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Title: Linguistic Structure as a Relational Network Sydney Lamb Rice University lamb@rice.edu


1
Linguistic Structure as a Relational
NetworkSydney LambRice Universitylamb_at_rice.e
du
National Taiwan University
9 November 2010
2
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

3
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

4
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

5
NCL seeks to learn ..
  • How information is represented in the
  • linguistic system
  • How the system operates in speaking and
  • understanding
  • How the linguistic system is connected to
  • other knowledge
  • How the system is learned
  • How the system is implemented in the brain

6
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

7
Cognitive Linguistics
  • First occurrence of the term in print
  • The branch of linguistic inquiry which aims at
    characterizing the speakers internal information
    system that makes it possible for him to speak
    his language and to understand sentences received
    from others.
  • (Lamb 1971)

8
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)

9
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 persons mind is knowing
    how not knowing that
  • Information in operational form
  • Able to operate without manipulation from some
    added performance system

10
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

11
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

12
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. Hocketts Linguistic units and their
    relations (Language, 1966)
  • Early primitive notations showed units with
    connecting lines to related units

13
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
  • Hallidays notation used different nodes for
    paradigmatic (or) and syntagmatic (and)
    relationships
  • Just what I was looking for

14
The downward or
DIFFICULT
hard diffricult
15
The downward and
a b
16
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

17
Downward (ordered) and
Vt
Nom
18
Upward and Downward
meaning
  • Expression (phonetic or graphic) is at the bottom
  • Therefore, downward is toward expression
  • Upward is toward meaning (or other function)
    more abstract

network
expression
19
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

20
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

21
Morpheme as item and its phonemic representation
boy b - o - y
Symbols? Objects?
22
Relationship of boy to its phonemes
As a morpheme, it is just one unit Three
phonemes, in sequence
boy
b o y
23
The nature of this morphemic unit
  • BOY Noun

boy
The object we are considering
b o y
24
The morpheme as purely relational
  • BOY Noun

We can remove the symbol with no loss of
information. Therefore, it is a connection, not
an object
boy
b o y
25
Another way of looking at it
  • BOY Noun

boy
b o y
26
Another way of looking at it
  • BOY Noun

b o y
27
A closer look at the segments
boy
(toy)
(Bob)
o
b
y
The phonological segments also are just
locations in the network not objects
Phonological features
28
Relationships of boy
  • BOY Noun

boy Just a label not part of the structure
b o y
29
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

30
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?

31
Relations all the way
  • Perhaps all of linguistic structure is relational
  • Its 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

32
Objects in the mind?
When the relationships are fully identified, the
objects as such disappear, since they have no
existence apart from those relationships
33
Quotation
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)
34
Syntax is also purely relationalExample The
Actor-Goal Construcion
Semantic function
CLAUSE
Syntactic function
DO-SMTHG
Material process (type 2)
Variable expression
Vt
Nom
35
Syntax Linked constructions
TOPIC-COMMENT
CL
DO--SMTHG
Nom
Material process (type 2)
Vt
Nom
36
Add another type of process
THING-DESCR
CL
BE-SMTHG
DO-TO-SMTHG
Vt
be
Adj
Loc
Nom
37
More of the English Clause
CL
FINITE
Subj Pred
to
ltVgt-ing
Predicator
DO-TO-SMTHG
BE-SMTHG
Conc Past Mod
Vi
Vt
be
38
The downward ordered or
  • For the or relation, we dont 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

39
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
40
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
41
OptionalitySometimes the unmarked choice is
nothing
b
unmarked choice marked
choice In other words, the
marked choice is an
optional constituent
42
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

43
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 wasnt 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

44
What are meanings?
In the Mind
For example, DOG
The World Outside
C
DOG
Perceptual properties of dogs
All those dogs out there and their
properties
45
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

46
The great cognitive arch

The Top
47
Relational networksCognitive 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

48
Nodes are defined in terms of activationThe
downward ordered and
k
Downward activation from k goes to a and later
to b Upward activation from a and later from b
goes to k
a b
49
Nodes are defined in terms of activation
Downward unordered or
k p
q
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
a b
50
Nodes are defined in terms of activationThe or
k
Upward activation from either a or b goes to
k Downward activation from k goes to a and sic
b
a b
51
Nodes are defined in terms of activation
Downward unordered or
k p
q
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
a b
52
The Ordered AND Upward Activation
Activation moving upward from below
53
The Ordered AND Downward Activation
Activation coming downward from above
54
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
55
Upward activation through the or
bill1 bill2
Usually the context allows only one
interpretation, as in Ill send you a bill for it
bill
56
Upward activation through the or
bill1 bill2
But 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.
bill
57
Shadow MeaningsZhong Guo
CHINA
MIDDLE
KINGDOM
guo
zhong
58
The ordered ORHow does it work?
Ordered
This line taken if possible
default
Node-internal structure (not shown in abstract
notation) is required to control this operation
59
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

60
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

61
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?
62
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

63
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
64
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

65
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

66
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
67
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

68
Two different network notations
ab
  • Abstract notation
  • Bidirectional

a b
Downward
Upward
ab
b
a b
f
a b
  • Narrow notation

69
Downward Nodes Internal Structure
AND OR
2
1
70
Upward Nodes Internal Structure
AND OR
2
1
71
Downward and, upward direction
2
The Wait Element
W
72
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
73
Thresholds in Narrow Notation
OR AND
1
2
3
4
74
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 doesnt always work!
75
The Wait Element
Downward and, downward direction
Keeps the activation alive
w
A B Activation continues to B after A has been
activated
76
Structure of the Wait Element
1
W
2
www.ruf.rice.edu/lngbrain/neel
77
Node Types in Narrow Notation
Junction
T
Branching
Blocking
78
Two Types of Connection
Excitatory Inhibitory
Type 1 Type 2
79
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

80
Type 2 Connects to a line
TWO ORDINAL
2
-th
two
second
81
Additional details of structurecan be shown in
narrow notation
  • Varying degrees of connection strength
  • Variation in threshold strength
  • Contrast

82
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

83
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

84
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

85
The node as a cortical column
  • The properties of the cortical column are
    approximately those described by Vernon
    Mountcastle

The effective unit of operationis 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
86
Three views of the gray matter
Different stains show different features Nissl
stain shows cell bodies of pyramidal neurons
87
The Cerebral Cortex
  • Grey matter
  • Columns of neurons
  • White matter
  • Inter-column connections

88
Layers of the Cortex
From top to bottom, about 3 mm
89
The Cerebral Cortex
  • Grey matter
  • Columns of neurons
  • White matter
  • Inter-column connections

90
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

91
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)

92
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

93
The (Mini)Column
  • Width is about (or just larger than) the diameter
    of a single pyramidal cell
  • About 3050 ?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

94
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

95
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

96
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)

97
More properties as hypotheses
  • Neurons have different thresholds of activation
  • Inhibitory connections are of two kinds
  • (Type 2 axo-axonal)
  • All are verified
  • Nodes have differing thresholds of activation
  • Inhibitory connections are of two kinds
  • Additional properties (too technical for this
    presentation)

Type 1 Type 2
98
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

99
Levels of precision in network notationHow
related?
  • They operate at different levels of precision
  • Compare chemistry and physics
  • Chemistry for molecules
  • Physics for atoms
  • Both are valuable for their purposes

100
Levels of precision
  • (E.g.) Systemic networks (Halliday)
  • Abstract relational network notation
  • Narrow relational network notation

101
Three levels of precision
Systemic Relational Networks
Networks
a b
a b
2
2
Abstract Narrow
(downward)
102
Different levels of investigation Living Beings
  • Systems Biology
  • Cellular Biology
  • Molecular Biology
  • Chemistry
  • Physics

103
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, cant cover as much ground
  • More difficult for consumer to grasp
  • Too many trees, not enough forest

104
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.

105
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

106
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

107
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

108
Linguistic examples
  • At the cognitive level we clearly see that every
    persons linguistic system is different from that
    of everyone else
  • We also see variation within the single persons
    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.

109
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

110
The properties of a category have different
weights
The cardinal node for cup
CUP
T
MADE OF GLASS
SHORT
CERAMIC
The properties are represented by nodes which
are connected to lower-level nodes
HAS HANDLE
111
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.

112
Prototypical exemplars provide stronger and more
rapid activation
Activation threshold (can be satisfied to
varying degrees)
CUP
T
MADE OF GLASS
SHORT
CERAMIC
HAS HANDLE
Stronger connections carry more activation
113
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
    cant fly)
  • Borderline items may or may not produce enough
    activation to satisfy threshold

114
Activation of different sets of properties
produces greater or lesser satisfaction of the
activation threshold of the cardinal node
Inhibitory connection
CUP
MADE OF GLASS
SHORT
CERAMIC
HAS HANDLE
More important properties have stronger
connections, indicated by thickness of lines
115
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 dont 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

116
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

117
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

118
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
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Threshold function
Outgoing activation
--------------- Incoming activation
-------------------
120
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

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T h a n k y o u f o r y o u r a t t e
n t I o n !
122
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 Benjamins Lamb, Sydney M., 2004a.
Language as a network of relationships, in
Jonathan Webster (ed.) Language and Reality
(Selected Writings of Sydney Lamb). London
Continuum Lamb, Sydney M., 2004b. Learning
syntax a neurocognitive approach, in
Jonathan Webster (ed.) Language and Reality
(Selected Writings of Sydney Lamb). London
Continuum Mountcastle, Vernon W. 1998.
Perceptual Neuroscience The Cerebral Cortex.
Cambridge Harvard University Press.
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For further information..
www.rice.edu/langbrain lamb_at_rice.edu
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