CHAPTER 20

The Representation of States

20.1 States and Perceptions

In Chapter 17 we discussed some aspects of human perception and the organisation of memory. We suggested that internal representations of the meaning of linguistic utterances made use of the same structures as other types of representation (section 17.4). The consequence is that our method of representation for states should lean heavily on the representation of percep­tions. In fact a state is a perceptual 'snapshot' of the world (real or imaginary).

In this chapter we develop a method of representing states, taking the requirements discussed in Chapter 17 into account. The method will serve as a basis for discussion for the remainder of the book. It is by no means the only form of representation which we could have chosen, but unlike some of the exotic formalisms it does not call for a deep understanding of logic. Instead it is based upon simple data structures, and each state is represented by a record structure. We attempt below to determine the appropriate elements or fields of that record structure, and to do that we will return once more to the features of human perception. State-id. Each state will have a unique identifier so that we can cross-reference it from other states in a perspicuous way.

Time-stamp. Each state will have a time-stamp. This will be represented by a formal parameter which mayor may not be instantiated (see Chapter 8).

Channel. We have five senses through which our perceptions of the external world are filtered. These are sight, hearing, touch, taste and scent. When we perceive the world we are aware of which senses we are using, and so it is reasonable that our representation of state should have a parameter which records the sense involved. We will call that the channel of the perception (and of the state).

Aspect. Consider the sight channel. When we look at the world we are able to discriminate between and be aware of several different aspects of the scene. We recognise 'entities', we note their 'colour', their 'shape', their 'location', and so on. Each of these we shall refer to as an aspect of a perception.

Model. Consider the aspect of location. When we observe the location of an object we can think about it in terms of different frames of reference. We might use ourselves as the point of origin and think about the location of the object relative to ourselves in terms of some kind of polar coordinate system, or we might use a plan view of the scene. When children of a certain age are asked to sketch a house, they invariably sketch the house in vertical elevation and the garden in plan view. This is obviously not how they would see a house if they looked at it, or how it would appear in a photograph, but it does indicate how they 'perceive' it. We shall refer to a system of coordinates of this kind as a model.

Axis. When we talk about locations we refer only to a particular quantity like distance, height or depth. When we talk about the shape of an object, we talk about its height, thickness, width, length and so on. When we discuss a complex shape (like a face) we can compare it with some standard shape, like a template of a 'standard face'. We will also need some function which compares such shapes and provides a measure of difference which we shall call a metric. Always we are referring to a singular quantity which coincides with one axis of the coordinate system involved. For a quantity like area we use a model which has only one axis. Length and width are not distinguished one from another. We shall call this the axis of the perception. A metric is an axis. Various metrics have been proposed which measure, for example, the symmetry of a shape, the ratio of perimeter to area, and so on.

Value and relative value. We perceive the value of some quantity. As we indicated in section 17.5, human perceptions are poor with respect to absolute each quantity value perceived with an individual identifier (a unique string). The relative measure of that value will be provided in terms relative to other identifiers (including 'standard values' - see section 7.7). Once we have identified the channel, aspect, model, and axis of a perception, and have two identifiers X and Y which indicate the positions of certain values on that axis, we can readily understand what the relationship X> Y means. Reference. Finally we note that these properties (height, shape, size, distance etc.) all belong to some entity. We require some means of representing an entity, and each state which represents a property of that entity must be cross­referenced to it. These, then, are the parameters which we suggest should be present in the representation of a state, so that we can write: state( state- id, time-starnp, channel, aspect, model, axis, value, reference )

As we develop our argument we hall have cause to add more parameters to that set, but the basic set will not be changed. We shall call the set of four parameters (channel,aspect,model,axis) a framework.

The impressive thing about the way we, as humans, deal with complex descriptions of a scene is the speed and ease with which we can flip from one framework to another, or even maintain several different frameworks in operation at the same time.

The internal channel. We are aware of ourselves in a way that does not require the use of any of the normal sensory channels. To allow internal feeling to be represented we therefore introduce an additional channel which we shall call the 'internal channel'.

Entities. We noted earlier (in Chapter 4) that an entity is a manifestation of human perception, and that the identity of an entity is not dependent upon the set of properties it may have at any particular time. It has an object history and an existence which can outlast its physical disappearance. We could fit the representation of an entity into the framework idea, but it is simpler to provide a special state for the purpose. It will still have a state identifier and a time-stamp which indicates the period of time for which it is perceived by the person concerned. The state identifier becomes the identifier for the entity and it is often convenient to have a name for an entity. The representation structure is therefore: state( state-id,time-stamp, 'entity' ,entity-name)

Causal links. We discussed the representation of a causal link in Chapter 19, and concluded that it could be represented by means of a 'state'. Again the simplest method is to introduce a special kind of state for this purpose. It will have an identifier, a time-stamp, and two lists of state identifiers to indicate the set of states which comprise the cause, and the set of states which comprise the effect of the causal link. We will allow 'and' and 'or' connectors within the lists of states so that we can have contributing and alternative causes and effects. The representation has the form:

state( state-id,time-stamp, 'cause' ,causing-state,effect -state)

0.2 Representations of Representations

We have remarked frequently that it is important that a formalism for representation should be capable of dealing with the representation of other people's representations. To this end we introduce a new structure which, for want of a better name, we shall call a rep-box. A rep-box will be able to contain a variable number of states of all kinds and provide them with a common identity. We can think of it as a cardboard box into which we can put all of the states of some representation, and on the lid of the box we can write global information about the contents. This will include a relationship between the relative time-stamps on the state within the box and absolute 'now'. We can also indicate on the lid whether this is a real or a fictitious representation, and to whom the representation belongs. We can think of the whole of the computer memory being one very large box which belongs to the computer itself. In a sense then all representations belong to it. (It can call itself 'me' or 'us'.) All other representations are held within that global box, and represent its representations of someone else's representation.




The representation of that 'someone else' will be an entity outside the box belonging to that person but within the computer's box. We will develop this idea further in Chapter 22.