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IntroductionLearning Long Distance AgreementConclusionsLearning Long-Distance Agreement PhonotacticsJeffrey [email protected] of California, Los AngelesThe 81st meeting of the LSAAnaheim, CaliforniaJ. Heinz (1)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyIntroductionI will present a learning algorithm that learns long-distanceagreement phonotactic patterns without a prioriOptimality-theoretic constraints (Prince and Smolensky 1993,2004).The proposed algorithm simply keeps track of precedencerelations.This approach demonstrates the utility of factoring the learningproblem.J. Heinz (2)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyOutline1IntroductionLong-Distance AgreementLearning in Phonology2Learning Long Distance AgreementRepresenting LDA PatternsPrecedence Grammars3ConclusionsSummaryRemaining QuestionsJ. Heinz (3)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyOutline1IntroductionLong-Distance AgreementLearning in Phonology2Learning Long Distance AgreementRepresenting LDA PatternsPrecedence Grammars3ConclusionsSummaryRemaining QuestionsJ. Heinz (4)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyWhat is Long-Distance Agreement?Long Distance Agreement (LDA) patterns are those withinwhich particular segments, separated by at least one othersegment, must (dis)agree in some feature (Hansson 2001, Roseand Walker 2004).Hansson (2001) adds that the intervening segments are notaudibly affected by the agreeing feature.This is in order to clearly distinguish LDA from spreading (seealso Gafos 1999 and Walker 1998).J. Heinz (5)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyExamples of Long-Distance AgreementConsonantal Harmony (Hansson 2001, Rose and Walker 2004)Sibilant HarmonyLiquid HarmonyDorsal Harmony.Vowel Harmony with transparent vowelsFinnish, Hungarian, Nez Perce (see Baković 2000 and referencestherein)But see also Gordon (1999), Gafos and Benus (2003), and Gicket. al. (2006).J. Heinz (6)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyLDA with No Blocking: NavajoIn well formed words, sibilants agree in the feature [anterior].1.2.[s,z,ts,ts',dz] are never preceded by [S,Z,tS,tS',dZ].[S,Z,tS,tS',dZ] are never preceded by [s,z,ts,ts',dz].Examples (Sapir and Hojier 1967):1.2.Si:te:Zdasdo:lis‘we (dual) are lying’‘he (4th) has his foot raised’3.4. Si:te:z(hypothetical)(hypothetical) dasdo:liSJ. Heinz (7)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyLDA with Local Blocking: Ineseño ChumashIn well formed words:1.2.[S] is never preceded by [s].[s] is never preceded by [S] unless the nearestpreceding [S] is immediately followed by [n,t,l].Examples (Applegate 1972, Poser 1982):1.ksunonus‘I obey him’5.S‘he tells him’2.3.4.kSunotS‘I am obedient’(hypothetical)(hypothetical)6.7. sustimeS ksunonuS(hypothetical)‘they (dual) aregone awry’ kSunotsJ. Heinz (8)tijepusSiSlusisinLearning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyWhy LDA Patterns are Thought to be a Challenge to LearnArbitrarily many segments may intervene between agree-ers.Albright and Hayes (2003a) observe that “the number oflogically possible environments. . . rises exponentially with thelength of the string.”Thus there are potentially too many environments for a learner toconsider in discovering LDA patterns.J. Heinz (9)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyThe Meaning of “arbitrarily many”However, does “arbitrarily many” really require a learner toconsider every logically possible nonlocal environment?J. Heinz (10)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyOutline1IntroductionLong-Distance AgreementLearning in Phonology2Learning Long Distance AgreementRepresenting LDA PatternsPrecedence Grammars3ConclusionsSummaryRemaining QuestionsJ. Heinz (11)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyLearning in PhonologyLearning in Optimality Theory[Tesar(1995), Boersma(1997), Tesar(1998), Tesar and Smolensky(1998), Hayes(1999), Boersma and Hayes(2001),Lin(2002), Pater and Tessier(2003), Pater(2004), Prince and Tesar(2004), Hayes(2004), Riggle(2004),Alderete et al.(2005)Alderete, Brasoveanua, Merchant, Prince, and Tesar, Merchant and Tesar(to appear),Wilson(2006), Riggle(2006), Tessier(2006)]Learning in Principles and Parameters[Wexler and Culicover(1980), Dresher and Kaye(1990), Niyogi(2006)]Learning Phonological Rules[Gildea and Jurafsky(1996), Albright and Hayes(2002), Albright and Hayes(2003a), Albright and Hayes(2003b)]Learning Phonotactics[Ellison(1992), Goldsmith(1994), Frisch(1996), Coleman and Pierrehumbert(1997),Frisch et al.(2004)Frisch, Pierrehumbert, and Broe, Albright(2006), Goldsmith(2006), Heinz(2006a), Heinz(2006b),Heinz(To appear), Hayes and Wilson(To appear)]J. Heinz (12)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyThe Learning FrameworkLanguageof GGrammar GSampleLearnerGrammar G2What is Learner so that Language of G2 Language of G?See Nowak et. al. (2002) and Niyogi (2006) for overviews.J. Heinz (13)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyInductive Learning and the Hypothesis SpaceLanguageof GGrammar GSampleLearnerLearning cannot take place unless thehypothesis space is restricted.G2 is not drawn from an unrestricted setof possible grammars.Grammar G2The hypotheses available to the learner ultimately determine:(1) the kinds of generalizations made(2) the range of possible natural language patternsUnder this perspective, Universal Grammar (UG) is the set ofavailable hypotheses.J. Heinz (14)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyDifferent Kinds of Hypothesis Spaces are LearnedDifferently.The set of syntactic hypotheses available to children is not thesame as the set of phonological hypotheses available to children.- The two domains do not have the same kind of patterns and so weexpect them to have different kinds of learners.Likewise, the set of Long Distance Agreement patterns aredifferent from patterns which restrict the distribution of adjacentsegments.J. Heinz (15)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsLong-Distance AgreementLearning in PhonologyFactoring the Phonotactic Learning ProblemDifferent kinds of phonotactic constraints can be learned bydifferent learning algorithms.A complete phonotactic learner is a combination of thesedifferent learning algorithms.Here, I am only showing how one part of the whole learner—thepart that learns LDA constraints—can work.J. Heinz (16)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsOutline1IntroductionLong-Distance AgreementLearning in Phonology2Learning Long Distance AgreementRepresenting LDA PatternsPrecedence Grammars3ConclusionsSummaryRemaining QuestionsJ. Heinz (17)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsRepresenting LDA Patterns with Finite-state MachinesLDA patterns are regular—that is, describable by a finite-stateacceptor [Johnson(1972), Kaplan and Kay(1981), Kaplan and Kay(1994), Ellison(1992), Eisner(1997),Albro(1998), Albro(2005), Karttunen(1998), Frank and Satta(1998), Riggle(2004), Karttunen(2006)]Finite-state acceptors(1) accept or reject words. So it meets the minimum requirement fora phonotactic grammar– a device that at least answers Yes or Nowhen asked if some word is possible. (Chomsky and Halle 1968,Halle 1978)(2) can be related to finite state OT models, which allow us tocompute a phonotactic finite-state acceptor (Riggle 2004), whichbecomes the target grammar for the learner.(3) are well-defined and can be manipulated.(Hopcroft et. al. 2001).J. Heinz (18)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLDA with No Blocking: Navajo1.2.[s,z,ts,ts',dz] are never preceded by [S,Z,tS,tS',dZ].[S,Z,tS,tS',dZ] are never preceded by [s,z,ts,ts',dz].sC,VC,Vs01C any consonant except sibilantss [ anterior] sibilantsV any vowelS [-anterior] sibilants s, S, si, S i, ss, AcceptsSS, sis, S iS, sns,. SnS, . . .SSC,V2J. Heinz (19)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsThe Finite-State Representation of the LDA Pattern inNavajosC,VC,Vs01SSC,V2This grammar recognizes an infinitenumber of legal words, just like thegenerative grammars of earlierresearchers.It does accept words like[tnSSSSttttttS iiii]—but this violates otherconstraints on well-formedness (e.g.syllable structure constraints).If the OT analyses of LDA given in Hansson (2001) or Rose andWalker (2004) were written in finite-state terms, this acceptor isexactly the one returned by Riggle’s (2004) algorithm.J. Heinz (20)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLDA with Local Blocking: Chumash1.2.[S] is never preceded by [s].[s] is never preceded by [S] unless the nearestpreceding [S] is immediately followed by [n,t,l].C,V,NSC,V,NN1S0C,VS2C any consonant except [s,S,n,t,l]V any vowelN [n,t,l] s, S, si, S i, ss,.SS, sis, S iS, sns, SnS,Accepts Sns, Snis, Sniis, . . .s C,V,N,s3J. Heinz (21)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsThe Learning Question in ContextLDA with No Blocking(Navajo)sC,VC,Vs0SLDA with Local Blocking (Chumash)C,V,NSC,V,N N1S10SC,VC,VS2s C,V,N,s32How can the acceptors above be acquired from finite samples ofNavajo and Chumash, respectively?The class of patterns describable by finite state acceptors isknown to be insufficiently restrictive for learning to occur (Gold1967, Osherson et. al. 1986).J. Heinz (22)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsThe Learning Question in ContextLDA with No Blocking(Navajo)sC,VC,Vs0SLDA with Local Blocking (Chumash)C,V,NSC,V,N N1S10SC,VC,VS2s C,V,N,s32How can the acceptors above be acquired from finite samples ofNavajo and Chumash, respectively?The class of patterns describable by finite state acceptors isknown to be insufficiently restrictive for learning to occur (Gold1967, Osherson et. al. 1986).J. Heinz (23)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsOutline1IntroductionLong-Distance AgreementLearning in Phonology2Learning Long Distance AgreementRepresenting LDA PatternsPrecedence Grammars3ConclusionsSummaryRemaining QuestionsJ. Heinz (24)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsRecalling How We Can Describe LDA with No Blocking:Navajo1.2.[s,z,ts,ts',dz] are never preceded by [S,Z,tS,tS',dZ].[S,Z,tS,tS',dZ] are never preceded by [s,z,ts,ts',dz].J. Heinz (25)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsRecalling How We Can Describe LDA with No Blocking:Navajo1.2.[s,z,ts,ts',dz] are never preceded by [S,Z,tS,tS',dZ].[S,Z,tS,tS',dZ] are never preceded by [s,z,ts,ts',dz]. [s] can be preceded by [s].[s] can be preceded by [t].[t] can be preceded by [s].[S] can be preceded by [S].[S] can be preceded by [t].J. Heinz (26)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsPrecedence GrammarsA precedence grammar is a list of the allowable precedencerelations in a language.J. Heinz (27)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)Precedence G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.J. Heinz (28) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)Precedence G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.J. Heinz (29) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,t) (s,o)(s,s) (S,S) (S,t) (S,o)Precedence G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.J. Heinz (30) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)Precedence G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.J. Heinz (31) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)Precedence G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.J. Heinz (32) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)Precedence G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.J. Heinz (33) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)Precedence G (t,s) (t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.(2) The Language of G excludes sotoS.J. Heinz (34) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLanguages Recognized by Precedence GrammarsWords recognized by a precedence grammar are those for whichevery precedence relation is in the grammar.Example. (Assume Σ {s,S,t,o}.) x(s,t) (s,o)(s,s) (S,S) (S,t) (S,o)Precedence G (t,s) (t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)(1) The Language of G includes sotos.(2) The Language of G excludes sotoS.J. Heinz (35) . Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsPrecedence Languages are Regular.These grammars are notational variants.LDA with No Blocking(e.g. Navajo)st,ot,os01SSt,oPrecedence Grammar (s,s)(s,t) (s,o) (S,S) (S,t) (S,o)G (t,s)(t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)2See appendix on how to write a finite-state acceptor given aprecedence grammar.J. Heinz (36)Learning Long-Distance Agreement Phonotactics .

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.[s] is never preceded by [S].[S] is never preceded by [s]. (s,t) (s,o) (S,S) (S,t) (S,o).Precedence G (t,s) (t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o) (s,s) The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (37)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.Learning[s] is never preceded by [S].[S] is never preceded by [s].Precedence G Sample { } . The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (38)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.Learning[s] is never preceded by [S].[S] is never preceded by [s].Precedence G Sample { tosos } (s,s) (t,s) (o,s) (s,o) (t,o) (o,o)The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (39)Learning Long-Distance Agreement Phonotactics.

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.[s] is never preceded by [S].[S] is never preceded by [s]. (s,s) (s,o)(S,S) (S,t) (S,o)LearningPrecedence G (t,o)(t,s) (t,S) (o,s) (o,S) (o,t) (o,o)Sample { tosos , SotoS }The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (40)Learning Long-Distance Agreement Phonotactics .

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.[s] is never preceded by [S].[S] is never preceded by [s]. (s,t) (s,o) (S,S) (S,t) (S,o)Learning.Precedence G (t,s) (t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)Sample { tosos , SotoS , stot } (s,s) The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (41)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.[s] is never preceded by [S].[S] is never preceded by [s]. (s,t) (s,o) (S,S) (S,t) (S,o)Learning.Precedence G (t,s) (t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)Sample { tosos , SotoS , stot } (s,s) The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (42)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Precedence GrammarsNavajo Fragment. (Assume Σ {s,S,t,o}.)1.2.[s] is never preceded by [S].[S] is never preceded by [s]. (s,t) (s,o) (S,S) (S,t) (S,o)Learning.Precedence G (t,s) (t,S) (t,t) (t,o) (o,s) (o,S) (o,t) (o,o)Sample { tosos , SotoS , stot } (s,s) The learner has already generalized; it accepts [SoS], [Stot],[sototos]but not words like [Stos] or [sosoS]J. Heinz (43)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLocal SummaryAny LDA with no blocking pattern (e.g. Navajo) can bedescribed with a precedence grammar.Any LDA with no blocking pattern can be learned efficiently inthe manner described above.J. Heinz (44)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLDA with Local Blocking and Precedence Grammars:Chumash1.2.[S] is never preceded by [s].[s] is never preceded by [S] unless the nearestpreceding [S] is immediately followed by [n,t,l].Precedence Grammars as given cannot describe the pattern inChumash. kSinotstijepusS(hypothetical)‘he tells him’Next I will show how to extend precedence grammars to capturepatterns like those found in Chumash.Bigram PrecedenceRelative PrecedenceJ. Heinz (45)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsBigram PrecedenceThe grammar contains elements of the form (ab,c):“[c] can be preceded by [ab]”.The idea is that in Chumash(St,s) is in the grammar, but (Si,s) is not. kSinotsStijepusJ. Heinz (46)(hypothetical)‘he tells him’Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsRelative Precedence[ab relatively precedes [c] iff(1) [ab] precedes [c] and(2) no [a] intervenes between [ab] and [c]The second conjunct captures the “nearest-preceding” aspect ofthe Chumash description above.S iSlusisin[ S i ‘they (dual) are gone awry’precedes [s]but [ S i does not relatively precede [s]Thus local blocking is achieved by not including (Si,s) in thegrammar but including (St,s).J. Heinz (47)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsRelative Precedence[ab relatively precedes [c] iff(1) [ab] precedes [c] and(2) no [a] intervenes between [ab] and [c]The second conjunct captures the “nearest-preceding” aspect ofthe Chumash description above.S iSlusisin[ S i ‘they (dual) are gone awry’precedes [s]but [ S i does not relatively precede [s]Thus local blocking is achieved by not including (Si,s) in thegrammar but including (St,s).J. Heinz (48)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Relativized Precedence Bigram GrammarsThe learner simply records the relativized precedence bigramrelations observed. Precedence G Sample { }The learner has already generalized: it accepts [S iS, S in, Slun, Slis,sisisin]but not to words like [Sis, Silus].J. Heinz (49)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Relativized Precedence Bigram GrammarsThe learner simply records the relativized precedence bigramrelations observed.Precedence G ( S i,S )(iS,l)(iS,u)( Sl,u) (iS,s)(iS,i)(iS,n)( Sl,s)( Sl,i)( ,n)(is,i)Sample { S iSlusisin } The learner has already generalized: it accepts [S iS, S in, Slun, Slis,sisisin]but not to words like [Sis, Silus].J. Heinz (50)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Relativized Precedence Bigram GrammarsThe learner simply records the relativized precedence bigramrelations observed.Precedence G ( S i,S )(iS,l)(iS,u)( Sl,u) (iS,s)(iS,i)(iS,n)( Sl,s)( Sl,i)( ,n)(is,i)Sample { S iSlusisin } The learner has already generalized: it accepts [S iS, S in, Slun, Slis,sisisin]but not to words like [Sis, Silus].J. Heinz (51)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLearning Relativized Precedence Bigram GrammarsThe learner simply records the relativized precedence bigramrelations observed.Precedence G ( S i,S )(iS,l)(iS,u)( Sl,u) (iS,s)(iS,i)(iS,n)( Sl,s)( Sl,i)( ,n)(is,i)Sample { S iSlusisin } The learner has already generalized: it accepts [S iS, S in, Slun, Slis,sisisin]but not to words like [Sis, Silus].J. Heinz (52)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsLocal SummaryAny LDA with local blocking pattern such as the one inChumash can be described with a Relativized PrecedenceBigram Grammar.Any pattern describable by a Relativized Precedence BigramGrammar can be learned efficiently by the algorithm describedabove.J. Heinz (53)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsRepresenting LDA PatternsPrecedence GrammarsRelativized Bigram Precedence Patterns include PrecedencePatternsRelativized Precedence Bigram Patterns LDA with Local Blocking PatternsChumashPrecedence Patterns LDA with No Blocking PatternsNavajoAny pattern that can be described with a Precedence Grammarcan be described with a Relativized Precedence BigramGrammar.J. Heinz (54)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsSummaryRemaining QuestionsOutline1IntroductionLong-Distance AgreementLearning in Phonology2Learning Long Distance AgreementRepresenting LDA PatternsPrecedence Grammars3ConclusionsSummaryRemaining QuestionsJ. Heinz (55)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsSummaryRemaining QuestionsRegular Patterns include Relativized Bigram PrecedencePatternsRelativized Precedence Bigram Patterns LDA with Local Blocking PatternsChumashPrecedence Patterns LDA with No Blocking PatternsNavajoRegular PatternsThe class of relativized precedence bigram patterns shown here:(1) is a small subset of regular patterns(2) includes LDA patterns attested in natural language phonotactics(3) is learned simply in the manner described.J. Heinz (56)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsSummaryRemaining QuestionsWhy Learning LDA is SimpleThe number of logically possible nonlocal environments increasesexponentially with the length of the word.Precedence-based learners do not consider every logicallypossible nonlocal environment. They cannot learn logicallypossible nonlocal patterns like:(1) If the third segment after a sibilant is a sibilant, they must agree in[anterior].(2) If the second, third, or fifth segments after a sibilant is a sibilant,they must agree in [anterior].(3) and so onThese learners do not distinguish on the basis of distance at all.The notion of “arbitrarily many”—not being able to count—issufficiently restrictive for learning to occur.J. Heinz (57)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsSummaryRemaining QuestionsWhy Learning LDA is SimpleThe number of logically possible nonlocal environments increasesexponentially with the length of the word.Precedence-based learners do not consider every logicallypossible nonlocal environment. They cannot learn logicallypossible nonlocal patterns like:(1) If the third segment after a sibilant is a sibilant, they must agree in[anterior].(2) If the second, third, or fifth segments after a sibilant is a sibilant,they must agree in [anterior].(3) and so onThese learners do not distinguish on the basis of distance at all.The notion of “arbitrarily many”—not being able to count—issufficiently restrictive for learning to occur.J. Heinz (58)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Distance AgreementConclusionsSummaryRemaining QuestionsSummaryA learner can keep track of precedence relations to learn attestedLong Distance Agreement patterns.This algorithm is properly thought of as one part of a completephonotactic learner—the part which returns LDA-typeconstraints.Factoring the learning problem is a useful way to address howphonological learning can occur.J. Heinz (59)Learning Long-Distance Agreement Phonotactics

IntroductionLearning Long Dista

Learning Long Distance Agreement Conclusions Learning Long-Distance Agreement Phonotactics Jeffrey Heinz [email protected] University of California, Los Angeles The 81st meeting of the LSA Anaheim, California J. Heinz (1) Learning Long-Distance Agreement Phonotactics. Introduction