Download Relational Networks

National Taiwan University
Linguistic Structure as a Relational Network
Sydney Lamb
Rice University
[email protected]
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
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 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
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







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
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
meaning
network
 Upward is toward meaning (or
other function) – more abstract
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







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
Morpheme as item and its
phonemic representation
boy
Symbols?
Objects?
b-o-y
Relationship of boy to its phonemes
boy
As a morpheme, it
is just one unit
b o y
Three phonemes,
in sequence
The nature of this “morphemic unit”
BOY
Noun
boy
b o y
The object we
are considering
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
Another way of looking at it
BOY
Noun
boy
b o y
Another way of looking at it
BOY
Noun
b o y
A closer look at the segments
boy
(Bob)
b
Phonological
features
o
(toy)
y
The phonological
segments also
are just locations
in the network –
not objects
Relationships of boy
BOY
Noun
boy
b o y
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
Quotation
The postulation of objects as something 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)
Syntax is also purely relational:
Example: The Actor-Goal Construcion
Semantic
function
Syntactic
function
CLAUSE
DO-SMTHG
Material process (type 2)
Variable
expression
Vt
Nom
Syntax: Linked constructions
TOPIC-COMMENT
CL
DO--SMTHG
Nom
Material process (type 2)
Vt
Nom
Add another type of process
THING-DESCR
CL
BE-SMTHG
Vt
be
Adj
Nom
Loc
DO-TO-SMTHG
More of the English Clause
CL
Subj
Pred
FINITE
to
<V>-ing
Predicator
BE-SMTHG DO-TO-SMTHG
Conc
Past
Mod
Vi
be
Vt
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
marked choice
b
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
unmarked choice
(a.k.a. default )
b
marked choice
The unmarked choice is the one that goes right through.
The marked choice is off to the side – either side
Optionality
Sometimes 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?
For example, DOG
C
In the Mind
The World
Outside
DOG
Perceptual
properties
of dogs
All those dogs
out there and
their properties
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
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
Nodes are defined in terms of activation
Downward unordered OR
k
p
q
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
Nodes are defined in terms of activation:
The OR
k
Upward activation from either a or
b goes to k
Downward activation from k goes
to a and [sic] b
a
b
Nodes are defined in terms of activation
Downward unordered OR
k
p
q
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
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
BILL1
BILL2
Usually the context allows
only one interpretation, as
in I’ll send you a bill for it
bill
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
Shadow Meanings:
Zhong Guo
CHINA
MIDDLE
KINGDOM
zhong
guo
The ordered OR:
How does it work?
Ordered
This line taken
if possible
default
Node-internal structure (not shown in abstract
notation) is required to control this operation
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
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
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
eat apple
eat
apple
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
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
ab
Abstract notation

Bidirectional
a
b
a
b
ab
Upward
b
a
Narrow notation
f
Downward
b
Downward Nodes: Internal Structure
AND
2
OR
1
Upward Nodes: Internal Structure
AND
2
OR
1
Downward AND, upward direction
The ‘Wait’
Element
2
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
OR
AND
1
2
3
4
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
Downward AND,
downward direction
Keeps the
activation
alive
A
B
Activation continues to B
after A has been activated
Structure of the ‘Wait’ Element
1
2
www.ruf.rice.edu/~lngbrain/neel
Node Types in Narrow Notation
Junction
Branching
Blocking
T
Two Types of Connection
Excitatory
Type 1
Inhibitory
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
-th
two
second
Additional details of structure
can be shown in narrow notation
 Varying degrees of connection strength
 Variation in threshold strength
 Contrast
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
The node of narrow RN notation
vis-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 notation
vis-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 twodimensional 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
Type 1
 Neurons have different
thresholds of activation
 Inhibitory connections are
of two kinds
• (Type 2: “axo-axonal”)
Type 2
 Additional properties –
(too technical for this
presentation)
 All are verified
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
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
Systemic
Networks
Relational Networks
a
b
a
b
Abstract
2
2
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







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
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
The cardinal node for
CUP
CUP
T
MADE OF GLASS
SHORT
CERAMIC
The properties are
represented by
nodes which are
connected to lowerlevel nodes
HAS HANDLE
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
Activation threshold
(can be satisfied to
varying degrees)
CUP
T
MADE OF GLASS
SHORT
CERAMIC
Stronger
connections carry
more activation
HAS HANDLE
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
Inhibitory
connection
MADE OF GLASS
SHORT
CERAMIC
HAS HANDLE
More important properties have stronger
connections, indicated by thickness of lines
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
Outgoing activation
Threshold function
--------------- Incoming activation -------------------
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
Thank you for your attentIon!
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.
For further information..
www.rice.edu/langbrain
[email protected]