Linguistic Structure as a Relational Network Sydney Lamb Rice University [email protected] National Taiwan Universit 9 November 2010
Dec 13, 2015
Linguistic Structure as a Relational Network
Sydney Lamb
Rice University
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
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
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 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
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
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
Relationship of boy to its phonemes
boy As a morpheme, it is just one unit
Three phonemes, in sequence
b o y
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
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)
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
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
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
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“.
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 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
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
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
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
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
Additional details of structurecan 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 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 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
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
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
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
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
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
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.