Edge1 of Cat1 and Edge2 of Cat2 coincide. Where Cat1, Cat2 PCat GCat Edge1, Edge2 {Right, Left} Some observations One violation mark per locus of violation One violation mark per {Cat1, Edge1, Cat2, Edge2}. If there is no Cat1, the constraint is vacuously satisfied. Some examples Some examples ALIGN(stress, R, word, R) For every stress(ed syllable), there should be a word, such that the right edge of the stress(ed syllable) and the right edge of the word coincide. ALIGN(stress, R, word, R) ALIGN(word, R, stress, R)
Order matters! ALIGN(stress, R, word, R) For every stress(ed syllable), there should be a word, such that the right edge of the stress(ed syllable) and the right edge of the word coincide. ALIGN(word, R, stress, R) For word, there should be a every stress(ed syllable), such that the right edge of the word and the right edge of the every stress(ed syllable) coincide. More examples ALIGN(foot, R, word, R) and ALIGN(word, R, foot, R) ALIGN(foot, R, word, L) and ALIGN(word, R, foot, L)... ALIGN(word, L, phrase, L) and ALIGN(phrase, R, word, L)... Beyond stress morpheme position assimilation Exercise: Nasal harmony
Conclusions We have seen several predictions of OT. Lower ranked constraints matter (in some cases, for some candidates). OT constraints can be satisfied in different ways. Formalizing and grounding OT constraints is a challenging task. How to do OT? EGG 2011 Peter Jurgec ~ peter@jurgec.net Summary so far... Gen, Con ROTB, Input, Output, Tableaux Correspondence Theory TETU HoPHoP Generalized Alignment Today s question: How to do OT?
How to analyze data using OT? Figure out the generalizations Figure out possible and impossible segments/sequences Propose constraints Faithfulness constraints Markedness constraints How to analyze data using OT? Figure out the ranking out these constraints Method #1: Trial and error Method #2: Factorial Typology Method #3: Algorithms Method #4: Software (e.g. OTsoft) How do we know what constraints are needed? Markedness constraints (MCs) M penalizes structures/segments/sequences If an MC is high ranked, the relevant structure will not be attested in a language Sometimes, several different MCs interact Keep in mind that MCs are usually phonetically grounded How do we know what constraints are needed? Markedness constraints are of two types: context-free context-specific
How do we know what constraints are needed? How do constraints work? Faithfulness constraints a small set of constraints Correspondence Theory (all constraints are either markedness or faithfulness constraints) How do constraints work? If your analysis doesn t work... The idea: constraints are needed to exclude unattested candidates. Constraints are evidence why some candidates are attested, but others are not. Check *, constraints, rankings... Consider other constraints Try to figure out where s the problem
The Predictive Power of OT Exercise: Farsi, Greek OT makes strong predictions about crosslinguistic typologies. Constraint interaction is a simple and straightforward tool to achieve this. Thank you Contact me: peter@jurgec.net http://www.jurgec.net www.facebook.com/phonology