Tải bản đầy đủ - 0trang
2 Relational concepts, arguments and values
an i n t r o d u c t io n t o wo r d g r a mm ar
this leave properties such as ‘drinks milk’ and ‘has fur’ (for cats) or ‘flies’ and
‘has wings’ (for birds)?
Conceptual propertiesâ•‡ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
These properties look very different from the examples considered so
far, and not least because ‘drinking’, ‘fur’, ‘flying’ and ‘wings’ are themselves
concepts. We can call them CONCEPTUAL PROPERTIES. Thus if purring is
a property of cats, equally cats are (in some sense) a property of purring:Â€purring
is the sound made by cats. This rather simple idea leads inevitably to the theory
that conceptual properties are nothing but links to other concepts.
To see how this works, take the ‘bird’ example. In this theory, there are concepts for ‘flying’, ‘feather’, ‘wing’ and so on as well as for ‘bird’, and the properties of ‘bird’ consist of links to these other concepts. In terms of taxonomies,
of course, the other concepts are not at all closely related to ‘bird’ (for example,
‘flying’ is a kind of activity, not a kind of creature) and these links cut right across
the taxonomic hierarchies. But the taxonomic relations still exist and need to be
included in an analysis that tries to understand how the whole system works.
Towards a notation for propertiesâ•‡ nnnnnnnnnnnnnnnnnnnnnnnnnnn
The result is a rather complicated analysis which combines the taxonomic hierarchy with whatever links are needed from concept to concept. This
makes a convenient visual notation even more important. The obvious notation
for links between two concepts is a line between them, but in order to emphasize
the difference between these links and those for the isA relation, Word Grammar
uses curved lines as in Figure 3.3.
What this diagram shows is that ‘bird’ is related in some way to the concepts
‘wing’, ‘feather’ and ‘flying’, and that although bird isA creature, the same is
not true for any of these other concepts. Psychologists call these links ‘associations’ and describe the memory containing them as ‘associative memory’.
(Wikipedia:Â€‘Semantic memory’.) There’s a great deal of evidence that our minds
do in fact contain these associative links between concepts, and we shall review
some of the evidence in Section 3.5. This idea, then, is well supported so far as
The trouble is that it doesn’t go far enough. It’s not enough to say that a bird is
associated with flying, wings and feathers, because the same would be true of a
butterfly riding on a feather or of a severed bird-wing (whose function is flying).
What’s missing is a classification of the associations which would say that the
bird’s association with its wing is different from its association with flying.
Relations, arguments and valuesâ•‡ nnnnnnnnnnnnnnnnnnnnnnnnnnn
We need to replace mere associations with RELATIONS. In this terminology, the bird has a ‘body-part’ relation to its wing, and this relation can be
Figure 3.3 Properties shown as links
defined even more precisely as a ‘front-limb’ relation (comparable with our relation to our arms); but it has a ‘covering’ relation to its feathers (compare our hair)
and a ‘locomotion’ relation to flying. The point is that the theory must allow us to
distinguish these relations. Psychologists aren’t generally interested in these distinctions, but linguists and artificial intelligence researchers are. Consequently
it’s these disciplines that provide the ideas that we need.
The first step is to develop a suitable labelling system to distinguish one relation from another, and to distinguish these labels from the basic concept labels;
in Word Grammar, relation labels, unlike entity labels, are written in a ‘bubble’.
This allows us to distinguish the ‘front-limb’ relation from the ‘locomotion’ relation, but it doesn’t tell us which thing related by ‘front-limb’ is the limb and
which is the owner. In technical terms, we need to distinguish the ARGUMENT
from the VALUE.
The term argument as used here has nothing to do with arguing, but is used in
the mathematical sense where a mathematical operation such as doubling can be
applied to an argument to produce a value. For example, in the equation ‘3 × 2 =
6’, the operation is doubling, its argument is 3 and its value is 6; in other words,
if you take 3 (the argument) and double it (the operation) you get 6 (the value).
Other kinds of relation such as ‘front-limb’ have a similar structure; for example,
if you take a bird (argument) and look for its front limb (relation), you find a
wing (value). In this way of thinking, a relation is like a journey which starts at
the argument and ends at the value, which is why Word Grammar notation has an
arrow-head pointing towards the value.
Adding these extra bits of information to Figure 3.3 gives Figure 3.4 (page 40).
We now have the beginnings of a proper definition of ‘bird’ in terms of other
concepts, but of course the analysis also helps to define these other concepts; for
example, one of the things we know about a wing is that it’s the front limb of
a typical bird. You can probably imagine how this little network could grow by
adding more properties to each of these concepts, each new property bringing in
further concepts; and how the network might eventually, after a massive amount
of effort (comparable perhaps with mapping the genome), include everything
that some person knows, though it could obviously never include everything that
an i n t r o d u c t io n t o wo r d g r a mm ar
Figure 3.4 Properties shown as labelled links
Primitive relations, relational concepts and the
relation taxonomyâ•‡ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
The big question for researchers in this area is where these relations
come from. One view is that they come from a general theory which lists them
and defines them once and for all. This approach is particularly popular among
linguists, who like to imagine a small set of universal relations with names such
as ‘agent’, ‘experiencer’ and ‘instrument’ (8.7.4). (Wikipedia:Â€ ‘Thematic relation’.) But a moment’s thought raises serious questions for this approach. How
do very specific relations such as ‘front-limb’ and ‘back-limb’ fit into a small
set of very general categories? If we don’t already have specific relations such
as these in our relational tool-kit, why can’t we learn them from our experience?
Why should we expect the number of relations to be so much smaller than the
number of ordinary concepts like ‘bird’, which is clearly open-ended and very
My view is that relations form an equally open-ended collection of concepts
to which we can add at any time:Â€ a RELATION TAXONOMY; the same
assumption has been used in a number of successful knowledge-representation systems in artificial intelligence, notably one called Conceptual Graphs.
If this is right, then there must be two different kinds of concept. First there
are the basic concepts such as ‘bird’, ‘creature’, ‘wing’ and ‘flying’, which may
stand for people, things, activities, times, places and so on and on. For lack of a
better term, these are often called ENTITY CONCEPTS, or just ENTITIES.
Entities are the basic building blocks of thought, but what makes each entity distinctive is the way it’s linked to other entities by concepts of the other kind such
as ‘front-limb’, ‘cover’ and ‘locomotion’, which we can call RELATIONAL
Although we can shorten this to plain ‘relation’, it’s important to remember
that there are also PRIMITIVE RELATIONS which are not represented in
Word Grammar by relational concepts. We’ve already met the most important of
these, which is the ‘isA’ relation, and I’m about to introduce three more. Using
this terminology, then, we can classify the elements in Figure 3.4 as six entity
Figure 3.5 Social relations shown as labelled links
concepts (creature, bird, wing, feather, flying and activity), three relational concepts (front-limb, locomotion and cover) and two examples of the primitive isA
Relational concepts are very familiar in our social life. Each of us has a mental
network which contains all the people we know and what we know about their
relations to each other and to us. In this network, the people are the entities and
their social relations are the relational concepts. For example, Figure 3.5 shows
a tiny fragment of my family network including my father, my mother and my
wife, and also classifying us all as male or female.
All these relations are part of what I know about myself and about these people,
so they’re properties just like the properties of birds listed above. Of course, my
relation to my wife is quite different from a bird’s relation to its wing, but that’s
exactly why it’s important to distinguish different relational concepts by labelling them.
A notation for relationsâ•‡ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Relational concepts need labels to show not only when they are different but also when they are the same. For example, my relation to my mother
(Gretta) has enough in common with her relation to her mother (Mary) for us
to give them the same label:Â€‘mother’. We might extend Figure 3.5 by adding
another arrow labelled ‘mother’ from Gretta to Mary.
But in the case of entities, we don’t use labels to show similarities; for instance,
we don’t classify a bird as a robin simply by labelling it ‘robin’. Instead, we add
an isA link from the bird to the category ‘robin’. At least in principle, Word
Grammar applies the same logic to relational concepts, using isA links rather
than shared labels to show that two relations are examples of the same general
category. Instead of duplicating the label ‘mother’ we add isA links from the
relations concerned to the general relational category ‘mother’.
This purist notation is shown in Figure 3.6, but you can see how impractical it
is. It immediately doubles the number of lines in any diagram, so you won’t see
it again (except when it’s essential). For the sake of user-friendliness, we’ll settle
an i n t r o d u c t io n t o wo r d g r a mm ar
Figure 3.6 Relations shown as a taxonomy
for an impure notation in which similarities are shown by isA for entities but by
duplicated labels for relationals.
Another impure part of the notation for relational concepts is literally hidden
by the labels. As explained earlier, a relational concept applies to an argument
and a value, two entities with different statuses; in Figure 3.5, the ‘mother’ relation between Gretta and me has me as its argument and Gretta as its value. (If
you start with me, the mother relation takes you to GrettaÂ€– not the other way
round.) In other words, Gretta and I have different relations to this (relational)
concept, and the notation actually decomposes the relation between Gretta and
me into three parts:Â€a relational concept with an argument relation to me and a
value relation to Gretta.
But what about ‘argument’ and ‘value’ themselves? Should we decompose
these relations in the same way, each producing another pair of relations which
have to be decomposed, and so on? This outcome would undermine the whole
analysis because we certainly don’t have room in our minds for an infinite number of relations, but fortunately it can be avoided by declaring ‘argument’ and
‘value’ to be primitive relations like ‘isA’.
This move gives the following types of relation, each with its own notation:
• ‘isA’, shown by a straight line with a triangle resting on the
• ‘argument’, shown by a curved line without an arrow-head
• ‘value’, shown by a curved line with an arrow-head pointing
towards the value
relational concepts, shown by a label inside an ellipse.
In case you’re wondering how many other primitive relations I’m going to offer
you, the answer is just three, called ‘or’ and ‘identity’, plus ‘quantity’ which I’m
about to explain.
As you can see in the last three figures, the notation actually cheats by using
an ellipse box to cut what is actually a single curved arrow into two parts, one
for the argument and the other for the value. For example, Figure 3.5 shows
a ‘mother’ arrow from me to Gretta. Purists can read this as an example of
the ‘mother’ relational concept with separate relations to its argument and its
Figure 3.7 New relations are defined in terms of existing ones
value; but those who don’t care can read it as a ‘mother’ relation from me to
This is as good a point as any to mention a primitive relation that’s
part of the official Word Grammar list (Hudson 2007c:Â€ 19–20) but which I’ll
hardly mention again in this textbook:Â€QUANTITY. For example, the ‘quantity’
of legs that a typical cat has is four, so when we’re dealing with a cat exemplar,
we expect four legs. On the other hand, a collar is optional, which means that its
quantity is either zero or one. Consequently we’re not surprised either if it does
have a collar or if it doesn’t. This mechanism is useful in many areas of cognition, but we can ignore it until we reach valency (7.2).
Defining new relations, relational triangles and recursionâ•‡ nnn
If relational concepts do in fact constitute an open-ended collection,
it’s easy to see that new relations can easily be defined on the basis of existing
ones. On the one hand, we can create specialized concepts such as ‘step-mother’
as a special kind of mother, or ‘parent’ as a merger of mother and father; and on
the other, we can create new relations on the basis of a chain of relations.
An easy example of both these processes would be ‘grandmother’, defined as
the mother of a parent. Figure 3.7 shows how ‘mother’ and ‘father’ provide the
basis for both ‘parent’ and ‘child’, and how ‘grandmother’ can then be built on
these relations. (The dots in the diagram are a convenient way of indicating a
node without bothering to give a name; as I’ll explain in Section 3.5, all nodes are
an i n t r o d u c t io n t o wo r d g r a mm ar
really just unlabelled dots, and labels are just a convenience for human readers.
You can think of a dot as meaning ‘some node or other’.)
The definition of ‘grandmother’ in terms of two other relations is a typical
example of an important network structure, the relational TRIANGLE. This pattern plays an important role in syntactic theory (7.2).
Another characteristic of networks which is important in syntax (7.1) is the
possibility of using these new relations to define even more general ones such as
‘descendant’ and ‘ancestor’ using a pattern called RECURSION.
Here’s a recursive definition of ‘ancestor’:Â€a person’s ancestor is either their
parent, or an ancestor of their parent. This definition is recursive because it
includes the term that it’s defining, which means that it can apply repeatedly
through a long chain of relations. For example, since my father is my ancestor
and for the same reason his father is his ancestor, the recursive definition means
that his father is also my ancestor and so on and on right up through my family
tree back to Adam and Eve.
This possibility of creating new relational concepts on the basis of existing
ones allows a very rich vocabulary of relational concepts to grow on top of each
other, rather like coral polyps.
The main point of this section has been to introduce the idea that an entity concept’s properties include some properties which link it to another such concept
via a relation which is itself a concept. According to this theory, therefore, conceptual structure consists of two kinds of conceptÂ€– entities and relationsÂ€– with
a separate taxonomy for each kind. But that’s not all, because the relations link
pairs of entity concepts to one another.
This degree of complexity and detail is typical of models in artificial intelligence and linguistics, though less typical of psychological models. On the other
hand, the Word Grammar model isn’t actually that complex compared with a lot
of complex systems that you’re probably quite familiar with already, such as the
internet or even the remote control for your TV; and of course, the whole point
of this theory is that your mind already has precisely this degree of complexity.
The main challenge for you may not be so much the complexity as the unfamiliarity of thinking about your mind in this way. Section 3.4 will try to help you
by applying the general ideas to three very familiar and quite concrete areas of
Advanced:Â€Part II, Chapter 7.1:Â€Dependencies and phrases
Choices, features and cross-classification
Section 2.4 introduced the idea that some categories are grouped
together as choices:Â€man or woman, Republican or Democrat, 1 or 2 or 3 or…
Figure 3.8 Sex as a choice between ‘male’ and ‘female’
and so on. We can now consider how to build these choices into a network, with
the help of a new primitive relation called ‘or’.
Think of sex (aka ‘gender’, a term that I prefer to keep for grammar), one
of the most important choices that we make when classifying people. Sex contrasts ‘male’ and ‘female’ and we assume that everyone must have either male
or female sex, and nobody can have both. The question is how to include this
information in network structure.
The first step is to recognize that the sex called ‘male’ is different
from the type of person we call ‘male’. A male person has the sex ‘male’, which
isn’t a person but a property of a person. Similarly, an old person has the property
‘old age’; but old age isn’t itself a person.
What then is the sex ‘male’ or the age ‘old’? It’s a concept, but a very abstract one compared with, say, ‘person’. It probably doesn’t have any properties
of its own, and its main job in our minds is to help us to organize our ideas into
contrasting sets of alternatives. Even more abstract is the relation ‘sex’ or ‘age’,
which links a person to one of these concepts. To anticipate the discussion of
such things in language (7.3), we can call sex and age a FEATURE. A feature is
a kind of relational concept whose value is one of these abstract concepts, shown
in Figure 3.8 as the male and female symbols. The diamond arrows are explained
A notation for choice setsâ•‡ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
The second step in understanding features such as sex and age is
to look at the way in which the alternatives are organized so that we know, for
example, that ‘male’ is a possible value for ‘sex’, but not for ‘age’. In each case,
the alternatives are defined either by a list of members (e.g. ‘male’, ‘female’) or
by a description of the typical member (‘a measure of time’); in more technical
terms, they’re defined by a SET, a notion that you may have met in mathematics.