Table

Summary of the major differences between propositional and analogical representations Propositional Analogical

Discrete

Non-discrete

Explicit

Implicit

Strong combination rules

Loose combination rules

Amodal (abstract)

Modality-specific

of on between them. Analogical representations are non-discrete, can represent things implicitly, have loose rules of combination, and are concrete in the sense that they are tied to a particular sense modality. These differences between propositional and analogical representations are now widely accepted in psychological theory. However, as a counterpoint, you should be aware that some commentators have argued that it is next to impossible to really distinguish between the two forms of representation (for good discussions see Boden, 1988, and Hayes, 1985).

In conclusion, several aspects of external representations have parallels in mental representations. In later sections, we consider the differences between mental representations in some detail. Most of this chapter, and of the literature on analogical representations, concentrates on visual images. More immediately, we now turn to the way in which prepositional representations have been used to characterise object concepts, relational concepts, and schemata.

WHAT IS A PROPOSITION?

As we saw earlier, prepositional representations are considered to be explicit, discrete, abstract entities that represent the ideational content of the mind. They represent conceptual objects and relations in a form that is not specific to any language (whether it be it Russian, Serbo-Croat, or Urdu) or to any modality (whether it be vision, audition, olfaction, or touch). Thus, they constitute a universal, amodal, mentalese. By mentalese, we mean that propositions are a fundamental language or code that is used to represent all mental information. However, this leaves us with a puzzle. If prepositional representations are abstract, language-non-specific, and amodal how do we characterise them? Well, when theorists want to be explicit about the use of propositional representations they use aspects of a logical system called the predicate calculus.

One can imagine that the contents of the mind might be object-like entities that are related together in various ways by conceptual relations. The predicate calculus provides a convenient notation for realising these intuitions; the links on relations are represented as predicates and the object-entities as arguments of these predicates. By definition, a predicate here is anything that takes an argument or a number of arguments. The terminology sounds daunting but the idea is relatively simple. If you want to express the idea that "the book is on the table"; then the link or relationship between the book and the table is represented by the predicate on (where the italics represent the notion that we are dealing with the mental content of on and not the word "on"). The arguments that the on-predicate links are the conceptual entities, the book and the table. In order to indicate that on takes these two arguments, the objects are usually bracketed in the following manner:

on(book, table)

Predicates can take any number of arguments; so, the sentence "Mary hit John with the stick and the stick was hard" can be notated as follows:

hit(mary, john, stick) and hard(stick)

The predicates hit and hard are first-order predicates; that is, they take object constants as their arguments. Whenever one has a predicate and a number of arguments combined in this fashion the whole form is called a proposition, as can the combination of a number of such forms (i.e., the whole of the above expression is also a proposition).

There are also second-order predicates that take propositions as their arguments. So, in characterising the sentence "Mary hit John with the stick and he was hurt" we can use the second-order predicate cause to link the two other propositions:

cause[ hit(mary, john, stick),

Cognitive psychologists have used these notations to express mental, propositional representations. However, psychologists do not use all the strictures employed by logicians when they use the predic ate calculus. In logic, a proposition can be either true or false and this has important consequences for logical systems. Most psychologists are not overly concerned with the formal properties of propositions (one important exception is the work on deductive reasoning described in Chapter 16). In short, typically, theorists merely use the notion that ideational content can be stated in terms of predicates taking one or more arguments.

In an empirical context, the basic properties of propositions are rarely tested directly but are simply assumed. Their characteristics are, however, tested at a more gross level when they are combined to represent knowledge. In this chapter and the next, we review several areas where propositional representations have been used heavily to represent semantic networks and schemata (see e.g., Collins & Quillian, 1969; Rumelhart & Ortony, 1977). Finally, in practical terms propositional representations are very useful for computational modelling. The predicate calculus can be implemented very easily in artificial intelligence computing languages like LISP (Norvig, 1992; Steele, 1990) or PROLOG (Clocksin & Mellish, 1984; Shoham, 1993). This has allowed researchers to be very precise about theories based on propositional representations and to construct and run computer models of cognitive processes.

PROPOSITIONS: OBJECTS AND RELATIONS

In broad terms, it makes sense to distinguish between objects, relations, and complex combinations of these things (e.g., events and scenes). At the simplest level, an important part of what we know is that there are things or objects; there are specific things, my pet dog Peg, and more general things, pets, dogs, and furniture. An object concept (like dog) can be distinguished from relational concepts (like hit, bounce, and kiss). When one combines objects and relations, with some other assumptions, one is starting to characterise schematic structures to characterise events; for example, the dog bit the man causing him to bleed. All of these entities have been characterised using propositional representations.

In object concepts, the meaning of dog has tended to be characterised by attribute lists; for instance, a dog is defined by the attributes four-legs, fur, barking, panting-a-lot, and so on. The attributes are also propositional representations, and have been variously termed semantic features, semantic primitives, semantic markers by generations of philosphers, linguists, and psychologists. They are viewed as the fundamental meaning units that are used to constitute the meaning of all of our concepts. A particular thing in the world— my dog Peg—can be identified as a dog by virtue of having these attributes; if she had other attributes she might be categorised as a cat or a chinchilla. These propositional definitions help to define categories of things and are seen to play a crucial role in driving our ability to classify things and organise our conceptual knowledge. Object concepts have been the main focus of research in studies of semantic memory, concepts, and categorisation. For this reason, the next chapter is devoted to a complete review of this literature. We merely mention them here to place them in the wider context of the human conceptual system. Our main concern in this chapter is on this wider context, on how relational concepts and schemata have been characterised from the propositional perspective.

Representing relational concepts

Relational concepts have, until recently, received much less attention in the literature on knowledge. One reason for this may have been the difficulties inherent in characterising relations in terms of the attribute lists that appeared to work for object concepts (see Chapter 10). One solution, proposed by the linguist Charles Fillmore (1968), is that relational concepts could be represented as a case grammar: that is, as predicates taking a number of arguments (see e.g., Kintsch, 1974; Norman & Rumelhart, 1975, and Chapter 10). For example, the representations for the concepts hit and collide are:

hit(Agent, Recipient, Instrument) collide(Objectl, Object2)

Here hit and collide are predicates and Agent, Recipient, and Instrument are the arguments of this predicate. On understanding a sentence about hitting and colliding, people were supposed to construct a mental representation of this sort. So, the sentence:

Karl hit Mark with a champagne bottle.

would be represented as hit(Karl, Mark, champagne-bottle) People must know which objects can fill the argument slots in the representation; that is, they should be able to determine that Karl is an agent, Mark is a recipient, and that the champagne-bottle is an instrument, and therefore assign them to their proper roles or cases in the situation.

This method of representing relations has been used widely. Most semantic network models of concepts have used this sort of representation; relational concepts, like hit and kick, were represented as labelled links between the nodes in the network (see Anderson, 1976, 1983; Collins & Loftus, 1975; Norman & Rumelhart, 1975; Quillian, 1966). However, this treatment of relational concepts is not without its critics. Johnson-Laird, Herrmann, and Chaffin (1984) have argued, convincingly, that these propositional representations are not constrained enough to constitute an adequate theory of the meaning of relations; any theory of meaning can be represented by these network representations. In Johnson-Laird et al.'s terms they were "only connections". Johnson-Laird et al. (1984) also pointed out, using the intensional-extensional distinction, that these theories say little about extensional phenomena (see Chapter 10 for a discussion of the intensional-extensional distinction). For example, semantic networks ignore the gap that exists between a linguistic description and a mental representation of that description. The statement "The cat is on the mat" could be mentally represented in many different ways; for instance, the cat in the middle of the mat, the cat on the left corner of the mat, the cat wearing a red-striped, top-hat standing with one foot on the mat. These are alternative mental models of the linguistic description that have semantic implications (see Johnson-Laird et al., 1984; Johnson-Laird, 1983, on mental models).

Semantic decomposition of relational concepts

One partial answer to Johnson-Laird et al.'s criticisms is to specify more about the semantic primitives that underlie a particular relation (see e.g., Gentner, 1975; Norman & Rumelhart, 1975; Miller & Johnson-Laird, 1976). Roger Schank's conceptual dependency theory is one influential attempt to do this in artificial intelligence (see Schank, 1972).

Schank proposed that the core meaning of a whole set of action verbs could be captured by 12 to 15 primitive actions. These primitives were called acts and the main ones are listed in Table 9.2. These primitive acts are used in a case-frame fashion to characterise the semantic basis of a whole range of verbs. For example, ATRANS can characterise any verb that involves the transfer of possession:

Actor: person

Act: ATRANS

Object: physical object

Direction TO: person-1

FROM: person-2

This structure is a type of schema; it is made up of a series of variables (the terms Actor, Act, Object etc.) and in a specific case certain values are assigned to these variables. So, "John gave Mary a necklace" would be represented as:

Actor: John

Act: ATRANS

Object: necklace

Direction TO: Mary

FROM: John

A variable, as its name suggests, can take on any of a number of values. Computer scientists often use the term slot for variable and slot filler for a value; this taps into a spatial metaphor which suggests that slots are like holes in the schema into which specific objects are put (like necklace). ATRANS can be used to characterise many relations: like receive, take, buy, and sell. In a more

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