Lecture17-ComplexSystems3

Lecture17-ComplexSystems3 - Complex Linguistic Systems...

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Unformatted text preview: Complex Linguistic Systems Psych 215L: Language Acquisition What is the generative system that creates the observed (structured) data of language (ex: metrical phonology)? Observable data: stress contour EMphasis Lecture 17 Complex Systems Complex Linguistic Systems What is the generative system that creates the observed (structured) data of language (ex: metrical phonology)? The Hypothesis Space Which syllable of a larger unit is stressed? {Leftmost, Rightmost} Are all syllables included? {Yes, No-not leftmost, No-not rightmost} Observable data: stress contour (H L ) H EM pha sis (S S ) S EM pha sis Are syllables differentiated? {No, Yes-2 distinctions, Yes-3 distinctions} EMphasis (H L L) EM pha sis (S S S) EM pha sis Linguistic parameters = finite (if large) hypothesis space of possible grammars Knowledge Representation Motivations Modeling learnability vs. modeling acquirability Modeling learnability “ideal”, “rational”, or “computational-level” learners “Can it be learned at all by a simulated learner?” what is possible to learn Modeling acquirability (Johnson 2004) more “realistic” or “cognitively inspired” learners Argument from constrained cross-linguistic variation “Can it be learned by a simulated learner that is constrained in the ways humans are constrained?” what is possible to learn if you’re human Knowledge Representation Motivations One traditional motivation for proposals of knowledge representation (such as parameters): The knowledge representation helps explain the constrained variation observed in adult linguistic knowledge across the languages of the world Another (sometimes implicit) motivation for proposals of knowledge representation: Having this knowledge representation pre-specified allows children to acquire the right generalizations from the data as quickly as they seem to do Knowledge Representation Motivations Argument from acquisition Easier if knowledge structure available a priori Another (sometimes implicit) motivation for proposals of knowledge representation: Having this knowledge representation pre-specified allows children to acquire the right generalizations from the data quickly as they seem to do Argument from acquisition Pearl 2008, 2009, 2011 abstraction/ generalization Input Output Using computational methods and available empirical data, we can quantify this argument and explicitly test different proposals for knowledge representation At the same time, we can explore how acquisition could proceed if children were using these different knowledge representations Learning Parametric Linguistic Systems Linguistic parameters give the benefit of a finite hypothesis space. Still, the hypothesis space can be quite large. Learning Parametric Linguistic Systems Also, data are often ambiguous between competing hypotheses, since multiple grammars can account for the same data point. EM pha sis For example, assuming there are n binary parameters, there are 2n core grammars to choose from. Exponentially growing hypothesis space (H L L) EM pha sis (H L ) H EM pha sis (Clark 1994) (S S S) EM pha sis (S S ) S EM pha sis Parametric Metrical Phonology Parametric Metrical Phonology Metrical phonology: What tells you to put the EMphasis on a particular SYLlable Metrical phonology: What tells you to put the EMphasis on a particular SYLlable Process speakers use: Basic input unit: syllables Process speakers use: Basic input unit: syllables em pha sis Larger units formed: metrical feet The way these are formed varies from language to language. Stress assigned within metrical feet The way this is done also varies from language to language. Observable Data: stress contour of word em pha sis Larger units formed: metrical feet (em pha) sis (EM pha) sis EMphasis The way these are formed varies from language to language. Stress assigned within metrical feet The way this is done also varies from language to language. Observable Data: stress contour of word (em pha) sis (EM pha) sis EMphasis system parameters of variation - to be determined by learner from available data Parametric Metrical Phonology Metrical phonology system here: 5 main parameters, 4 sub-parameters (adapted from Dresher 1999 and Hayes 1995) - 156 viable grammars Feet Headedness Quantity Sensitivity Boundedness Parametric Metrical Phonology Metrical phonology system here: 5 main parameters, 4 sub-parameters (adapted from Dresher 1999 and Hayes 1995) - 156 viable grammars Sub-parameters: options that become available if main parameter value is a certain one Extrametricality Feet Directionality All combine to generate stress contour output Parametric Metrical Phonology Metrical phonology system here: 5 main parameters, 4 sub-parameters (adapted from Dresher 1999 and Hayes 1995) - 156 viable grammars All combine to generate stress contour output A Brief Tour of Parametric Metrical Phonology Are syllables differentiated? No: system is quantity-insensitive (QI) Most parameters involve metrical foot formation All combine to generate stress contour output S S S CVV CV CCVC lu di crous A Brief Tour of Parametric Metrical Phonology Are syllables differentiated? Are syllables differentiated? No: system is quantity-insensitive (QI) S S S CVV CV CCVC lu di crous Only allowed method: differ by rime weight onset kr di Yes: system is quantity-sensitive (QS) narrowing of hypothesis space Only allowed method: differ by rime weight Only allowed number of divisions: 2 Heavy vs. Light VV always Heavy V always Light rime nucleus ə crous S S S CVV CV CCVC lu di crous No: system is quantity-insensitive (QI) kr´s crous Syllable Yes: system is quantity-sensitive (QS) lu A Brief Tour of Parametric Metrical Phonology coda s Option 1: VC Heavy (QS-VC-H) Option 2: VC Light (QS-VC-L) Are all syllables included in metrical feet? Yes: system has no extrametricality (Em-None) ( L … L VC af VC ter ) H VV noon L H H L L lu A Brief Tour of Parametric Metrical Phonology H di crous lu di crous A Brief Tour of Parametric Metrical Phonology Are all syllables included in metrical feet? Yes: system has no extrametricality (Em-None) ( L … L VC af VC ter ) H VV noon No: system has extrametricality (Em-Some) Only allowed # of exclusions: 1 Only allowed exclusions: Leftmost or Rightmost syllable narrowing of hypothesis space A Brief Tour of Parametric Metrical Phonology ( L VC af Are all syllables included in metrical feet? Yes: system has no extrametricality (Em-None) … L VC ter ) H VV noon No: system has extrametricality (Em-Some) Only allowed # of exclusions: 1 Only allowed exclusions: Leftmost or Rightmost syllable narrowing of hypothesis space Leftmost syllable excluded: Em-Left ( … ) Rightmost syllable excluded: Em-Right ( … ) L H L H L VC gen V da VV lu V di What direction are metrical feet constructed? Two logical options From the left: Metrical feet are constructed from the left edge of the word (Ft Dir Left) Ft Left ( H L VV lu V di H L VV lu From the right: Metrical feet are constructed from the right edge of the word (Ft Dir Right) H V a A Brief Tour of Parametric Metrical Phonology V di H VC crous ) VC crous A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). narrowing of hypothesis space H VC crous A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). Ft Dir Left L L L H L (L L L H L ( L L L )(H L ( L L L )(H L) A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? Are metrical feet unrestricted in size? Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). Ft Dir Left Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). Ft Dir Right ( L L L )(H L) A Brief Tour of Parametric Metrical Phonology L L L H L L L H Ft Dir Right L) Ft Dir Left/Right ( L L L H) (L) L) L L L Ft Dir Left ( L L L )(H L (L L L H) (L) L (L L L L L) S S S ( L L L H) (L) L S S) (S S S S S) A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? ( L L L H) (L) Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). ( L L L )(H L) (L L L L L) (S S S S S) No: Metrical feet are restricted (Bounded). The size is restricted to 2 options: 2 or 3. ( L L L H) (L) Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). ( L L L )(H L) (L L L L L) (S S S S S) No: Metrical feet are restricted (Bounded). narrowing of hypothesis space The size is restricted to 2 options: 2 or 3. Ft Dir Left 2 units per foot (Bounded-2) x x x x 3 units per foot (Bounded-3) x x x x ( x x ) (x x (x x x) ( x ( x x ) (x (x x x) ( x ) x) narrowing of hypothesis space A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? ( L L L H) (L) Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). ( L L L H) (L) Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). ( L L L )(H L) (L L L L L) (S S S S S) No: Metrical feet are restricted (Bounded). The size is restricted to 2 options: 2 or 3. ( L L L )(H L) (L L L L L) (S S S S S) No: Metrical feet are restricted (Bounded). narrowing of hypothesis space x) B-2 x) ( x ) B-3 ( x x ) (x (x x The size is restricted to 2 options: 2 or 3. The counting units are restricted to 2 options: syllables or moras. Ft Dir Left Bounded-2 xx narrowing of hypothesis space (x x (H x) B-2 x) ( x ) B-3 ( x x ) (x L)(L H) ( L L ) (L H) Count by syllables (Bounded-Syllabic) ( S S) ( S S) A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? A Brief Tour of Parametric Metrical Phonology Are metrical feet unrestricted in size? ( L L L H) (L) Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). ( L L L H) (L) Yes: Metrical feet are unrestricted, delimited only by Heavy syllables if there are any (Unbounded). ( L L L )(H L) (L L L L L) (S S S S S) No: Metrical feet are restricted (Bounded). The size is restricted to 2 options: 2 or 3. The counting units are restricted to 2 options: syllables or moras. Count by syllables (Bounded-Syllabic) (H L)(L H) Ft Dir Left Bounded-2 xx Count by moras (Bounded-Moraic) xx H x x xx L L H ( H ) ( L L) ( H ) ( L L L )(H L) (L L L L L) (S S S S S) No: Metrical feet are restricted (Bounded). narrowing of hypothesis space x) B-2 x) ( x ) B-3 ( x x ) (x (x x The size is restricted to 2 options: 2 or 3. The counting units are restricted to 2 options: syllables or moras. Moras (unit of weight): H = 2 moras xx L = 1 mora x Count by syllables (Bounded-Syllabic) (H Ft Dir Left Bounded-2 L)(L H) Count by moras (Bounded-Moraic) ( H ) ( L L) ( H ) compare narrowing of hypothesis space x) B-2 x) ( x ) B-3 ( x x ) (x (x x A Brief Tour of Parametric Metrical Phonology Generating a Stress Contour Process speaker uses to generate stress contour Within a metrical foot, which syllable is stressed? Two options, hypothesis space restriction Leftmost: Stress the leftmost syllable (Ft Hd Left) ( H ) ( L L) ( H ) ( H ) ( L L) ( H ) Rightmost: Stress the rightmost syllable (Ft Hd Right) ( H ) (L L) ( H ) em Generating a Stress Contour pha sis Generating a Stress Contour Process speaker uses to generate stress contour Quantity Sensitivity Process speaker uses to generate stress contour Extrametricality Are any syllables extrametrical? Are syllables differentiated? Yes. Yes - by rime. VC & VV syllables are Heavy, V syllables are Light. H L em pha H sis Rightmost syllable is not included in metrical foot. ( … ) H L em pha H sis Generating a Stress Contour Generating a Stress Contour Process speaker uses to generate stress contour Process speaker uses to generate stress contour Boundedness Feet Directionality Which direction are feet constructed from? Are feet unrestricted in size? No. From the right. 2 syllables per foot. H L) ) H em pha (H L) sis em pha Generating a Stress Contour Feet Headedness H sis Generating a Stress Contour Process speaker uses to generate stress contour Process speaker uses to generate stress contour Which syllable of the foot is stressed? Learner’s task: Figure out which parameter values were used to generate this contour. Leftmost. (H L) em pha H (H L) sis EM pha H sis Non-trivial case study: English Non-trivial because there are many data that are ambiguous for which parameter value or constraint ranking they implicate Cognitively inspired learners using parameters Non-trivial because there are many irregularities Analysis of child-directed speech (8 -15 months) from Brent corpus (Brent & Siskind 2001) from CHILDES (MacWhinney 2000): 504084 tokens, 7390 types For words with 2 or more syllables: 174 unique syllable-rime type combinations (ex: closed-closed (VC VC)) 85 of these 174 have more than one stress contour associated with them (unresolvable): no one grammar can cover all the data Ex for VC VC type: her SELF AN swer SOME WHERE Biased learner, using only unambiguous data Pearl (2008): Success is guaranteed as long as the parameters are learned in a particular order. However…this requires the learner to identify unambiguous data and know/derive the appropriate parameter-setting order, which may not be trivial. So…is this selective learning bias really necessary? How well do unbiased learners do? Target state = grammar for English (Halle & Vergnaud 1987, Dresher & Kaye 1990, Dresher 1999) derived from cross-linguistic variation and adult linguistic knowledge: quantity sensitive, VC syllables are heavy, rightmost syllable is extrametrical, feet are constructed from the right, feet are 2 syllables, feet are headed on the left Premise: This is the grammar that best describes the systematic data of English, even if there are exceptions. Two psychologically plausible probabilistic update procedures Naïve Parameter Learner (NParLearner) Probabilistic generation & testing of grammars. (incremental) Hypothesis update: Linear reward-penalty Yang (2002) (Bush & Mosteller 1951) Two psychologically plausible probabilistic update procedures Cognitively inspired learners using parameters Naïve Parameter Learner (NParLearner) Probabilistic generation & testing of grammars. (incremental) Hypothesis update: Linear reward-penalty Yang (2002) (Bush & Mosteller 1951) Learner’s algorithm: Probabilistic generation and testing of parameter value combinations [grammars] (Yang 2002) For each parameter, the learner associates a probability with each of the competing parameter values. Initially all values are equiprobable. Ex: Quantity Sensitivity Value 1: Quantity Sensitive (0.5) Value 2: Quantity Insensitive (0.5) MAP Bayesian Learner (BayesLearner) Probabilistic generation & testing of grammars. (incremental) Hypothesis update: Bayesian updating For each data point, a grammar is probabilistically generated, based on the probabilities associated with each parameter’s values. (Chew 1971: binomial distribution) OCtopus Cognitively inspired learners using parameters Probabilistic learning for English Probabilistic generation and testing of grammars (Yang 2002) Update parameter value probabilities The selected grammar is then used to generate a stress contour, based on the syllable structure of the word. VC oc OC to pus NParLearner (Yang 2002): Linear Reward-Penalty Parameter values v1 vs. v2 If the generated contour matches the observed contour, all participating parameter values are rewarded. If it mismatches, all values are punished. OCtopus V VC to pus oc TO pus Over time (as measured in data points encountered), the probability associated with a parameter value will approach either 1.0 or 0.0, based on rewards and/or punishments. Once the probability is close enough, the learner sets the appropriate parameter value. Learning rate γ: small = small changes large = large changes ! pv1 = pv1 + " (1- pv1) pv2 = 1- pv1 pv1 = (1- " )pv1 pv2 = 1- pv1 reward v1 punish v1 ! Probabilistic learning for English Probabilistic learning for English: Modifications Probabilistic generation and testing of grammars (Yang 2002) Probabilistic generation and testing of grammars (Yang 2002) Update parameter value probabilities Update parameter value probabilities NParLearner (Yang 2002): Linear Reward-Penalty Parameter values v1 vs. v2 Learning rate γ: small = small changes large = large changes pv1 = pv1 + " (1- pv1) pv2 = 1- pv1 pv1 = (1- " )pv1 pv2 = 1- pv1 reward v1 punish v1 Count-learning: smooth out some of the irregularities in the data, better deal with complex systems (Yang 2002) Implementation (Yang 2002): Matching contour = increase parameter value’s batch counter by 1 Mismatching contour = decrease parameter value’s batch counter by 1 BayesLearner: Bayesian update of binomial distribution (Chew 1971) ! ! Parameters α, β: α = β: initial bias at p = 0.5 α, β < 1: initial bias toward endpoints (p = 0.0, 1.0) Parameter value v1 reward: success + 1 Invoke update procedure (Linear Reward-Penalty or Bayesian Updating) when count limit c is reached. punish: success + 0 here: α = β = 0.5 Probabilistic learning for English: Modifications Cognitively inspired learners using parameters Probabilistic generation and testing of grammars (Yang 2002) Update parameter value probabilities + Count Learning Empirical grounding NParLearner (Yang 2002): Linear Reward-Penalty Parameter values v1 vs. v2 Invoke when the batch counter for pv1 or pv2 equals c. pv1 = pv1 + " (1- pv1) pv2 = 1- pv1 pv1 = (1- " )pv1 pv2 = 1- pv1 reward v1 punish v1 BayesLearner: Bayesian update of binomial distribution (Chew 1971) ! ! Parameter value v1 Invoke when the batch counter for pv1 or pv2 equals c. Note: total data seen + 1 Learner’s input based on the number of words likely to be heard on average in a 6 month period: 1,666,667. (Akhtar et al. (2004), citing Hart & Risley (1995)). " + 1+ successes pv = " + # + 2 + total data seen reward: success + 1 ! punish: success + 0 Input distributions derived from child-directed speech distributions. Brent corpus (Brent & Siskind 2001): 8 - 15 months Associated stress contour: CALLHOME American English Lexicon (Canavan et al. 1997) Child’s syllabification of words: MRC Psycholinguistics Database (Wilson 1988) Cognitively inspired learners using parameters Probabilistic learning for English Goal: Converge on English values after learning period is over Learner’s algorithm: Incremental update: words are processed one at a time, as they are encountered. (Assumes word segmentation is operational. Jusczyk, Houston, & Newsome (1999) suggests that 7-month-olds can segment some words successfully.) Words are divided into syllables, with syllable rime identified as closed (VC), short (V), long (VV), or superlong (VVC). Jusczyk, Goodman, & Baumann (1999) and Turk, Jusczyk, & Gerken (1995) suggest young infants are sensitive to syllables and properties of syllable structure. Learning Period Length: 1,666,667 words (based on estimates of words heard in a 6 month period, using Akhtar et al. (2004)). Sub-parameters are not set until the main parameter is set. This is based on the idea that children only consider information about a sub-parameter if they have to. Probabilistic learning for English Goal: Converge on English values after learning period is over Learning Period Length: 1,666,667 words (based on estimates of words heard in a 6 month period, using Akhtar et al. (2004)). QS, QSVCH, Em-Some, Em-Right, Ft Dir Right, Bounded, Bounded-2, BoundedSyllabic, Ft Hd Left Model NParLearner, γ = .001, .0025, .01, .025 Success rate (1000 runs) 0.0% BayesLearner 0.0% Examples of incorrect target grammars NParLearner: Em-None, Em-None Ft Hd Left, Unb Ft Dir Left QI Unb, Left, QS, Em-None QSVCH, Ft Dir Rt, Ft Hd Left, B-Mor Bounded, Bounded-2 Em-None, B-Mor, BayesLearner: QS, Em-Some, Em-Right, QSVCH, Ft Hd Left, Ft Dir Rt, Unb Bounded, B-Syl, QI Ft Hd Left, Em-None Ft Dir Left, B-2 QI, Em-None, QS, QSVCH, Em-Some, Em-Right, Ft Dir Right, Bounded, Bounded-2, BoundedSyllabic, Ft Hd Left Probabilistic learning for English Goal: Converge on English values after learning period is over Learning Period Length: 1,666,667 words (based on estimates of words heard in a 6 month period, using Akhtar et al. (2004)). QS, QSVCH, Em-Some, Em-Right, Ft Dir Right, Bounded, Bounded-2, BoundedSyllabic, Ft Hd Left Model NParLearner, γ = .001, .0025, .01, .025 BayesLearner NParLearner + Counting, γ = .001, .0025, .01, .025, c = 2, 5, 7, 10, 15, 20 Success rate (1000 runs) 0.0% 0.0% 0.033% BayesLearner + Counting, c = 2, 5, 7, 10, 15, 20 0.0% Acquirability results: parameters Four different implementations of reward/punishment tried (two Naïve Parameter Learner variants that use Linear reward-penalty schemes (Yang 2002) and two incremental Bayesian variants) Only one variant (one of the linear reward-penalty ones) was ever successful at converging on the adult English grammar, and then only once every 3000 runs! This seems like very poor performance from these cognitively inspired learners. Problem with constrained learners? Maybe the problem is with the constrained learning algorithms: Are they identifying sub-optimal grammars for the data they encounter? If so, ideal learners should find the optimal grammars that are most compatible with the English child-directed speech data Premise: The adult English grammar is the grammar that best describes the systematic data of English, even if there are exceptions. Implication: The adult English grammar is the grammar that is best able to generate the stress contours for the English data (most compatible). English grammar compatibility with data: Problem for any parametric learner Note: not expected to be at 100% because of irregularities in English data Problem for any parametric learner Average compatibility of grammars selected by constrained learners: 73.6% by tokens (63.3% by types) (Highest compatibility in hypothesis space: 76.5% by tokens, 70.3% by types) Generates contours matching 73.0% observable data tokens, where every instance of a word is counted (62.1% types, where frequency is factored out and a word is counted only once no matter how often it occurs) The cognitively inspired learners are identifying the more optimal grammars for this data set - it’s just that these grammars don’t happen to be the adult English grammar! Learnability Implication: The problem isn’t because these learners are constrained. Unconstrained learners would have the same problem. English grammar compared to other 155 grammars Ranked 52nd by tokens, 56th by types English grammar is barely in the top third - unsurprising that probabilistic learners rarely select this grammar, given the child-directed speech data! Parametric child learner has a learnability problem: can’t get to adult target state given the data available to children Getting out of the learnability problem: 2 options A different target state Child-directed speech Adult knowledge (target state) Initial knowledge state of learner Maybe young children don’t acquire the adult English grammar until later, after they are exposed to more word types and realize the connection between stress contour and the English morphological system (connection to English morphological system: Chomsky & Halle 1968, Kiparsky 1979, Hayes 1982) Brown 1973: morphological inflections not used regularly till 36 months Option 1: change the target state Child-directed speech Initial knowledge state of learner Prediction: Children initially select non-English grammars, given these data. If so, we should be able to use experimental methods to observe them using non-English grammars for an extended period of time. Other data Other target state Adult knowledge (target state) Getting out of the learnability problem: 2 options Child-directed speech Kehoe 1998: elicitation task with English 34-month-olds used items that were compatible with the grammars modeled learners often chose here A different (enriched) initial state Adult knowledge (target state) Initial knowledge state of learner Maybe young children have additional boosts Pearl (2008) explores the effects of a bias to only learn from data perceived as unambiguous for a parametric learner, and finds that the learners with this knowledge are successful if parameters are set in certain orders. Required knowledge at the initial state: Option 2: change the initial state Child-directed speech Initial knowledge state of learner importance of unambiguous data (and a method for identifying Adult knowledge (target state) these data for each parameter value) parameter-setting order constraints (and potentially a method for deriving these constraints) Unambiguous data bias Bigger picture: Testing proposals of knowledge representation However, they make up a small percentage of the available data (never more than 5%) so their effect can be washed away in the wake of ambiguous data if the ambiguous data are learned from as well and the parameters are not learned in an appropriate order. Began by exploring cognitively plausible learners to test theories about knowledge representation (argument from acquisition) When they failed at the acquisition task, we asked what the cause of the failure was - due to learners being constrained or due to something about the language acquisition computation? Why learning from unambiguous data works: The unambiguous data favor the English grammar, so English becomes the optimal grammar. Led us to examine learnability considerations, given the data A useful framework: what comes next Change knowledge representation Highlighted learnability issues for probabilistic learners seeking optimal solutions given child-directed speech data A useful framework: what comes next Change premise about trajectory of children’s acquisition Theoretical + computational investigations: perhaps different parameters or constraints make the adult English grammar more acquirable from child-directed speech Experimental investigations: exploring English children’s initial knowledge states before they have knowledge of morphology and adult lexicon items Different theoretical proposals can be motivated and tested via computational methods This then informs future computational investigations and thus any arguments from acquisition for a given theoretical proposal of knowledge representation About that target state… Analysis of adult-directed conversational speech CALLFRIEND corpus (Canavan & Zipperlen 1996), North American English portion: recorded telephone conversations between adults 82,487 word tokens, 4,417 word types Parametric English grammar (somewhat better but not the best): 63.7% token compatibility, 52.1% type compatibility ranked 34th by tokens, 36th by types Interesting: Best grammar in hypothesis space differs only by one parameter value (QI instead of English’s QS): 66.6% token compatibility, 56.3% type compatibility A useful framework: what comes next Change learner’s initial knowledge state Computational investigations: strategies learners can use to solve acquisition problem as currently defined Describe the required initial knowledge state to make acquisition possible for learners using specific knowledge representations, thereby creating a way to explicitly compare different knowledge representations Knowledge representations requiring a less enriched initial state may be more desirable Parametric English grammar is not the best for adult conversational speech either Potential explanation: linguists use items that appear infrequently in conversations when making their theories, under the assumption that these items are part of the adult knowledge state Worth testing experimentally: the English adult knowledge state (do adults make the generalizations that linguists think they do, or are some of the crucial items exceptions that adults do not include in their generative system?) ...
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