systemic networks, relational networks, and neural networks sydney lamb lamb@rice
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Systemic Networks, Relational Networks, and Neural Networks
Sydney Lamblamb@rice.edu
Part II: GuangZhou 2010 November 3 Sun Yat Sen University
Topics in this presentation
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
Topics
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
Aims of SFL
SFG aims (primarily) to describe the network of choices available in a language• For expressing meanings
“SFL differs from Firth, and also from Lamb, in that priority is given to the system”
(Halliday, 2009:64)
“The organizing concept of a systemic grammar is that of choice (that is, options in ‘meaning potential’…)”
(Halliday 1994/2003: 434
Aims of Neurocognitive linguistics (“NCL”)
NCL aims to describe the linguistic system of a language user• As a dynamic system
• It operates• Speaking, comprehending, learning, etc.
• It changes as it operates Evidence that can be used
• Texts • Findings of SFL• Slips of “tongue” and mind• Unintentional puns• Etc.
NCL seeks to learn ..
• How information is represented in the linguistic systemHow information is represented in the linguistic system
• How the system operates in speaking and understandingHow the system operates in speaking and understanding
• How the linguistic system is connected to other knowledge How the linguistic system is connected to 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”
Topics
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
“Cognitive Linguistics”
First occurrence 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)
Relational network notation
Thinking in cognitive linguistics was facilitated by relational network notation
Developed under the influence of the notation used by Halliday for systemic networks
Earlier steps leading to relational network notation appear in papers written in 1963
More on the early days
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 (which I first saw in 1964) used different nodes for paradigmatic (‘or’) and syntagmatic (‘and’) relationships• Just what I was looking for
From systemic networks to relational networksThree notational adaptations
Rotate 90 degrees, so that • upwards would be toward meaning (at the
theoretical top) and • downwards would be toward phonetics (at the
theoretical bottom) Replace the brace for ‘and’ with a (more
node-like appearing) triangle; Retaining the bracket for ‘or’, allow the
connecting lines to connect at a point
The downward OR
a
b
a b
The downward AND
a
b
a b
The 90° Rotation: 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
Orientation of Nodes
Downward AND and OR nodes:• Branching on the expression side
Multiple branches to(ward) expression
Upward AND and OR nodes:• Branching on the content side
Multiple branches to(ward) content
Downward and upward branching
a b
a b
a b
a b
The meaning of up/down:Neurological interpretation
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
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
a b
First a then b
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.
The line connecting to the left takes precedence• If conditions allow for its activation to be
realized, it will be chosen in preference to the other line
The downward ordered or (original notation)
a b
marked choice unmarked choice (a.k.a. default )
The marked choice takes precedence: It is chosen if the conditions that constitute the marking are present
The downward ordered or (revised notation)
a b
marked choice unmarked 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
The downward ordered or (revised notation)
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
Sometimes the unmarked choice has zero realization
b
unmarked choice marked choice
The unmarked choice is nothing. In other words, the marked choice is optional.
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
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 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
Downward ordered AND
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
Downward unordered OR
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
Downward Activation
AND OR
Upward
Downward
Upward Activation
AND OR
Upward
Downward
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“.
Zhong Guo: Shadow Meaning
CENTRALCHINA
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
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
A purely relational network
After making these adaptations to systemic network notation, resulting in relational network notation (abstract form), it became apparent (one afternoon in the fall of 1964) that relational networks) need not contain any items at all
The entire structure could be represented in the nodes and their interconnecting lines
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)
boy as label (not part of the structure)
BOY Noun
b o y
boy Just a label – to make the
diagram easier to read
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, as 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)
Compare SF Networks – nodes and lines, plus symbols
SF networks have and and or nodes They also have symbols for linguistic items
E.g., polarity, positive, negative And symbols for relationships/operations
Symbol Meaning Example
+ insertion + x
/ conflation X / Y
· expansion X (P · Q)
^ ordering X ^Z
: preselection : w
:: classification ::z
= lexification =t
Syntax is also purely relational:Example: The Actor-Goal Construction
CLAUSE DO-SMTHG
Vt Nom
Material process (type 2)
Syntactic function
Semantic function
Variable expression
Syntax is also purely relational: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 system of THEME,
THEMESELECTION
predicator theme <unmarked in imperative>
other
THEMESELECTION
THEMESELECTION
adjunct theme
other
non-wh-theme
wh-theme<unmarked in
WH-interrogative and exclamative>
THEMESELECTION
other
subject theme<unmarked in declarative and
yes/no interrogative>
System network for THEME SELECTION
Halliday (2004: 80)
THEME SELECTION PREDICATOR THEME
ADJUNCT THEME WH- THEME
SUBJECT THEME
(Unmarked in imperative)
Non-wh-theme
Other
(Unmarked in wh-interrogativeand exclamative)
(Unmarked in declarative and yes/no interrogative)
Direct translation of Halliday’s system network
Theme selection in operation
This direct translation seems not to represent the way theme selection works in the cognitive system of the person forming a clause
Rather, whatever will be the theme• the specific item, not a high-level category
to which it belongs, • is active at the start of the clause formation
Having been activated it comes first, as theme and the rest of the clause follows, as Rheme
(Getting ready to add Theme)
BE-SMTHG
Vi
to
<V>-ing
CL
Subj Pred
Conc
Past Mod
Predicator
FINITE
Add Theme-Rheme
BE-SMTHG
Vi
to
<V>-ing
CL
Subj Pred
Predicator
FINITE
THEME RHEME
Nom
DECLARE
Yes-No Questions
to <V>-ing
Pred
VPPerf Prog
Subj
ASKDECLARE
Finite
Yes-No Questions:Finite as Theme
Pred
Subj
ASK
Finite
CL
THEME RHEME
DECLARE
Nom
Circumstance in the Verb Phrase
be Vt
Vi
VP
Obj
Vbl Phrase
Circumstance
They did itI saw themHe was walking
in the garden a couple of days ago while she was away
Circumstance as Theme
Vi
VP
Vbl Phrase
Circumstance
THEME RHEME
Conclusion: Relationships all the way to..How far?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?
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”
Topics
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
Systemic Networks vis-à-vis Relational Networks: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
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
Three Levels of precision for language
Systemic networks Abstract relational network notation Narrow relational network notation
(coming up)
Topics
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
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
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?
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
The two notations are like different scales for making a map
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
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 hi or lo degree of activation required to cross
Thresholds in Narrow Notation
1 2 3 4
OR AND
– You no longer need a basic distinction AND vs. OR
– You can have intermediate degrees, between AND and OR
– 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
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
Connections between upward and downward directions
Varying degrees of connection strength Variation in threshold strength Contrast
The two Directions
1
2
ww
The Two Directions
ww
Two Questions:
1. Are they really next to each other?
2. How do they “communicate” with each other?
1
2
Separate but in touch
ww
1
2
Down UpIn phonology, we know from aphasiology and neuroscience that they are in different parts of the cerebral cortex
Phonological nodes in the cortex
ww
1
2
Arcuate fasciculus
Frontal lobe
Temporal lobe
Topics
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
Another level of precision
Systemic networks Abstract relational network notation Narrow relational network notation Cortical columns and neural fibers Neurons, axons, dendrites, neurotransmitters
Narrow RN notation as a set of hypotheses
Question: Are relational networks related in any way to neural networks?
We can find out Narrow RN notation can be viewed as a
set of hypotheses about brain structure and function• Every 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
The node of narrow RN notationvis-à-vis neural structures
The node corresponds not to a single neuron but to a bundle of neurons
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
Microelectrode penetrations in the paw area of a cat’s cortex
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
Levels of precision
Systemic networks 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
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
Competition vis-à-vis Halliday’s systems
Halliday (not an exact quote):Putting the emphasis on systems gives recognition to the importance of Saussure's principle that everything meaningful has meaning in contrast to what could have been selected instead
Paradigmatic contrast: Competition
a b2 2
For example, /p/ vs. /k/
Simplified model of minicolumn II:Inhibition of competitors
Thalamus
Other corticallocations
IIIII
IV
V
VI
Cells in neighboring columns
Cell Types
Pyramidal
Spiny Stellate
Inhibitory
Local and distal connections
excitatory
inhibitory
Paradigmatic contrast: Competition
a b
a
b
Paradigmatic contrast: Competition
a b2 2
a
b
Competition vis-à-vis Halliday’s systems
Halliday (not an exact quote):Putting the emphasis on systems gives recognition to the importance of Saussure's principle that everything meaningful has meaning in contrast to what could have been selected instead
Topics
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
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.
Variation 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
N.B. All of these properties are found in neural structures
Threshold function
--------------- Incoming activation -------------------
Out
goin
g ac
tivati
on
Topics in this presentation
Aims of SFL and NCL From systemic networks to relational networks Relational networks as purely relational Levels of precision in description Narrow relational network notation Narrow relational networks and neural networks Enhanced understanding of systemic-functional choice Enhanced appreciation of variability in language
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 Halliday, M.A.K., 1994/2003. Appendix: Systemic Theory. In On Language and Linguistics (vol. 3 in the Collected Works of M.A.K. Halliday (ed. Jonathan Webster). London: ContinuumHalliday, M.A.K., 2009. Methods – techniques – problems. In Continuum Companion to Systemic Functional Linguistics (eds. M.A.K. Halliday & Jonathan Webster). London: ContinuumHockett, 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
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