Knowledge Representation

Arthur B. Markman

• Publisher: Psychology Press
• Year: 2013
• Topic: Psychology
• eBook ISBN:
  9781134802975
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

Knowledge representation is fundamental to the study of mind. All theories of psychological processing are rooted in assumptions about how information is stored. These assumptions, in turn, influence the explanatory power of theories. This book fills a gap in the existing literature by providing an overview of types of knowledge representation techniques and their use in cognitive models.

Organized around types of representations, this book begins with a discussion of the foundations of knowledge representation, then presents discussions of different ways that knowledge representation has been used. Both symbolic and connectionist approaches to representation are discussed and a set of recommendations about the way representations should be used is presented. This work can be used as the basis for a course on knowledge representation or can be read independently. It will be useful to students of psychology as well as people in related disciplines--computer science, philosophy, anthropology, and linguistics--who want an introduction to techniques for knowledge representation.

Chapter 1

Foundations

In the study of the mind, cognitive scientists seek explanations of mental life, which consists of perceptions, emotions, social interactions, and cognitive abilities. In many of these explanations, they refer to goals, beliefs, mental images, concepts, and other mental entities. They are also concerned with retrieval, analogy, inferencing, reasoning, categorization, and many other processes that create, combine, and use the information “in our heads.” The aim of this book is to consider ways of thinking about goals, beliefs, mental images, concepts, and other mental entities to understand how different decisions about the way to characterize these entities affects what is easy to do with them and what is hard to do with them.

In particular, this book is concerned with the question of mental representation. That is, what formats are used for the information that makes up mental life (and how is the information used)? In this book, I explore a variety of options for representing information and focus mainly on the assumptions made by different representational formats and on the ways these assumptions affect what is easy or hard to do with them. Before the discussion can proceed, however, several preliminary issues must be dealt with. First, what is a representation? Second, why worry about the nature of mental representations? Finally, how do representations fit into the study of cognition? Chapter 1 addresses these topics.

AN EXAMPLE

The issue of mental representation may seem uninteresting. Perhaps there are not many options for representing a situation, or the choice of representation may be irrelevant to what a model of mental processing can explain. Even if there are differences between models, these differences may have no practical significance for the way psychology is carried out as a science. In this section, I present an example demonstrating that there are often many different ways that something can be represented, that differences in representations do affect the explanatory capability of a model, and that the choice of representations has important implications for how psychology is done.

My example comes from the study of people’s ability to do logical reasoning. The prototypical version of the task was presented by Wason and Johnson-Laird (1972) and has become known as the Wason selection task. In this task, researchers show people four cards on a table and tell them that all the cards have a letter on one side and a number on the other. The four cards are laid out so that they face the subject as shown in Figure 1.1. Then, the subject is asked to point to the smallest number of cards necessary to test the truth of the rule “If there is a vowel on one side of the card, then there is an odd number on the other side of the card.”

Countless researchers (Johnson-Laird, 1983; Rips, 1994) have examined variations of this task. When the problem is framed as presented in Figure 1.1, people often have difficulty getting the right answer. Most people will say that the card with the letter A must be turned over. Few people think that they have to turn over the card with the letter J. People are split on what to do with the numbers. Some think that both numbers can be ignored, some feel the seven must be turned over, some feel the four must be turned over, and some feel that both cards must be turned over. The correct answer is that the A and the four must be turned over: If there is an even number on the other side of the A card, the rule is invalid, and if there is a vowel on the other side of the four card, the rule is invalid. The J need not be turned over; the rule does not apply to it, and it does not matter what is on the other side. The seven need not be turned over; if there is a vowel on the other side, the rule applies and is valid, but if there is a consonant on the other side, the rule simply does not apply. Thus, turning over the seven does not provide a way to invalidate the rule.

FIG. 1.1. Wason selection task.

How can I explain subjects’ difficulty with this task? Perhaps people represent the task as one of logical reasoning. Turning over the A card corresponds to the valid logical inference schema modus ponens:

This schema reads “If some statement P is true, then some statement Q is true. Statement Pis true. Therefore, Statement Q is true.” For this schema, any statement that can be either true or false may play the roles of P and Q Turning over the four card requires the logical schema modus tollens:

Not all schemas give rise to valid rules of inference. The valid rules are those for which if the premises (i.e., the statements above the line) are true, then the conclusion (i.e., the statement below the line) is guaranteed to be true. One example of an invalid schema is affirming the consequent:

The problem with this schema is that it fails to take into account that the statement Q can be the case for some reason other than the rule “If P, then Q.” This schema would be valid if the rule were “Q is true if and only if P is true” (sometimes written IFF P, then Q).

Taking logical rules seriously as a representation of people’s ways of reasoning suggests that correct performance on the Wason selection task requires both modus ponens and modus tollens, but not incorrect schemas like affirming the consequent. Because most people turn over the A card and fewer people turn over the four card, modus ponens must be an easier rule to learn than is modus tollens. Accounts of logical reasoning of this type have been proposed by Rips (1994) and Braine, Reiser, and Rumain (1984). This account of reasoning assumes that people use general rules of reasoning across domains. By adopting this framework, a researcher makes certain questions particularly interesting to answer. For example, a researcher who assumes this representation may focus on the rules people tend to have, the factors that promote the acquisition of new rules, and the factors that control whether people recognize that a particular rule is relevant in a given context.

According to an alternative account of logical reasoning ability, however, people do not have logical rules that apply across domains. After all, logical rules do not care about the content of the statements P and Q. As long as a situation has the right form, the logical rules apply. According to one such account, people have a mental model of a situation about which they are going to reason (see chap. 9). Mental models are not general schemas of inference but instantiations of particular situations. This account suggests that problems framed in an abstract way (like the Wason selection task) are difficult, because it is difficult to construct models for abstract situations. Thus, a problem with the same structure (an isomorphic problem) may be easier to solve if it is in a domain for which it is easy to construct a model.

This view of representation suggests that the selection task should be tried with different problem contents. As an example, imagine you are working for the security patrol of a college on a Saturday night, and it is your job to make sure that campus bars serve alcohol only to people of the legal drinking age (21 years old in the United States). You enter a bar and see one person you know to be 18 years old, a second you know to be 22 years old, a third person, whom you do not know, holding a beer, and a fourth, unknown to you, drinking club soda. Which people must you check to ensure that the bar is satisfying the rule “If a person has a drink, then he or she is over 21”? College undergraduates given versions of the selection task in familiar domains like this performed quite well. Nearly all knew that only the 18-year-old and the person drinking beer need to be checked. This problem is isomorphic to the task with the cards, but people have much less difficulty with the concrete version (see Johnson-Laird, Legrenzi, & Legrenzi, 1972).

Mental models are not exactly the same as logical rules. Although mental models can be described as having rules, the scope of these rules differs from that of logic. With a particular logical rule, anything with the proper form can be reasoned about. In contrast, the procedures for constructing mental models are domain specific. A person may have rules for reasoning about drinking in bars without having rules for reasoning about genetics or abstract logical forms. For those who have adopted a framework based on logical rules, the content effects discovered in the selection task are difficult to explain. Rips (1994) argued that content effects in this task may reflect people’s remembering what happened in their own personal experience and that this personal experience augments but does not replace logical rules. For example, when given the selection task in the context of verifying the rule about the legal age for drinking, people may just recall a situation in which they were in a bar and remember who was asked for identification. In this case, no rules were used at all; the answer to the problem was just remembered. Assuming that reasoning uses logical rules of inference makes it easy to explain logical reasoning abilities at the expense of making content effects more difficult to explain.

People’s performance on a psychological task may often be explained in many ways, each of which has a different approach to mental representation. Each way may provide a good account of the phenomenon being studied, but the approaches may differ in their predictions for subsequent studies that should be designed and carried out. Indeed, as I discuss next, adopting particular representational assumptions affects which new questions are most interesting to answer.

WHAT IS A REPRESENTATION?

Mental representation is a critical part of psychological explanation, but it has also been a source of great confusion. Different researchers have used the word representation in different ways. Psychologists have used representation in somewhat different ways from other cognitive scientists, such as philosophers and computer scientists, who are interested in representation. To avoid confusion, I offer a broad definition of representation, one that includes all things that cognitive scientists have considered representations, although it may admit some things that people may feel uncomfortable calling representations, or at least uncomfortable thinking of as psychological representations. My definition of representation has four components. The first two components of representation are:

1. A represented world: the domain that the representations are about. The represented world may be the world outside the cognitive system or some other set of representations inside the system. That is, one set of representations can be about another set of representations.

2. A representing world: the domain that contains the representations. (The terms represented world and representing world come from a classic paper by Palmer [1978a].)

As an example, consider various representations of the items pictured in the top row of Figure 1.2. These items are the represented world for this example. In this world, there are three objects of interest, an ice cube, a glass of water, and a pot of water on a fire. I can choose to represent many aspects of this world, but for now, I focus on the temperature of the water. This representational decision has consequences. If I represent only the temperature of the water, all the rest of the information about the situation is lost, including the shape of the ice cube, the size of the glass of water, and the degree of curvature of the handle of the pot. This point is not trivial: In all known representational systems, the representing world loses information about the represented world.

FIG. 1.2. Various ways of representing temperature. The top row depicts water that is frozen, at room temperature, and boiling. The next two rows depict possible analog representations. The two following rows show numerical temperature notations. Finally, the last row depicts temperature with the darkness of the

In modern culture, the representation of temperature, as in the second row of Figure 1.2, often appears as the height of mercury in a thermometer. That is, I can use the height of mercury as a representing world, in which the higher the line of mercury, the greater the temperature. In this representation, however, a few important issues lie buried. First, the height of mercury in a thermometer works as a representation of temperature, because there is a set of rules that determine how the representing world corresponds to the represented world. Thus, the third component of my definition of representation is:

3. Representing rules: The representing world is related to the represented world through a set of rules that map elements of the represented world to elements in the representing world. If every element in the represented world is represented by a unique element in the representing world, there is an isomorphism between the represented and representing worlds. If two or more elements in the represented world are represented by one element in the representing world, there is a homomorphism between the represented and the representing worlds.¹

As an illustration of this component of the definition, when temperature is represented as the height of mercury in a thermometer, each temperature is reflected by a unique height of mercury. The specific height that the mercury reaches is determined by the circumference of the thermometer as well as by the physical laws that govern the expansion of mercury with changes in temperature. Because each temperature has its own unique height, there is an isomorphism between the temperature in the represented world and the height of mercury in the representing world, but not all representations of temperature need to be isomorphisms. If a digital thermometer that gave readings on the Fahrenheit temperature scale (as in the second row of Figure 1.2) gave readings accurate to only 1 degree, any temperature between, say, 20.5 degrees and 21.4 degrees would be represented as 21 degrees. In this case, the relation between the represented and representing worlds is a homomorphism. When there is a homomorphism between the representing and represented worlds, the representation has lost information about what it is representing.

Another issue that arises with this example is that nothing inherent in a mercury thermometer alone makes it a representation. Since the dawn of time (or soon thereafter), mercury has had the property of expanding and contracting with changes in temperature, but mercury was not always a representation of temperature. For something to be a representation, some process must use the representation for some purpose. In this culture, having been schooled in the use of a thermometer, people can use the column of mercury as a representation of temperature. A vervet monkey who lacks the mathematical skills and cultural upbringing (among other things) to read a thermometer cannot use the column of mercury as a representation of temperature. More broadly, something is a representation only if a process can be used to interpret that representation. In this case, the combination of the thermometer and the person who can read it makes the thermometer a representation. More generally, the fourth component of a representation is:

4. A process that uses the representation: It makes no sense to talk about representations in the absence of processes. The combination of the first three components (a represented world, a representing world, and a set of representing rules) creates merely the potential for representation. Only when there is also a process that uses the representation does the system actually represent, and the capabilities of a system are defined only when there is both a representation and a process.

The importance of processes when thinking about representations cannot be underestimated (J. R. Anderson, 1978; Palmer, 1978a). In the temperature example, there is no representation until someone can use the thermometer to read off...

Table of contents

• Cover
• Halftile
• Title
• Copyright
• Dedication
• Contents
• Preface
• 1 Foundations
• 2 Spatial Representations: What Do We Mean by Space?
• 3 Featural Representations
• 4 Network Models
• 5 Structured Representations
• 6 Structure in Perceptual Representations
• 7 Structured Concept Representations
• 8 General and Specific Information in Representations
• 9 Mental Models
• 10 Using Representation
• References
• Author Index
• Subject Index