Foundations of Linguistics: the problem of the

interface Eric Reuland

Iris Mulders

Jakub Dotlačil

Today

• General background

• Design

• Learnability

The basis of all science

• Wonder (especially about the obvious)

• Formulating questions

• Articulating problems

• Hope these are solvable

• Make a plan

• Start your research

 

Problem Research  Theory Predictions  

- Observations- Precision- Explanation 

Empirical cycle

What is Language?

Language: Systematic relation between

• Forms: events in an (external) medium (sound, gesture, ink on paper)

&

• Interpretations: change in information state of the mind

Some Characteristics

• Humans identify certain (external) physical phenomena as expressions of their language

• They analyze and interpret them fast, automatically, unconsciously

•  The particular way in which humans do this is species specific

The study of language

• Answering big “How” questions

• Study of individual languages, and particular structures and their properties

• Elementary mental processes

Big Questions

• How did language emerge? Did it further evolve?• How is language related to thought?• How is language represented in the brain?• What is the relation between the language faculty and

other cognitive faculties?• How special is the language faculty?• How is language acquired?• What is the range of variation among languages?• Are there linguistic universals? If so, what are they,

and what do they follow from?

Toward precise models

• Language as a computational system

• Defines a mapping between forms and interpretations on the basis of a finite vocabulary of elementary form-meaning pairs.

discrete infinity of form-meaning pairings

Evolutionary fable

• Given a primate with the human mental architecture and sensori-motor apparatus in place, but not yet a language organ. What specifications does some language organ FL have to meet if upon insertion it is to work properly? (Chomsky (1998:6)

Language as a computational system

How (un)controversial?

• Some examples of computations;– Form: Dutch verb clusters

– Interpretation: English null objects

(1) a. Cindy hoort Pat b. Cindy hoort Pat een lied zingen

 (2) a. Cindy heeft Pat gehoord

b *Cindy heeft Pat gehoord een lied zingenc. *Cindy heeft Pat een lied gehoord zingen

 (3) a. Cindy heeft een lied gehoord

b. *Cindy heeft een lied horenc. Cindy heeft Pat een lied horen zingen

 (4) a. Cindy heeft Pat dat lied niet kunnen laten horen

b. *Cindy heeft Pat dat lied niet gekund laten horen 

Dutch Verb clusters

English null objects(1) a. I wonder who the men expected to see them

b. The men expected to see them

(2) a. John ate an appleb. John ate

(3) a. John is too stubborn to talk tob. John is too stubborn to talk to Bill

(4) a. John is too clever to expect us to catchb. John is too clever to expect us to catch Bill

Knowledge versus use

Systematic ambiguity between:• Grammar as an abstract system defining a

mapping between form and interpretation• Grammar as a system implemented in the brain

that is accessed and used in the actual computations the brain has to carry out in order to assign an interpretation to a form, or find a form for an (intended) interpretive effect issues about the relation between the grammar and the processing system

The minimal language system

PF interface C-I interface

Sensori- CHL Interpretation

Motor system system

Lexicon

- dedicated +dedicated(?) -dedicated

Tasks 1

Characterize

• Computational system (CHL)– Universal versus Language specific properties

• Lexicon– Universal versus Language specific properties

• PF-interface (relation to medium)• CI-interface (relation to thought)

Tasks 2: find map between linguistic operations and neurocognitive processesPF-interface

|Computational system of

Human Language (CHL) (+Lexicon)

|Conceptual-Intentional

Interface (C-I interface)

?

On the relation between linguistics and psycholinguistics

"The split between linguistics and psycholinguistics in the 1970’s has been interpreted as being a retreat by linguists from the notion that every operation of the grammar is a mental operation that a speaker must perform in speaking and understanding language. 

But, putting history aside for the moment, we as linguists cannot take the position that there is another way to construct mental representations of sentences other than the machinery of grammar.

 ....There is no retreat from the strictest possible interpretation of grammatical operations as the only way to construct linguistic representations" (Alec Marantz, lecture notes 2000)

Tasks 3 and 4

• Determine how the grammar is put to use in reasoning, realizing communicative intentions, etc?

• Determine the nature and locus of cross-linguistic variation, and how the child is able to arrive at the correct grammar of the language she is exposed to?

An aside: Form versus function and the theory of language

• Reinhart 2006:

The language system (hence our theory of it) must be compatible with the functions it serves, but cannot be determined by them, since many conceivable systems could potentially serve the same functions

Levels of adequacy

• Observational adequacy (bare facts)• Descriptive adequacy/Interface adequacy

(output readable to interface)– Processing system– Inference system

• Explanatory adequacy (acquisition)• Neuro-cognitive adequacy (“beyond”

explanatory adequacy, Chomsky 2005)

Tensions between requirements

• What do we need for easy description?• What do we need for explanation?• Nothing special:

Compare - Quantum physics- Newtonian mechanics

For understanding planetary motionFor understanding why there are no white holes

Required for explanation

• What do we minimally need to account for language structure?

• What do we minimally need to assume is dedicated to language?

• Behind these questions:– What kind of elements and what type of

properties can be plausibly represented in the brain?

An example: how do we compute dependencies?

• What did John see?

• What did John see –

• What did John [ [see - ] ]

One-step process or two-step process?

Grammatical system:Essential properties

Required:

• Inventory of vocabulary items/lexicon (elementary form-meaning combinations)

• Combinatory principles

• Abstract from: ‘size’ of basic vocabulary items

Definitions

• Given a vocabulary V, a language LV is a subset of V* (=the set of all strings over V)

• A grammar GL is a finite set of rules generating the strings over V that are members of L and none of the strings over V that are not members of L

A simple model

Intuitive procedure:

1. Identify the set L1 of possible first words of a sentence

2. Identify for each member i of L1 the set L2i of words by which it can be followed

3. Continue the procedure until you are done

Peripheral recursion

Peripheral: The calling of an instruction at the end of carrying out that instructionP(lan)

Realized P

Realized P … P?

Formalized as: finite state grammar Illustration:   oldThe man comes   men come S The S1S1 man S3S1 men S4S3 comesS4 comeS1 old S1

A hierarchy of grammar types• i. Finite state grammars: peripheral recursion

Rule schema’s (with x, y, strings over a given vocabulary):

S xS; Sy ii. Beyond finite state grammars (context free or higher): minimally allowing embedded recursion as in:

S xSy; SxyS aSb; S ab generates anbn

iii.iv,v, vi. More expressive power (full CFG, CS, URS)

Some formal languages

The following sets are formal languages:(i) ab, abb, aaabbb, ….. (i.e. n occurrences of a followed by

n occurrences of b)(ii) aa,bb,abba,baab,bbbb,aabbaa,abbbba, …. (X followed by

the mirror image of X)(iii) aa,bb,abab,baba,aaaa,bbbb,aabaab,abbabb, …. (X followed by

X) These are not finite state languages: It is impossible to constract a finite state grammar that would generate all and only the sentences of these languagesWhy: Insufficient means to encode relevant pattern

  

What about human language?

S

The birds1 S are1 arriving

that the man2 S is2 listening to

I3 was3 watching S

when …..

An informal proof (Chomsky 1957)I. Let S1,S2,S3 be declarative sentences in English, thenII(i) If S1, then S2(ii) Either S3 or S4(iii) The man who said that S5 is arriving today Interdependencies: if---then, either ---- or, man --- isInterdependencies can be embedded: if, either (iii), or S4, then S5 Hence: a + S1 + b; S1 = c + S2 + d

This pattern reflects the mirror properties of (ii).Hence: No theory of linguistic structure based exclusively on Markov process models and the like will adequately reflect the competence of a speaker of English

Result

• The finite state model is inadequate as a model of natural language.

• This does not just hold for FS grammars proposed so far, but extends to any possible grammar in the set of FS grammars

• This was a result of a new kind.

Interface adequacy

FS grammars and levels of adequacy

• Observational adequacy

• Descriptive/Interface adequacy

• Explanatory adequacy

• ….

Issues of language design

• The round square dog barked (at the lazy moon)

S1

The S2

round S2

square S3

dog S4

barked

What’s wrong?

What’s wrong with mere sequentiality?

• A grammar should encode expressions in such a way that the interface with the interpretive system can read them and use them for further processing

• A grammar should encode dependencies between expressions in such a way that the interface with the interpretive system can read them and use them for further processing

• [[The round square dog]SU [barked]Pred ]Sentence

A more powerful type of grammar:Types of phrase structure grammars are defined by different restrictions on rule types. A standard context free (CF) phrase structure grammar expresses hierarchical structure and uses rules of the general form: A BC (where B and C range over the categories of the grammar,

including A) A a (where a ranges over the terminal vocabulary (lexicon)

of the language) (i) Sentence NP + VP(ii) NP D + N(iii) VP Verb + NP(iv) D the(v) N man, ball, ….(vi) Verb hit, took, ….

Structure

Sentence 

NP VP 

D N Verb NP 

the man hit D N

the ball

The dependencies between the subparts of natural language expressions are best captured in terms of a hierarchical structure Tree diagrams represent: 1. The hierarchical grouping of parts of the sentence into

constituents2. The grammatical type of each constituent3. The left –to-right order of the constituents

Hierarchical structure

Constituent structure and interface adequacy

An analysis of the sentence into contiguous subparts such that:

• The subparts serve as the input for the computation of dependencies

• The subparts are readable to the interface(s)

Constituent structure guide lines

• Dislocation moves constituents

• Substitution observes constituency

• Dependencies obtain between constituents– Semantic role assigment– Case assignment

Issues in Learnability

The acquisition schema

From the initial state to the final – adult – state:

S0 ------ S1 ------ S2 ---.....---- Si ---........--- Sn ------ Sn------Sn

| | | | | |

D1 D2 Di Dn Dn+1 Dn+2 ......

• Adult state: convergence - input causes no more changes.• Question: How is this possible?

A simplified version

Questions: What does a person who knows a language

know? Quite a lot….What does a person who know a language

minimally know?A person who knows a language minimally

knows what strings of words are wellformed sentences and which do not.

  Question: What is the size of the set of sentences of a language? •Principled answer: Infinite; there is no longest sentence.• Practical answer: astronomical, also if one limits oneself to sentences that are not overly long.•Conjecture: The number of well-formed English sentences of 20 words and less is 1020 (Levelt 1967) Six seconds per sentence 19.000.000.000.000 years to hear and say them all. Six years of non-stop listening: the percentage of sentences heard is at most 0,000000000031%

 

Size

 1,2,3,4,5,6,7, ….

2,4,6,8,10, ….

1,5,25,125,625,3125, ….. 0,2,6,12,20,30, …..

(1x0, 2x1,3x2,4x3, …..) 

Abstract task: continue a series 1

1,5,11,19,29, …. Regularity 1:(1x2)-1, (2x3)-1, …. a(a+1)-1: (6x7)-1=41, (7x8)-1=55 Alternative (based on prime number series): 1, (2,3), 5, (7), 11, (13,17), 19, (23), 29, (31,37), 41, (43), 47,

(53, 59), 61, …..  

Continue a series 2

The abstract version

• I. Consider an infinite set of which a finite subset is given. Determine the full set on the basis of this subset.

II. Consider an infinite series of elements (e.g., the natural numbers). Determine, given a finite beginning of the series how it continues.

• III. Fundamental truth: Such tasks have an infinity of solutions

How comes it that human beings, whose contacts

withthe world are brief and personal and limited,

are nevertheless able to know as much as we do

know?(Chomsky 1986)

Plato’s Problem

Tasks of the sort Complete the series are impossible in theirgenerality.

They may be possible of the type of regularity is given in advance.

For instance: i) There is a constant difference between a member of the

series and its successor.ii) For each member in the series its successor is computed by

multiplying it with a constant factor. 

Restricting the hypothesis space

Complicating factors

• No negative evidence– No systematic corrections– Resistance to correction

• Non-homogeneity– Errors– Idiolectal variation

• Yet the child finds her way

Insufficient

• Analogy• Motherese• The data is so much richer• Restricted window

May be true: but make learning task harder instead of easier

Require substantive further restrictions on hypothesis space focus of current research

 Classical example (McNeill (1966) 

Child: Nobody don't like meMother: No, say "nobody likes me'Child: Nobody don't like me(this goes on 8 times)

Finally:Mother: No, now listen carefully; say " nobody likes me"Child: Oh, nobody don't likes me

Analogy – Negative evidence

(1) a. The members of the audience will standb. Will the members of the audience stand?

(2) a. Mary has lived in Princetonb. Has Mary lived in Princeton?

(1’)a. The members of the audience who have been enjoying themselves will stand

a. *Have the members of the audience who - been enjoying themselves will stand?

b. Will the members of the audience who have been enjoying themselves - stand?

Analogy versus structure

Minimal condition on operations in natural language

• Structure dependence

• Types of impossible operations:

- Mirroring a string

- Move the 25th word

- etc.