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Introduction to Introduction to

Language Acquisition TheoryLanguage Acquisition Theory

Janet Dean FodorJanet Dean FodorSt. Petersburg July 2013 St. Petersburg July 2013

Class 5. The Subset Principle: Class 5. The Subset Principle: Essential but impossible? Essential but impossible?

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TToday: How far to generalize?oday: How far to generalize?

If there is no reliable source of negative data for correcting If there is no reliable source of negative data for correcting overgeneralization errors, they must be overgeneralization errors, they must be preventedprevented in in advance. advance.

UG cannot do this alone. Not all languages have the sameUG cannot do this alone. Not all languages have the samebreadth of generalizations (breadth of generalizations (e.g. Verb-Second / aux-inversione.g. Verb-Second / aux-inversion).). The learner The learner must choosemust choose how far to generalize, from how far to generalize, from among the UG-compatible (parametric) alternatives. among the UG-compatible (parametric) alternatives.

Additional sources of innate guidance = strategies of Additional sources of innate guidance = strategies of the the learning mechanismlearning mechanism: : Uniqueness Principle (Class 3) Uniqueness Principle (Class 3)

Subset Principle: Subset Principle: “Guess conservatively” “Guess conservatively” (Class1)(Class1)

CRUCIAL QUESTION: Can the Subset Principle (SP) help CRUCIAL QUESTION: Can the Subset Principle (SP) help learners to find the right learners to find the right balancebalance between conservative (safe) between conservative (safe) learning and rapid progress toward the target grammar?learning and rapid progress toward the target grammar?

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Generalize how far? which way?Generalize how far? which way? Children don’t have unlimited memory resources. Children don’t have unlimited memory resources.

This makes wise grammar choice more difficult.This makes wise grammar choice more difficult.

A standard assumption: No storage of raw input. A standard assumption: No storage of raw input. Child cannot contemplate a huge stored collection of Child cannot contemplate a huge stored collection of examples and look for patterns (as linguists do).examples and look for patterns (as linguists do).

Incremental learningIncremental learning = retain or change grammar = retain or change grammar hypothesis after each input sentence. Memory-free!hypothesis after each input sentence. Memory-free!

So, on hearing a novel sentence, a child must adopt it So, on hearing a novel sentence, a child must adopt it and some other sentencesand some other sentences into her language. into her language. (Children don’t acquire (Children don’t acquire onlyonly sentences they’ve heard.) sentences they’ve heard.) But But whichwhich other sentences? other sentences?

What size and shape What size and shape is the generalization a learner is the generalization a learner formulates, based on that individual input sentence?formulates, based on that individual input sentence?

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LM strategies must also be innateLM strategies must also be innate Even with UG, a learner encountering a novel sentence Even with UG, a learner encountering a novel sentence

has to choose from among many possible generalizations.has to choose from among many possible generalizations.

Even in the P&P framework, the number of possible Even in the P&P framework, the number of possible grammars is in the millions or billions (2grammars is in the millions or billions (23030 ≈ a billion). ≈ a billion).

The choices that LM makes are evidently The choices that LM makes are evidently not randomnot random. . All children exposed to a target language arrive at more or All children exposed to a target language arrive at more or less the same grammar (as far as we can tell).less the same grammar (as far as we can tell).

Conclusion: Conclusion: Guessing strategies must also be genetically Guessing strategies must also be genetically givengiven. . (Perhaps these correspond to linguistic markedness.(Perhaps these correspond to linguistic markedness.))

Traditional term for this: an Traditional term for this: an evaluation metricevaluation metric. . An important component of the learning mechanism An important component of the learning mechanism (Chomsky, 1965). It (Chomsky, 1965). It prioritizesprioritizes grammar hypotheses. grammar hypotheses.

RESEARCH GOAL: Specify the evaluation metric. Is it RESEARCH GOAL: Specify the evaluation metric. Is it specific to language, or domain-general (e.g., simplicity)?specific to language, or domain-general (e.g., simplicity)?

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Evaluation metric: Evaluation metric: Err in the direction of Err in the direction of underunder-generalization-generalization

If LM If LM underundergeneralizes based on one input, the grammar generalizes based on one input, the grammar can be broadened later as more examples are heard.can be broadened later as more examples are heard.

And even if not, the consequences are not disastrous: And even if not, the consequences are not disastrous: as an adult, the learner might lack some means of as an adult, the learner might lack some means of expression in the language. (Would anyone notice?)expression in the language. (Would anyone notice?)E.g., someone might not acquire the English subjunctive.E.g., someone might not acquire the English subjunctive.

By contrast, if LM generalizes By contrast, if LM generalizes too broadlytoo broadly from an input from an input sentence, with insufficient negative data to correct it later, it sentence, with insufficient negative data to correct it later, it becomes a becomes a permanent errorpermanent error. Very noticeable if it occurs!. Very noticeable if it occurs!

As an adult, s/he would utter incorrect sentences, e.g. As an adult, s/he would utter incorrect sentences, e.g.

**Went she home? Went she home? I met the boy *(who) loves Mary.I met the boy *(who) loves Mary.

In L1 acquisition, this happens rarely, if ever.In L1 acquisition, this happens rarely, if ever.

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Overgeneralization rarely occursOvergeneralization rarely occurs Children rarely overgeneralize Children rarely overgeneralize syntacticsyntactic patterns (despite patterns (despite

informal impressions; Snyder 2011). informal impressions; Snyder 2011).

There are reports in the literature (e.g. Bowerman: There are reports in the literature (e.g. Bowerman: *Brush me my hair*Brush me my hair), but remarkably few (considering how ), but remarkably few (considering how noticeable/cute these errors are). And most are noticeable/cute these errors are). And most are lexicalexical: l: a wrong subcategorization for the verb a wrong subcategorization for the verb brushbrush..

More research needed: Search the CHILDES database to More research needed: Search the CHILDES database to establish the establish the frequencyfrequency and and typetype of overgeneralization of overgeneralization errors evidenced in children’s spontaneous speech. errors evidenced in children’s spontaneous speech. What proportion of them are pure syntax? What proportion of them are pure syntax? E.g., E.g., How good a dancer is he? How good a dancer is he? * * How good dancers are they?How good dancers are they?

In In morphologymorphology, there are , there are manymany overgeneralizations: overgeneralizations: *foots*foots, , *runned. *runned. But these can be driven out later by correct forms But these can be driven out later by correct forms (Uniqueness Principle, Class 3). (Uniqueness Principle, Class 3).

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SP’s job is to SP’s job is to fend offfend off overgeneralization overgeneralization SP SP informalinformal statement: “…the learner must guess the statement: “…the learner must guess the

smallest possible language compatible with the input at smallest possible language compatible with the input at each step”. (Clark 1992)each step”. (Clark 1992)

JDF: Good thought, but JDF: Good thought, but impreciseimprecise. If 2 input-compatible . If 2 input-compatible languages languages intersectintersect, LM may freely guess either. , LM may freely guess either.

But it’s in the right spirit: But it’s in the right spirit: A ‘small’ guess is always A ‘small’ guess is always safersafer. It guarantees that if the guess was wrong, there . It guarantees that if the guess was wrong, there will be a will be a positivepositive datum (trigger) to put it right later. datum (trigger) to put it right later.

However: Unexpectedly, However: Unexpectedly, we will see that hugging the we will see that hugging the input tightly with small guesses can input tightly with small guesses can impedeimpede learning! learning!

A paradox that we must solve:A paradox that we must solve: SP is essential for SP is essential for learning without negative evidence. But it impedes learning without negative evidence. But it impedes acquisition of valid linguistic generalizations.acquisition of valid linguistic generalizations.

SP: Adopt a ‘smallest superset’ of the input SP: Adopt a ‘smallest superset’ of the input

On hearing s, the learner may hypothesize either L1 or L2, but not L3.

A ‘smallest superset’ of some set S of sentences is a language which has no proper subset that contains S. Both L1 and L2 are smallest supersets of sentence s.

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L3

L2L1

s

Assume these are the only languages permitted by UG which contain s.

SP: Adopt a ‘smallest superset’ of the input SP: Adopt a ‘smallest superset’ of the input

On hearing s’, the learner must hypothesize L2, not L3.

Hypothesize L3 only on hearing s”.L3 is now the smallest superset of the current input, s”.

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L3

L2L1

s s”s’

Assume these are the only languages permitted by UG which contain s, s’ and/or s”.

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SP works badly, in older TG frameworkSP works badly, in older TG framework In terms of transformational rules: SP would favor the In terms of transformational rules: SP would favor the

maximum context restrictionsmaximum context restrictions on any transformation: on any transformation:

CORRECT: Invert aux in the context of a fronted CORRECT: Invert aux in the context of a fronted negativenegative. .

Not once did I think of my own safety.Not once did I think of my own safety.

WRONG : Invert aux in the context of a fronted WRONG : Invert aux in the context of a fronted elementelement. . **At onceAt once did I think of my own safety. did I think of my own safety.

SP favors SP favors maximum feature specificationsmaximum feature specifications for what fronts. for what fronts.

CORRECT: Invert [+AUX, +V, -N]. CORRECT: Invert [+AUX, +V, -N].

WRONG: Invert [+V, -N]. WRONG: Invert [+V, -N].

*Not once *Not once thought Ithought I of my own safety. of my own safety.

In other words: In a In other words: In a rule-basedrule-based framework, SP requires framework, SP requires the learner to prefer the the learner to prefer the most complex rules!most complex rules! Simplicity Simplicity yields generality. yields generality. Not a plausible evaluation metric.Not a plausible evaluation metric.

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Subset Principle in a parametric model Subset Principle in a parametric model Good: P&P theory doesn’t suffer from that dangerous Good: P&P theory doesn’t suffer from that dangerous

relation between simplicity (good) and over-generality relation between simplicity (good) and over-generality (incurable). Because (incurable). Because all P-values are equally simple.all P-values are equally simple.

What What isis required: If parameter triggering is to be automatic required: If parameter triggering is to be automatic & effortless (as the theory claims), LM must be able to tell & effortless (as the theory claims), LM must be able to tell without effort without effort when a subset-superset choice presents itselfwhen a subset-superset choice presents itself, , and and whichwhich of the competing grammars yields the subset. of the competing grammars yields the subset.

Is it sufficient for Is it sufficient for eacheach parameter to have a default parameter to have a default value? value? Simple Defaults ModelSimple Defaults Model. . ((Manzini & Wexler 1987Manzini & Wexler 1987))

That would make it easy to obey SP! If both values of a That would make it easy to obey SP! If both values of a parameter P are compatible with the input, adopt the default.parameter P are compatible with the input, adopt the default.

But no. Natural language examples suggest the parameters But no. Natural language examples suggest the parameters must must alsoalso be priority-ordered with respect to each other. be priority-ordered with respect to each other. (See below: the (See below: the OrderedOrdered Defaults Model Defaults Model))

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First, let’s check: Do s-s relations actually First, let’s check: Do s-s relations actually occur in the natural language domain?occur in the natural language domain?

Yes. Any parameter with values Yes. Any parameter with values optionaloptional vs vs obligatoryobligatory. . Also, every historical process of either addition or loss (but Also, every historical process of either addition or loss (but

not both at once!) creates a s-s relation. not both at once!) creates a s-s relation.

Imagine: Italian with split-DP (as in Latin). AdjImagine: Italian with split-DP (as in Latin). Adjii Verb Noun Verb Nounii Actual example: Expansion of the Actual example: Expansion of the 's's genitive since late genitive since late

Middle English, without loss of the Middle English, without loss of the ofof-genitive.-genitive. But not just s-s relations between But not just s-s relations between whole languageswhole languages. .

Must avoid superset errors parameter by parameter.Must avoid superset errors parameter by parameter. E.g. If target is English, don’t adopt long-distance E.g. If target is English, don’t adopt long-distance

anaphora – even if that language anaphora – even if that language as a wholeas a whole isn’t a isn’t a superset of English (e.g., learner has no passives yet).superset of English (e.g., learner has no passives yet).

Why? Because there’s no link between LDA and Passive Why? Because there’s no link between LDA and Passive that that could trigger a retreatcould trigger a retreat on LDA. on LDA.

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Binding theory parameters Binding theory parameters (Manzini & Wexler,1987)(Manzini & Wexler,1987)

Binding principles: Anaphors must be locally bound. Binding principles: Anaphors must be locally bound. Pronouns must be non-locally bound. What counts as local?Pronouns must be non-locally bound. What counts as local?

5 degrees of locality. An anaphor must be bound in the 5 degrees of locality. An anaphor must be bound in the minimal domain that includes it & a governor for it, & has:minimal domain that includes it & a governor for it, & has:

a. A subject a. A subject more local (fewer anaphors, more pronouns) more local (fewer anaphors, more pronouns)b. An Infl b. An Infl c. A tense c. A tense d. A ‘referential’ tense d. A ‘referential’ tense e. a ‘root’ tensee. a ‘root’ tense less local (more anaphors, fewer pronouns) less local (more anaphors, fewer pronouns)

Creates Creates nestednested subset languages (5-valued parameter!). subset languages (5-valued parameter!). Proof that s-s relations exist in natural languagesProof that s-s relations exist in natural languages ..

Other M&W assumptions: The Independence Principle (“the subset Other M&W assumptions: The Independence Principle (“the subset relations that are determined by the values of a parameter hold no relations that are determined by the values of a parameter hold no matter what the values of the other parameters are.”) matter what the values of the other parameters are.”)

M&W assumed the M&W assumed the SimpleSimple Defaults Model Defaults Model

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Do children actually apply SP?Do children actually apply SP? There are cases in which it is claimed that children do There are cases in which it is claimed that children do notnot

obey SP: they obey SP: they overgeneralize and then retreatovergeneralize and then retreat..

Chien & Wexler (1990) found that children apply Principle A Chien & Wexler (1990) found that children apply Principle A reliably, at least by age 6; but they reliably, at least by age 6; but they make Principle B errorsmake Principle B errors. .

Mama bear washed her. Mama bear washed her. Compatible w. picture of self-washing.Compatible w. picture of self-washing.

Is Principle B not innate? Does it mature late? Is Principle B not innate? Does it mature late? IfIf it’s innate it’s innate and accessible early, this is a clear and accessible early, this is a clear violationviolation of SP. of SP.

HOWEVER: C&W also found that the children did HOWEVER: C&W also found that the children did notnot make make mistakes when a quantified antecedent: mistakes when a quantified antecedent: Every bear washes her.Every bear washes her.

Explanation: Explanation: Principle B blocks co-indexationPrinciple B blocks co-indexation of a pronoun of a pronoun with a local antecedent. But only a with a local antecedent. But only a pragmaticpragmatic principle principle prevents contra-indexed expressions from having the same prevents contra-indexed expressions from having the same referent. It is this pragmatic principle that the children don’t yet referent. It is this pragmatic principle that the children don’t yet know. They do well with the quantified examples because know. They do well with the quantified examples because that’s not a matter of that’s not a matter of coreferencecoreference at all. at all.

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Do children apply SP? Another example.Do children apply SP? Another example. Déprez & Pierce (1993) claim that children sometimes Déprez & Pierce (1993) claim that children sometimes

overgenerate (= SP violation), and later retreatovergenerate (= SP violation), and later retreat . .

At approx 1½ to 3 years, learners of English have At approx 1½ to 3 years, learners of English have optionaoptional l raising of the subject from its VP-internal base positionraising of the subject from its VP-internal base position ..

No my play my puppet.No my play my puppet. Neg Subj Verb… Neg Subj Verb… (subj is low)(subj is low) He no bite you. He no bite you. Subj Neg Verb… Subj Neg Verb… (subj has (subj has raised) raised)

“…“…the errors described here as the result of failure to raise the errors described here as the result of failure to raise the subject out of the verb phrase are attributed to a valid the subject out of the verb phrase are attributed to a valid grammatical option to assign nominative Case to that position”grammatical option to assign nominative Case to that position”

How do these learners retreat later? Not clearly addressed. How do these learners retreat later? Not clearly addressed. ““earlier stages may be stages in which the grammar has earlier stages may be stages in which the grammar has

yet to ‘stabilize’ on unique settings of various parametersyet to ‘stabilize’ on unique settings of various parameters ””

So: Is this a real SP-violation? Or just vacillation between two So: Is this a real SP-violation? Or just vacillation between two values (maybe due to confusion in analyzing input - “values (maybe due to confusion in analyzing input - “nono”)? ”)?

SP: summary so farSP: summary so far Subset-superset relations do hold among natural Subset-superset relations do hold among natural

languages.languages.

Not all are attributable to a subset/superset choice Not all are attributable to a subset/superset choice within a single parameter. (See examples, next slide.) within a single parameter. (See examples, next slide.)

A Subset Principle that excludes global subset relations A Subset Principle that excludes global subset relations betweenbetween parameters is more complex for a learner to parameters is more complex for a learner to impose. impose.

Nevertheless, child learners in fact commit few or no Nevertheless, child learners in fact commit few or no superset errors. Some apparent violations of SP are superset errors. Some apparent violations of SP are explicable in other terms (e.g., pragmatic immaturity; explicable in other terms (e.g., pragmatic immaturity; input confusion).input confusion).

So our next question: How do they do it?So our next question: How do they do it?

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How can LM How can LM knowknow what’s a superset to avoid? what’s a superset to avoid? Simple Defaults Model: Simple Defaults Model: EasyEasy to read off s-s relations. to read off s-s relations.

Prefer 0 over 1. (0 = default; 1 = marked value)Prefer 0 over 1. (0 = default; 1 = marked value)

E.g. Grammar 01101 licenses languages that have proper E.g. Grammar 01101 licenses languages that have proper subsets licensed by grammars 00101, 01001, 01100, subsets licensed by grammars 00101, 01001, 01100, and their proper subsets: 00001, 00100, 01000 and 0000. and their proper subsets: 00001, 00100, 01000 and 0000.

So So avoid 01101avoid 01101 if any of these others fits the input. if any of these others fits the input.

But in the natural language domain, there are s-sBut in the natural language domain, there are s-srelations that exceed bounds of a single parameter.relations that exceed bounds of a single parameter.

Ex-1: WH-fronting Ex-1: WH-fronting (subset)(subset) versus Scrambling that includes versus Scrambling that includes scrambling of wh-items scrambling of wh-items (superset; WH may be initial or not). (superset; WH may be initial or not). A choice for learner to make: English versus Japanese.A choice for learner to make: English versus Japanese.

Ex-2: Ex-2: OptionalOptional topic topic (subset) (subset) versus obligatory topic that is versus obligatory topic that is optionally nulloptionally null (superset; obligatory XPs can be missing)(superset; obligatory XPs can be missing). . A choice for learner to make: English versus German.A choice for learner to make: English versus German.

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Ordered Defaults ModelOrdered Defaults Model (Fodor & Sakas)(Fodor & Sakas)

Child hears: Child hears: Which apples shall we buy?Which apples shall we buy? Decision: Which parameter to set to its marked value?Decision: Which parameter to set to its marked value?

SP requires the prioritization:SP requires the prioritization: (0 = default; 1 = marked value) (0 = default; 1 = marked value)

How could this crucial prioritization be economically mentally How could this crucial prioritization be economically mentally represented by learners? represented by learners?

One way: Innately One way: Innately order the parametersorder the parameters such that parameters such that parameters earlier in the ordering get set to their marked values before earlier in the ordering get set to their marked values before parameters later in the ordering. Cf. Gold’s ‘enumeration’!parameters later in the ordering. Cf. Gold’s ‘enumeration’!

Priority: 10000 > 01000 > 00100 etc. Priority: 10000 > 01000 > 00100 etc. And for two marked values: 11000 > 10100 > 10010 etc.And for two marked values: 11000 > 10100 > 10010 etc.

0 Wh-movt0 Wh-movt 0 Scrambling 0 Scrambling

1 Wh-movt1 Wh-movt 0 Scrambling 0 Scrambling

0 Wh-movt0 Wh-movt 1 Scrambling 1 Scrambling

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But: Where does the parameter ordering come from? But: Where does the parameter ordering come from?

Learning strategies cannot be learned! Must be innate.Learning strategies cannot be learned! Must be innate.

So: Learners couldn’t So: Learners couldn’t learnlearn this parameter ordering that enforces this parameter ordering that enforces SP. So what is its source?SP. So what is its source?

Could it be innate, supplied by UG? But HOW? Could it be innate, supplied by UG? But HOW?

(a) Could evolution have crafted a precise mental map of the (a) Could evolution have crafted a precise mental map of the s-s relationships between all possible natural languages? s-s relationships between all possible natural languages?

(b) Or could the LM calculate these complex subset-superset (b) Or could the LM calculate these complex subset-superset relations on-line? Surely a serious computational overload! relations on-line? Surely a serious computational overload!

Neither is plausible! Perhaps instead, the ‘black hole’ Neither is plausible! Perhaps instead, the ‘black hole’ explanation. There is an innate mental ordering but it’s explanation. There is an innate mental ordering but it’s completely arbitrary, not shaped by evolution. The learnable completely arbitrary, not shaped by evolution. The learnable languages (which are the only ones linguists know about) languages (which are the only ones linguists know about) are the ones that just are the ones that just happenhappen to precede their supersets. to precede their supersets.

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SP is necessary, but can be harmful tooSP is necessary, but can be harmful too SP can guide learners to making safe guesses, where a SP can guide learners to making safe guesses, where a

choice must be made in generalizing from a specific input. choice must be made in generalizing from a specific input. It can prevent learners from overshooting the target lg. It can prevent learners from overshooting the target lg.

But: it interacts badly with incremental learning. But: it interacts badly with incremental learning. For an incremental learner, SP may cause learning For an incremental learner, SP may cause learning

failures due to failures due to underundershooting the target language. shooting the target language.

When setting a parameter to accommodate a new When setting a parameter to accommodate a new sentence, SP requires LM to give up much of what it sentence, SP requires LM to give up much of what it had acquired from previous input. (Example below.) had acquired from previous input. (Example below.) We call this We call this retrenchmentretrenchment..

Why retrench? Because the combination of a previously Why retrench? Because the combination of a previously hypothesized language plus a new hypothesis might be hypothesized language plus a new hypothesis might be a superset of the target, violating SP. (See diagram). a superset of the target, violating SP. (See diagram). Must clean upMust clean up, when abandoning a falsified grammar., when abandoning a falsified grammar.

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SP demands maximum retrenchment!SP demands maximum retrenchment!

Sentences in the shaded area of Lcurrent must be given up when LM encounters input t which falsifies Lcurrent.

Lsuperset

Lother Lcurrent

t s

Learner first heard s, and happened to guessLearner first heard s, and happened to guess LLcurrentcurrent. .

Learner now hears t, so realizes that LLearner now hears t, so realizes that Lcurrentcurrent is wrong. is wrong.

Learner doesn’t know which Learner doesn’t know which partsparts of L of Lcurrentcurrent are wrong. are wrong.

So to be safe, So to be safe, allall of it must be discarded, except what of it must be discarded, except what

input sentence input sentence tt entails in conjunction with UG. entails in conjunction with UG.

All the striped sentences must be ditched. All the striped sentences must be ditched.

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Clark’s example (Class 2): Clark’s example (Class 2): retrenchment neededretrenchment needed

Without retrenchment, one mistake can lead to another.Without retrenchment, one mistake can lead to another.

Clark (1989) showed a sequence of steps that can end Clark (1989) showed a sequence of steps that can end in a superset error, although no one step violates SP.in a superset error, although no one step violates SP.

(1) (1) John believes John believes themthem((ACCACC) to have left.) to have left.

Is this exceptional case marking (ECM)? Is this exceptional case marking (ECM)? Or structural case assignment (SCA)?Or structural case assignment (SCA)?

(2) (2) They believe They believe themselvesthemselves to be smart. to be smart.

Is the anaphor in the binding domain of Is the anaphor in the binding domain of theythey? (yes, if ECM) ? (yes, if ECM)

Or is this long-distance anaphora (LDA)? (yes, if SCA)Or is this long-distance anaphora (LDA)? (yes, if SCA)

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Without retrenchment Without retrenchment errors errors

Suppose the target is English (ECM; no LDA).Suppose the target is English (ECM; no LDA).

Dangerous parameter-setting sequence:Dangerous parameter-setting sequence:

Guess SCA for sentence (1). Wrong, but no problem. Guess SCA for sentence (1). Wrong, but no problem. Then guess LDA for sentence (2). Still OK so far! Then guess LDA for sentence (2). Still OK so far!

Later, learner hears an unambiguous trigger for ECM:Later, learner hears an unambiguous trigger for ECM:

(3) (3) Sue is believed by John to have left. Sue is believed by John to have left.

On adopting ECM, learner must On adopting ECM, learner must give up SCAgive up SCA. .

And must also And must also give up LDA give up LDA (which was based on SCA). (which was based on SCA). Otherwise, would mis-generate: Otherwise, would mis-generate:

(4) (4) * * He wants us to like himself.He wants us to like himself.

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SP demands SP demands massivemassive retrenchment! retrenchment! Retrenchment must eliminate all sentences except those Retrenchment must eliminate all sentences except those

that LM that LM knowsknows are valid. are valid.

In incremental learning (usually assumed), LM cannot In incremental learning (usually assumed), LM cannot consult previously heard sentences. Only the current one!consult previously heard sentences. Only the current one!

In P&P framework: SP requires giving up all marked In P&P framework: SP requires giving up all marked parameter values except those that LM parameter values except those that LM knowsknows are correct. are correct.

Unless LM learns only from fully unambiguous triggers Unless LM learns only from fully unambiguous triggers (unrealistic?), it can’t be (unrealistic?), it can’t be suresure that that anyany previously set previously set parameters were set correctly. So give up parameters were set correctly. So give up allall that aren’t that aren’t entailed by the current input – set them back to defaults. entailed by the current input – set them back to defaults.

In real-life, retrenchment would be extreme. Child hears In real-life, retrenchment would be extreme. Child hears “It’s bedtime.” Must discard all knowledge previously “It’s bedtime.” Must discard all knowledge previously acquired except if entailed by that sentence plus UG.acquired except if entailed by that sentence plus UG.

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SP demands SP demands excessiveexcessive retrenchment retrenchment

Child hears “It’s bedtime” and discards topicalization, Child hears “It’s bedtime” and discards topicalization, wh-movement, aux-inversion, etc.wh-movement, aux-inversion, etc.

Could re-learn them. But retrenchment applies again Could re-learn them. But retrenchment applies again and again. No knowledge could be retained for long.and again. No knowledge could be retained for long.

Without SP Without SP overovergeneration.generation. WWith SP ith SP massive massive underundergeneration, if incremental. generation, if incremental.

The target grammar could be acquired only if all its The target grammar could be acquired only if all its parameters were set by a single input sentence! parameters were set by a single input sentence!

This disastrous interaction between SP and incremental This disastrous interaction between SP and incremental learning wasn’t noticed prior to Fodor & Sakas (2005).learning wasn’t noticed prior to Fodor & Sakas (2005).

Most SP discussions Most SP discussions implicitlyimplicitly assume without comment that assume without comment that LM has unlimited access to prior input. LM has unlimited access to prior input.

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How could SP be reconciled with incrementality?How could SP be reconciled with incrementality? How can retrenchment be tamed? By adding How can retrenchment be tamed? By adding memorymemory, ,

of one kind or another.of one kind or another.

Memory for previous inputs? Too many? But maybe ok to Memory for previous inputs? Too many? But maybe ok to store only inputs that triggered a parameter change.store only inputs that triggered a parameter change.

Problem: Now, LM has to fit parameter values to a Problem: Now, LM has to fit parameter values to a collectioncollection of accumulated input sentences. Could that of accumulated input sentences. Could that be done by triggering?? be done by triggering??

Instead: Memory for previously disconfirmed grammars? Instead: Memory for previously disconfirmed grammars? Then SP demands only that LM adopt a ‘smallest language’ Then SP demands only that LM adopt a ‘smallest language’ which fits the current input sentence and whichwhich fits the current input sentence and whichhasn’t yet been disconfirmedhasn’t yet been disconfirmed. The ‘smallest’ would get larger . The ‘smallest’ would get larger and larger as learning proceeds and larger as learning proceeds less retrenching. less retrenching.

Problem: How to mentally represent which grammars Problem: How to mentally represent which grammars have been disconfirmed? A huge list? A point on an have been disconfirmed? A huge list? A point on an enumeration? – but Pinker’s objection! enumeration? – but Pinker’s objection!

A lattice representing all s-s relationsA lattice representing all s-s relations This (as shown) is less than 1% of the total lattice for the This (as shown) is less than 1% of the total lattice for the

3,072 languages in the CoLAG domain. 3,072 languages in the CoLAG domain. But only 7-deep.But only 7-deep.

LM must select a grammar from the lowest level. LM must select a grammar from the lowest level. When a grammar is disconfirmed, delete it.When a grammar is disconfirmed, delete it. Lattice shrinks from the bottom up Lattice shrinks from the bottom up larger languages. larger languages.

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Supersets Supersets

Subsets Subsets

Fodor, Sakas & Fodor, Sakas & Hoskey 2007Hoskey 2007

The lattice model would work, but….The lattice model would work, but…. But, a very But, a very ad hocad hoc solution. Why would this huge data solution. Why would this huge data

structure be part of a child’s innate endowment?structure be part of a child’s innate endowment?

Worse still: It codes relations between E-languages, Worse still: It codes relations between E-languages, whereas we would like to assume that the human mind whereas we would like to assume that the human mind stores only I-language facts. stores only I-language facts.

The only alternative to adding memory is: The only alternative to adding memory is: Trust only unambiguous input.Trust only unambiguous input.

SP does not demand any retrenchment if LM knows that all SP does not demand any retrenchment if LM knows that all the marked parameter values it has adopted so far are the marked parameter values it has adopted so far are correct – because they were adopted in response to correct – because they were adopted in response to unambiguousunambiguous triggers. triggers.

We’ll explore this solution next time (Class 6). We’ll explore this solution next time (Class 6). 28

Writing assignmentWriting assignment A young child acquires the syntax of Russian in 5 or 6 A young child acquires the syntax of Russian in 5 or 6

years. Many linguists have worked for many decades years. Many linguists have worked for many decades (centuries!) to discover the syntactic properties of (centuries!) to discover the syntactic properties of Russian. Russian.

Are children smarter than linguists? If not, what else might Are children smarter than linguists? If not, what else might explain this discrepancy? explain this discrepancy?

In what relevant respects do linguists have stronger In what relevant respects do linguists have stronger resources than children? In what respects do children resources than children? In what respects do children have stronger resources? have stronger resources?

2 or 3 pages, please, to hand in at Monday’s class.2 or 3 pages, please, to hand in at Monday’s class.

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