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6 External and Internal Grounding: Breaking the Symbolic Circularity

# 6 External and Internal Grounding: Breaking the Symbolic Circularity

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1.6 External and Internal Grounding: Breaking the Symbolic Circularity

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represented by some sort of “ground-level” constructs that they refer to. Then, it

will be alright for other symbols to be defined in terms of these symbols, because

there will then be no circularity.

For example, the “real” idea of the concept Move is a change of physical

location over time. Suppose we use spatiotemporal representations such as that in

Fig. 1.12 to represent the concept Move. The representations in Fig. 1.12 represent

1-dimensional (1D) spatial movements over (1D) time. Each small square in the

representation represents an elemental discrete spatial or temporal location. Figure 1.12a shows a specific kind of movement in which the Object moves one

elemental spatial location over one elemental time frame and in the upward

direction. Figure 1.12b shows a general movement over any number of spatial

locations in any amount of time, and in either the upward or the downward direction

(in 1D space, there are only two directions – upward or downward in this case). The

horizontal and vertical Range Bars represent any amount of space and time intervals respectively, that correspond to any amount of spatial and temporal displacement respectively for the Object involved (see Chap. 4, Sect. 4.3.7.1 – discussion in

connection with Figs. 4.14 and 4.15 that further elaborates on how this representation works). The “Up-Down Flip” symbol specifies that the pictorial representation

can be flipped in the upward-downward direction, hence representing the upward

and downward movements accordingly. The representation in Fig. 1.12b represents

the general and grounded concept of Move.

Why do we claim that this is a ground level representation that truly captures the

meaning of the concept Move? The reason is simple: Since Move is a spatiotemporal concept connoting a change in location of an object over time, just represent it

accordingly. Of course, there has to be an attendant computational process that

operates on the representations of Fig. 1.12 as well to fully utilize them in order for

the intelligent system that has this concept to be able to claim to have a full

understanding of it. For example, one question posed to the system could be:

Since you know the meaning of Move, can you move an object? To do so, the

system will retrieve the spatiotemporal representations of Fig. 1.12 and use it to

operate on an object, and the consequence of which would be that the object would

change position over time, thus showing that it “understands” by knowing how to

“operate” with the representations. The circular definition above will not allow the

system to achieve this. (If the process uses Fig. 1.12a, then the object changes its

position by one elemental spatial location over one elemental time frame and in the

upward direction. If Fig. 1.12b is used, then the object can change its position by

any number of elemental locations over any amount of time and in any direction –

upward or downward direction in the case of 1D movement.) Later, in Chap. 5, we

will see more extensive examples of how a series of ground level representations

allows a system to solve complex problems at the ground level, hence, in the real

world.

Another question can also be asked: Since you know the meaning of Move, can

you recognize an instance of the concept? The answer is, again, yes, as the

spatiotemporal templates of Fig. 1.12 can be used to recognize that a movement

has taken place for an object by matching these templates with events that take

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1 Introduction

a

Range Bars

b

Move

Up-Down

Flip

Space

Space

Object

Time

Object

Time

Fig. 1.12 The ground level (symbolic) representation of the concept Move. Each square represents an elemental discrete spatial or temporal location. (a) A specific Move in which the Object

moves over an elemental spatial location over an elemental time frame and in the upward

direction. (b) A general Move in which the Object moves over any number of spatial locations

over any amount of time and in the up or down direction

place in the environment, either for a specific Move-ment such as in Fig. 1.12a, or a

general Move-ment such as in Fig. 1.12b. Again, the circular definition above will

not allow the system to achieve this.

An interesting question arises here: Are the spatiotemporal representations

shown in Fig. 1.12 not also a kind of symbol? A symbol is “something that stands

for or suggests something else” (Merriam-Webster). The spatiotemporal “pictures”

of Fig. 1.12 stand for the “real world event” of “move.” Therefore, the distinction

is actually between ground-level symbolic representation and high-level (or

non-ground level) symbolic representation. We submit that Fig. 1.12 depicts

ground-level symbolic representations of the concept Move. In fact, the spatiotemporal representations of Move in Fig. 1.12 have equivalent predicate logic representations, which are made up of symbols of predicates and arguments. We will

discuss this further in Chap. 4.

With Move having operationally represented, the other concepts such as Go

above that is defined in terms of Move symbolically can then acquire the operational definition and the system hence “understands” what Go really means as well.

In the field of linguistics, many attempts in the past have been devoted to the

study of meaning or semantics. Among the different paradigms, cognitive linguistics (Evans and Green 2006; Geeraerts 2006; Langacker 2008, 2009) stands out as

having succeeded in providing a framework for grounded meaning representations.

Chapter 4 explores the issue of semantic grounding more fully.

Note that the concept of Move such as represented in Fig. 1.12 can be applied to

external events – e.g., the movement of a physical object in the real world – or

internal events – e.g., the moving up and down of hunger level (this is further

discussed in Sect. 4.3.8). Therefore, Move can be applied to internally grounded

concepts such as hunger or externally grounded concepts such as a physical object

and hence it can participate in both internally or externally grounded processes.

1.7 Perception, Conception, and Problem Solving

1.7

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Perception, Conception, and Problem Solving

In the foregoing discussion we have emphasized that problem solving represents the

processing backbone of a noological system (Fig. 1.7), and that perception and

conception perform service functions to the system. Moreover, the primary purpose

of problem solving is to address the basic needs and motivations of the noological

system which represent the internal ground of the system. We have discussed this

using a simple example in Sect. 1.2 (Figs. 1.5 and 1.6). In this section we use a more

complex computational model of a functional definition for visual recognition to tie

together these various issues discussed in the foregoing sections.

issue of visual recognition: despite the fact that some objects that purportedly

belong to the same category look very different from each other in terms of their

visual appearances, they are nevertheless classified under the same category.

Figures 1.13a–e show a number of chairs that do not all have the same set of

necessary and sufficient visual features that are nevertheless all called “chairs.”

There may be a possibility of using the concept of “family resemblance” to explain

the grouping of these objects into the same category (Rosch and Mervis 1975) – a

first object shares some common features with a second object, and the second

object shares yet another set of common features with a third object, but the third

object may in turn share very few or no common features with the first object. The

objects involved are thus grouped based on some kinds of disjunctive conditions –

for example, a chair could have four legs or one leg, and the seat could be square or

circular in shape, etc. However, without a set of necessary and sufficient conditions

to group these objects together, it would be difficult to recognize novel instances.

Suppose now there is a new kind of chair with a triangular seat, does it still belong

to the chair category? More interestingly, Ho (1987) pointed out that there is a kind

of chair called Balans chair, shown in Fig. 1.13f, that has very little visual similarity

to those in Fig. 1.13a–e – it doesn’t even have a back, which all the chairs in

Fig. 1.13a–e have, otherwise those same chairs would have been called stools.

Interestingly, the way the Balans chair supports a human body, as shown in

Fig. 1.13g, allows it to function like a chair. Normally the back of a chair prevents a

person’s upper body from falling backward when his muscles are relaxed. That is

what fundamentally distinguishes a chair from a stool. However, due to the way the

thigh and the lower leg portions are supported in a Balans chair, the muscles of a

person can be relaxed and yet the upper body does not fall backward. Therefore, the

Balans chair functions more like a chair than a stool. Figure 1.13h shows how a

normal chair supports a human body for comparison.

Ho (1987) devised a computational model to recognize all kinds of chair based

on a functional definition – how the object supports a human body comfortably in a

sitting position. To achieve that, the recognition system attempts to fit a model of a

human body onto the object involved, and if it can support the human body in a

sitting position (say, like that shown in Fig. 1.13h), it is then recognized as an

instance of chair. There are a few other criteria for a chair to be a good chair, such as

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1 Introduction

Fig. 1.13 (a–e) Various kinds of chairs. (f) A Balans® chair. (g) How a person sits in a Balans®

chair. (h) How a person sits in a normal chair (From Ho 1987)

it allows not only just one position of human body support, but it also allows the

human body to move around a bit and still be supported, etc. A fuzzy measure is

used to characterize “how good a chair an object is.”9

The process of functional reasoning is shown in Fig. 1.14. Firstly, the image of

the object to be recognized is loaded into a Physical Configuration Array. There is a

built-in Physical Reasoner that encodes the laws of physics – how objects interact in

various physical situations of mutual contact and under the law of gravity as well.

Then the Functional Reasoner, encoding the above functional definition of a chair,

invokes the Physical Reasoner with an internal model of a human body (a threesectioned jointed model as shown in the figure) and see how the human body

interacts with the purported chair object and whether or how well the object satisfies

the functional definition of a chair.

The complete structure of a concept is shown in Fig. 1.15 (Ho 1987) in which

there are two portions. One is the Functional Definition portion and the other is

called Symptomatic Perceptual Conditions. These correspond to what psychologists call core and identification procedure of a concept respectively (Miller and

Johnson-Laird 1976; Nelson 1974). The core of a concept consists of the basic

definition of the concept which would include a set of necessary and sufficient

conditions and the identification procedure specifies how an instance can be

identified, such as through perceptual characteristics. The possibly disjunctive set

of symptomatic perceptual conditions for the concept is hence learned under the

9

There are other constraints such as the “economy constraint” that states that a good chair should

not have more parts than necessary to achieve the stated function – this means a chair with an

extremely tall back is not a very good chair. These are discussed in Ho (1987).

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6 External and Internal Grounding: Breaking the Symbolic Circularity

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