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2 Relational concepts, arguments and values

2 Relational concepts, arguments and values

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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 properties╇ 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:€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 properties╇ 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:€‘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

it goes.

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 values╇ 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

Network structure







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

everybody knows.



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Figure 3.4 Properties shown as labelled links


Primitive relations, relational concepts and the

relation taxonomy╇ 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:€ ‘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:€ 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.

(Wikipedia:€‘Conceptual graph’.)

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

Network structure










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 relations╇ 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:€‘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



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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 Gretta€– 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:€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:

primitive relations:

• ‘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

Network structure










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



Quantity╇ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

This is as good a point as any to mention a primitive relation that’s

part of the official Word Grammar list (Hudson 2007c:€ 19–20) but which I’ll

hardly mention again in this textbook:€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 recursion╇ 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



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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’:€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 concept€– entities and relations€– 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


Where next?

Advanced:€Part II, Chapter 7.1:€Dependencies and phrases


Choices, features and cross-classification

Section 2.4 introduced the idea that some categories are grouped

together as choices:€man or woman, Republican or Democrat, 1 or 2 or 3 or…

Network structure








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.


Features╇ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

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 sets╇ 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.



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2 Relational concepts, arguments and values

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