Some Interpretations of Nodes and Links

Despite the very good recent research of cognitive psychologists, there is still no agreement as to how facts are represented in human semantic memory, what kinds of things these facts are, nor even that they are 'represented' at all. (Recent research in Connectionism and Neural Networks has, in any case, cast doubt on the classical notion of representation; see chapter 9). The lack of consensus among psychologists has been mirrored in many computer programs using semantic nets in which the meaning of nodes and links has, unfortunately, been interpreted intuitively rather than described rigorously and systematically; if we are using a semantic network to represent an area of knowledge, we ought to be clear about what kinds of things we are depicting in the nodes of our networks and what kinds of relations we are specifying in the links between the nodes. That is, we ought to specify the semantics of our formalism. We will consider just three interpretations of nodes and links -- though if you are interested, and are prepared for more advanced reading, you could look at Brachman (1983).

One kind of interpretation is that of semantic inclusion or logical entailment. Generic nodes are taken to be word senses, or intensions (which we explained in the last chapter), and the ISA relationship to be one of sense inclusion: to state that a canary is a bird is really to claim that part of the meaning of 'canary' is that it is a bird, or in other words that to be a canary is by definition to be a bird.

The ISA link between the child node and its parent node is therefore one of logical entailment. For example, given the sentences "Tweetie is a canary" and "Tweetie is a bird", it is logically impossible to conceive of circumstances in which the first sentence is true and the second false. But this kind of interpretation then runs into difficulties with the principle of property inheritance: if part of the meaning of 'bird' is, in turn, not only that it is an animal but also such other sense-components of the node as that it can fly, then we are committed to the position that part of the meaning of any child node of 'bird' is also that it can fly. But this is patently not the case with 'ostrich'.

An alternative interpretation of generic nodes is as sets of individuals. Thus the relation holding between a generic node at one level of a hierarchy and that at a higher level is that of subset to superset. If, for example, we indicate in our network that a canary is a bird, what we are in effect stating is that the set of all canaries is a subset of the set of all birds; alternatively, that if some individual falls within the set of all canaries then it necessarily also falls within the set of all birds. This is shown diagrammatically in Figure 6.


Figure 6.

Everything that lies within the circle labeled BIRDS is a bird -- the circle schematically represents the set. Within BIRDS lies the circle CANARIES. Thus a, c, d, e, and f are all birds, since they (c and e included) are all contained by the larger circle. But c and e are also canaries, since they alone are contained within the smaller circle. Whatever b is, on the other hand, it is not a bird, as it lies outside the larger circle.

If the generic node is interpreted as a set, then the relation of nodes representing individuals to generic nodes in the network is that of set membership. Thus the meaning of the left-most fragment of the network in Figure 4, Tweetie-->inst-->canary, is represented in figure 6 by the relationship of c or e to the circle CANARIES.

There are problems, however, with the set-theoretic interpretation. Sets are effectively conceived as abstract containers -- like the circles in the figure -- with individuals either inside a particular container or outside. Things grouped together inside a container are so by virtue of properties they are taken to have in common; conversely, it is those properties that members of the category have in common that define the category. If the category 'bird' is partially defined by the set of all those individuals who can fly, and an ostrich can not fly, then we are in effect claiming that an ostrich is not wholly a bird. An ostrich is not mostly a bird, but partly something else, however: it is all bird, but it just so happens that it is not a highly typical one. (For a contrasting argument, however, you might like to look at Zadeh, 1983.)

This appeal to the notion of typicality leads us on to a third interpretation -- of generic nodes as prototypes, and of instance nodes as individuals for whom the generic nodes provide a prototypic description. By prototype we mean something like a typical instance. Rather than describing an individual or picking out a class of individuals, a prototype describes what the most typical exemplar of the class is like, in terms of its physical characteristics, its behaviour, diet, habitat, and so on. Individuals will then be more or less like the prototype. Thus, for example, mammals are prototypically thought of as land-animals which give birth to live young; a cow or a rabbit is a typical mammal in these respects, though a dugong is atypical on the first count, a platypus on the second. Canaries prototypically are yellow and can sing; so we recognize Tweetie, who is yellow and can sing, as a fairly typical instance of what we imagine a canary to be. A detailed model of concept organization, based on prototypes, has been proposed by Rosch (1983).