Linguistic Structure as a Relational Network Sydney Lamb Rice University [email protected] National...

Linguistic Structure as a Relational Network

Sydney Lamb

Rice University

[email protected]

National Taiwan University

9 November 2010

Topics

Aims of Neurocognitive Linguistics The origins of relational networks Relational networks as purely relational Narrow relational network notation Narrow relational networks and neural networks Levels of precision in description Appreciating variability in language

Aims of Neurocognitive Linguistics (“NCL”)

NCL aims to understand the linguistic system of a language user• As a dynamic system

• It operates• Speaking, comprehending,

learning, etc.

• It changes as it operates• It has a locus

• The brain

NCL seeks to learn ..

• How information is represented in theHow information is represented in the linguistic systemlinguistic system• How the system operates in speaking andHow the system operates in speaking and understandingunderstanding

• How the linguistic system is connected toHow the linguistic system is connected to other knowledge other knowledge • How the system is learnedHow the system is learned• How the system is implemented in the brainHow the system is implemented in the brain

The linguistic system of a language user: Two viewing platforms

Cognitive level: the cognitive system of the language user without considering its physical basis• The cognitive (linguistic) system• Field of study: “cognitive linguistics”

Neurocognitive level: the physical basis• Neurological structures• Field of study: “neurocognitive linguistics”

“Cognitive Linguistics”

First occurrence of the term in print:

• “[The] branch of linguistic inquiry which aims at characterizing the speaker’s internal information system that makes it possible for him to speak his language and to understand sentences received from others.”

(Lamb 1971)

Operational Plausibility

To understand how language operates, we need to have the linguistic information represented in such a way that it can be used for speaking and understanding

(A “competence model” that is not competence to perform is unrealistic)

Operational Plausibility

To understand how language operates, we need to have the information represented in such a way that it can be directly used for speaking and understanding

Competence as competence to perform The information in a person’s mind is “knowing

how” – not “knowing that” Information in operational form

• Able to operate without manipulation from some added “performance” system

Topics


Relational network notation

Thinking in cognitive linguistics was facilitated by relational network notation

Developed under the influence of the notation used by M.A.K. Halliday for systemic networks

Precursors

In the 1960s the linguistic system was viewed (by Hockett and Gleason and me and others) as containing items (of unspecified nature) together with their interrelationships• Cf. Hockett’s “Linguistic units and their relations”

(Language, 1966) Early primitive notations showed units with

connecting lines to related units

The next step: Nodes

The next step was to introduce nodes to go along with such connecting lines

Allowed the formation of networks – systems consisting of nodes and their interconnecting lines

Halliday’s notation used different nodes for paradigmatic (‘or’) and syntagmatic (‘and’) relationships• Just what I was looking for

The downward or

DIFFICULT

hard diffricult

The downward and

a b

The ordered AND

We need to distinguish simultaneous from sequential

For sequential, the ‘ordered AND’ Its two (or more) lines connect to

different points at the bottom of the triangle (in the case of the ‘downward and’)• to represent sequential activation

leading to sequential occurrence of items

Downward (ordered) AND

Vt Nom

Upward and Downward

Expression (phonetic or graphic) is at the bottom

Therefore, downward is toward expression

Upward is toward meaning (or other function) – more abstract

network

meaning

expression

Neurological interpretation of up/down

At the bottom are the interfaces to the world outside the brain:• Sense organs on the input side• Muscles on the output side

‘Up’ is more abstract

Topics


Morpheme as item and its phonemic representation

boy

b - o - y

Symbols?Objects?

Relationship of boy to its phonemes

boy As a morpheme, it is just one unit

Three phonemes, in sequence

b o y

The nature of this “morphemic unit”

BOY Noun

b o y

boy The object we are considering

The morpheme as purely relational

BOY Noun

b o y

We can remove the symbol with no loss of information. Therefore, it is a connection, not an object

boy

Another way of looking at it

BOY Noun

b o y

boy

Another way of looking at it

BOY Noun

b o y

A closer look at the segments

b

boy

y

Phonologicalfeatures

o The phonological segments also are just locations in the network – not objects

(Bob) (toy)

Relationships of boy

BOY Noun

b o y

boy Just a label – not part of the

structure

Objection I

If there are no symbols, how does the system distinguish this morpheme from others?

Answer: Other morphemes necessarily have different connections

Another node with the same connections would be another (redundant) representation of the same morpheme

Objection II

If there are no symbols, how does the system know which morpheme it is?

Answer: If there were symbols, what would read them? Miniature eyes inside the brain?

Relations all the way

Perhaps all of linguistic structure is relational

It’s not relationships among linguistic items; it is relations to other relations to other relations, all the way to the top – at one end – and to the bottom – at the other

In that case the linguistic system is a network of interconnected nodes

Objects in the mind?

When the relationships are fully identified, the objects as such disappear, since they have no existence apart from those relationships

The postulation of objects as some- thing different from the terms of relationships is a superfluous axiom and consequently a metaphysical hypothesis from which linguistic science will have to be freed.

Louis Hjelmslev (1943/61)

Quotation

Syntax is also purely relational:Example: The Actor-Goal Construcion

CLAUSE DO-SMTHG

Vt Nom

Material process (type 2)

Syntactic function

Semantic function

Variable expression

Syntax: Linked constructions

CL

Nom

DO--SMTHG

Vt Nom

Material process (type 2)

TOPIC-COMMENT

Add another type of process

CL

DO-TO-SMTHG

THING-DESCR

BE-SMTHG

be

Nom

Vt

AdjLoc

More of the English Clause

DO-TO-SMTHGBE-SMTHG

be Vt

Vi

to

<V>-ing

CL

Subj Pred

Conc

Past Mod

Predicator

FINITE

The downward ordered OR

For the ‘or’ relation, we don’t have sequence since only one of the two (or more) lines is activated

But an ordering feature for this node is useful to indicate precedence• So we have precedence ordering.

One line for the marked condition• If conditions allow for its activation to be realized,

it will be chosen in preference to the other line The other line is the default

The downward ordered or

a b

marked choice unmarked choice (a.k.a. default )

The unmarked choice is the line that goes right through. The marked choice is off to the side – either side

The downward ordered or

a b

unmarked choice marked choice(a.k.a. default )

The unmarked choice is the one that goes right through. The marked choice is off to the side – either side

OptionalitySometimes the unmarked choice is nothing

b

unmarked choice marked choice

In other words, the marked choice is an optional constituent

Conclusion: Relationships all the way to..What is at the bottom?

Introductory view: it is phonetics In the system of the speaker, we have

relational network structure all the way down to the points at which muscles of the speech-producing mechanism are activated• At that interface we leave the purely relational

system and send activation to a different kind of physical system

For the hearer, the bottom is the cochlea, which receives activation from the sound waves of the speech hitting the ear

What is at the top?

Is there a place up there somewhere that constitutes an interface between a purely relational system and some different kind of structure? • This question wasn’t actually asked at first• It was clear that as long as we are in language we are in

a purely relational system, and that is what mattered Somehow at the top there must be meaning

What are meanings?

DOGC

Perceptual

properties

of dogsAll those dogs

out there and

their properties

In the Mind

The World Outside

For example, DOG

How High is Up?

Downward is toward expression Upward is toward meaning/function Does it keep going up forever? No — as it keeps going it arches over, through perception Conceptual structure is at the top

The great cognitive arch

The “Top”

Relational networks:Cognitive systems that operate

Language users are able to use their languages. Such operation takes the form of activation of

lines and nodes The nodes can be defined on the basis of how

they treat incoming activation

Nodes are defined in terms of activation:The downward ordered AND

a b

Downward activation from k goes to a and later to b

Upward activation from a and later from b goes to k

k

Nodes are defined in terms of activation

a b

The OR condition is notAchieved locally – at the node itself – it is just a node, has no intelligence. Usually there will be activation coming down from either p or q but not from both

Downward unordered OR

k p q

Nodes are defined in terms of activation:The OR

a b

Upward activation from either a or b goes to k

Downward activation from k goes to a and [sic] b

k

Nodes are defined in terms of activation

a b

The OR condition is not achieved locally – at the node itself – it is just a node, has no intelligence. Usually there will be activation coming down from either p or q but not from both

Downward unordered OR

k p q

The Ordered AND: Upward Activation

Activation moving upward from below

The Ordered AND: Downward Activation

Activation coming downward from above

Upward activation through the OR

The or operates as either-or for activation going from the plural side to the singular side.

For activation from plural side to singular side it acts locally as both-and, but in the context of other nodes the end result is usually either-or

Upward activation through the OR

bill

BILL1 BILL2

Usually the context allows only one interpretation, as in I’ll send you a bill for it

Upward activation through the or

bill

BILL1 BILL2But if the context allows both to get through, we have a pun:

A duck goes into a pub and orders a drink and says, “Put it on my bill“.

Shadow Meanings:Zhong Guo

MIDDLECHINA

KINGDOM

zhong guo

The ordered OR:How does it work?

default

Ordered

This line taken if possible

Node-internal structure (not shown in abstract notation) is required to control this operation

Topics


Toward Greater Precision

• The nodes evidently have internal structures• Otherwise, how to account for their behavior?• We can analyze them, figure out what internal structure would make them behave as they do

The Ordered AND: How does it know?

Activation coming downward from above

How does the AND node “know” how long to wait before sending activation down the second line?

How does it know?

How does the AND node “know” how long to wait before sending activation down the second line?

It must have internal structure to govern this function

We use the narrow notation to model the internal structure

Internal Structure – Narrow Network Notation

As each line is bidirectional, it can be analyzed into a pair of one-way lines

Likewise, the simple nodes can be analyzed as pairs of one-way nodes

Abstract and narrow notation

Abstract notation – also known as compact notation

A diagram in abstract notation is like a map drawn to a large scale

Narrow notation shows greater detail and greater precision

Narrow notation ought to be closer to the actual neural structures

www.ruf.rice.edu/~lngbrain/shipman

http://www.ruf.rice.edu/~lngbrain/shipman

Narrow relational network notation

Developed later Used for representing network

structures in greater detail• internal structures of the lines and

nodes of the abstract notation The original notation can be called

the ‘abstract’ notation or the ‘compact’ notation

Narrow and abstract network notation

Narrow notation Closer to neurological structure Nodes represent cortical columns Links represent neural fibers (or

bundles of fibers) Uni-directional

Abstract notation Nodes show type of relationship (OR,

AND) Easier for representing linguistic

relationships Bidirectional Not as close to neurological

structure

eat apple

eat apple

eat apple

eat apple

More on the two network notations

The lines and nodes of the abstract notation represent abbreviations – hence the designation ‘abstract’

Compare the representation of a divided highway on a highway map• In a more compact notation it is

shown as a single line• In a narrow notation it is shown as

two parallel lines of opposite direction

Two different network notations

Narrow notation

ab

a b

b

a b

Abstract notation Bidirectional

ab

a b f

Upward Downward

Downward Nodes: Internal Structure

AND

OR

2

1

Upward Nodes: Internal Structure

AND

OR

2

1

Downward AND, upward direction

W

2The ‘Wait’ Element

AND vs. OR

In one direction their internal structures are the same

In the other, it is a difference in threshold – hi or lo threshold for high or low degree of activation required to cross

Thresholds in Narrow Notation

1 2 3 4

OR AND

The Beauty of the Threshold

1 – You no longer need a basic distinction AND vs. OR

2 – You can have intermediate degrees, between AND and OR

3 – The AND/OR distinction was a simplification anyway — doesn’t always work!

The ‘Wait’ Element

wKeeps the activation alive

A B

Activation continues to B after A has been activated

Downward AND, downward direction

Structure of the ‘Wait’ Element

W

1

2

www.ruf.rice.edu/~lngbrain/neel

http://www.ruf.rice.edu/~lngbrain/neel

Node Types in Narrow Notation

TJunction

Branching

Blocking

Two Types of Connection

Excitatory

InhibitoryType 1

Type 2

Types of inhibitory connection

Type 1 – connect to a node Type 2 – Connects to a line

• Used for blocking default realization• For example, from the node for

second there is a blocking connection to the line leading to two

Type 2 – Connects to a line

TWO ORDINAL

2

secondtwo -th

Additional details of structurecan be shown in narrow notation

Varying degrees of connection strength Variation in threshold strength Contrast

Topics


The node of narrow RN notationvis-à-vis neural structures

It is very unlikely that a node is represented by a neuron• Far more likely: a bundle of neurons

At this point we turn to neuroscience Vernon Mountcastle, Perceptual

Neuroscience (1998)• Cortical columns

The node of narrow RN notationvis-à-vis neural structures

The cortical column A column consists of 70-100 neurons

stacked on top of one another All neurons within a column act together

• When a column is activated, all of its neurons are activated

The node as a cortical column

The properties of the cortical column are approximately those described by Vernon Mountcastle

“[T]he effective unit of operation…is not the single neuron and its axon, but bundles or groups of cells and their axons with similar functional properties and anatomical connections.”

Vernon Mountcastle, Perceptual Neuroscience (1998), p. 192

Three views of the gray matter

Different stains show different features

Nissl stain shows cell bodies of pyramidal neurons

The Cerebral Cortex

Grey matter• Columns of neurons

White matter • Inter-column connections

Layers of the Cortex

From top to bottom, about 3 mm

The Cerebral Cortex

Grey matter• Columns of neurons

White matter • Inter-column connections

The White Matter

Provides long-distance connections between cortical columns

Consists of axons of pyramidal neurons The cell bodies of those neurons are in the

gray matter Each such axon is surrounded by a myelin

sheath, which..• Provides insulation• Enhances conduction of nerve impulses

The white matter is white because that is the color of myelin

Dimensionality of the cortex

Two dimensions: The array of nodes The third dimension:

• The length (depth) of each column (through the six cortical layers)

• The cortico-cortical connections (white matter)

Topological essence of cortical structure

Two dimensions for the array of the columns

Viewed this way the cortex is an array – a two-dimensional structure – of interconnected columns

The (Mini)Column

Width is about (or just larger than) the diameter of a single pyramidal cell• About 30–50 m in diameter

Extends thru the six cortical layers• Three to six mm in length• The entire thickness of the cortex is

accounted for by the columns Roughly cylindrical in shape If expanded by a factor of 100, the

dimensions would correspond to a tube with diameter of 1/8 inch and length of one foot

Cortical column structure

Minicolumn 30-50 microns diameter Recurrent axon collaterals of

pyramidal neurons activate other neurons in same column

Inhibitory neurons can inhibit neurons of neighboring columns• Function: contrast

Excitatory connections can activate neighboring columns• In this case we get a bundle of contiguous

columns acting as a unit

Narrow RN notation viewed as a set of hypotheses

Question: Are relational networks related in any way to neural networks?

A way to find out Narrow RN notation can be viewed as a

set of hypotheses about brain structure and function• Each property of narrow RN notation can be

tested for neurological plausibility

Some properties of narrow RN notation

Lines have direction (they are one-way)

But they tend to come in pairs of opposite direction (“upward” and “downward”)

Connections are either excitatory or inhibitory

Nerve fibers carry activation in just one direction

Cortico-cortical connections are generally reciprocal

Connections are either excitatory or inhibitory (from different types of neurons, with two different neurotransmitters)

More properties as hypotheses

Nodes have differing thresholds of activation

Inhibitory connections are of two kinds

Additional properties – (too technical for this presentation)

Neurons have different thresholds of activation

Inhibitory connections are of two kinds • (Type 2: “axo-axonal”)

All are verified

Type 1

Type 2

Topics


Levels of precision in network notation:How related?

They operate at different levels of precision Compare chemistry and physics

• Chemistry for molecules• Physics for atoms

Both are valuable for their purposes

Levels of precision

(E.g.) Systemic networks (Halliday) Abstract relational network notation Narrow relational network notation

Three levels of precision

a b2 2

a

b

Systemic Relational Networks Networks

Abstract Narrow (downward)

Different levels of investigation: Living Beings

Systems Biology Cellular Biology Molecular Biology Chemistry Physics

Levels of Precision

Advantages of description at a level of greater precision:• Greater precision• Shows relationships to other areas

Disadvantages of description at a level of greater precision:• More difficult to accomplish

Therefore, can’t cover as much ground• More difficult for consumer to grasp

Too many trees, not enough forest

Levels of precision

Systemic networks (Halliday) Abstract relational network notation Narrow relational network notation Cortical columns and neural fibers Neurons, axons, dendrites, neurotransmitters Intraneural structures

• Pre-/post-synaptic terminals• Microtubules• Ion channels• Etc.

Levels of precision

Informal functional descriptions Semi-formal functional descriptions Systemic networks Abstract relational network notation Narrow relational network notation Cortical columns and neural fibers Neurons, axons, dendrites Intraneural structures and processes

Topics


Precision vis-à-vis variability

Description at a level of greater precision encourages observation of variability

At the level of the forest, we are aware of the trees, but we tend to overlook the differences among them

At the level of the trees we clearly see the differences among them

But describing the forest at the level of detail used in describing trees would be very cumbersome

At the level of the trees we tend to overlook the differences among the leaves

At the level of the leaves we tend to overlook the differences among their component cells

Linguistic examples

At the cognitive level we clearly see that every person’s linguistic system is different from that of everyone else

We also see variation within the single person’s system from day to day

At the level of narrow notation we can treat • Variation in connection strengths• Variation in threshold strength• Variation in levels of activation

We are thus able to explain• prototypicality phenomena• learning• etc.

Radial categories and Prototypicality

Different connections have different strengths (weights) More important properties have greater strengths Example: CUP,

• Important (but not necessary!) properties: Short (as compared with a glass) Ceramic Having a handle

Cups with these properties are more prototypical

The properties of a category have different weights

T

CUP

MADE OF GLASS

CERAMIC

SHORT

HAS HANDLE

The properties are represented by nodes which are connected to lower-level nodes

The cardinal node for CUP

Nodes have activation thresholds

The node will be activated by any of many different combinations of properties

The key word is enough – it takes enough activation from enough properties to satisfy the threshold

The node will be activated to different degrees by different combinations of properties• When strongly activated, it transmits stronger

activation to its downstream nodes.

Prototypical exemplars provide stronger and more rapid activation

T

CUP

MADE OF GLASS

CERAMIC

SHORT

HAS HANDLEStronger connections carry more activation

Activation threshold (can be satisfied to varying degrees)

Explaining Prototypicality

Cardinal category nodes get more activation from the prototypical exemplars • More heavily weighted property nodes

E.g., FLYING is strongly connected to BIRD • Property nodes more strongly activated

Peripheral items (e.g. EMU) provide only weak activation, weakly satisfying the threshold (emus can’t fly)

Borderline items may or may not produce enough activation to satisfy threshold

Activation of different sets of properties produces greater or lesser satisfaction of the activation threshold of the cardinal node

CUP

MADE OF GLASS

CERAMICSHORT

HAS HANDLE

More important properties have stronger connections, indicated by thickness of lines

Inhibitory connection

Explaining prototypicality: Summary

Variation in strength of connections Many connecting properties of varying strength Varying degrees of activation Prototypical members receive stronger activation from

more associated properties BIRD is strongly connected to the property FLYING

• Emus and ostriches don’t fly• But they have some properties connected with BIRD• Sparrows and robins do fly

And as commonly occurring birds they have been experienced often, leading to entrenchment – stronger connections

Variation over time in connection strength

Connections get stronger with use• Every time the linguistic system is used,

it changes Can be indicated roughly by

• Thickness of connecting lines in diagrams or by• Little numbers written next to lines

Variation in threshold strength

Thresholds are not fixed• They vary as a result of use – learning

Nor are they integral What we really have are threshold functions,

such that• A weak amount of incoming activation

produces no response• A larger degree of activation results in

weak outgoing activation• A still higher degree of activation yields

strong outgoing activation • S-shaped (“sigmoid”) function

Variation in threshold strength

Thresholds are not fixed• They vary as a result of use – learning

Nor are they integral What we really have are threshold functions,

such that• A weak amount of incoming activation

produces no response• A larger degree of activation results in

weak outgoing activation• A still higher degree of activation yields

strong outgoing activation • S-shaped (“sigmoid”) function

N.B. All of these properties are found in neural structures

Threshold function

--------------- Incoming activation -------------------

Out

goin

g a

ctiva

tion

Topics


T h a n k y o u f o r y o u r a t t e n t I o n !

References

Hockett, Charles F., 1961. Linguistic units and their relations” (Language, 1966)Lamb, Sydney, 1971. The crooked path of progress in cognitive linguistics. Georgetown Roundtable. Lamb, Sydney M., 1999. Pathways of the Brain: The Neurocognitive Basis of Language. John BenjaminsLamb, Sydney M., 2004a. Language as a network of relationships, in Jonathan Webster (ed.) Language and Reality (Selected Writings of Sydney Lamb). London: ContinuumLamb, Sydney M., 2004b. Learning syntax: a neurocognitive approach, in Jonathan Webster (ed.) Language and Reality (Selected Writings of Sydney Lamb). London: ContinuumMountcastle, Vernon W. 1998. Perceptual Neuroscience: The Cerebral Cortex. Cambridge: Harvard University Press.

For further information..

www.rice.edu/langbrain

[email protected]

http://www.rice.edu/langbrain

Linguistic Structure as a Relational Network Sydney Lamb Rice University [email protected] National...

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