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Modelling Common-Sense Psychology and the False Belief Test

Stuart Watt
Knowledge Media Institute and Department of Psychology
Open University
Walton Hall, Milton Keynes, MK7 6AA, UK

+44 1908 653169
S.N.K.Watt@open.ac.uk

Abstract

In this paper, we describe a cognitive modelling framework for common-sense psychology. We'll show a number of comparable cognitive models for different theories of common-sense psychology, and show that these models can help to illuminate some of similarities and differences between the differing theories.
Keywords

Common-sense psychology, theory of mind, false belief test, cognitive model

Introduction

Common-sense psychology - or people's common sense ability to think about our own and other people's minds - is currently being researched actively in several different disciplines. While this interdisciplinary collaboration can be very productive, it can lead to its own problems. This is exacerbated by complexity, both methodological and theoretical, of common-sense psychology itself.

Much of the problem is that nobody is really sure what common-sense psychology is, theoretically. Astington and Gopnik (1991), for example, distinguish between six different possible interpretations, all of which are subtly different. There are many different theories of common-sense psychology. Unfortunately, there is no common ground which allows these different theories to be compared and contrasted. In this paper, we'll introduce a cognitive model that can begin to play that role.

To compare the different theories, we'll use a standard tool from common-sense psychology, Baron-Cohen et al.'s (1985) false belief test. We'll begin by introducing and describing this test, and one of the theories of common-sense psychology, Leslie's (1987) 'decoupler' model. Although common-sense psychology is hugely complex, and can only be modelled in the most sketchy form, we'll show how Leslie's theory can be implemented as a cognitive model. Finally, we'll show how alternative theories of common-sense psychology can be represented as small variations on this model, and that we can draw some conclusions about the similarities and differences between the theories with this modelling framework.

Models of common-sense psychology

While common-sense psychology has been a focus for recent research, most work in this either has either been experimental or purely theoretical; there are few cognitive models in this area, even though it is precisely the kind of area that modelling has proved so helpful for in the past (Samet, 1993). The exception is the work of Shultz (1988, 1991). All the models which have been developed, though, focus on small parts of the problem; for example, studying how people assess whether or not planned actions were intentional (Shultz, 1988).

We propose a different strategy. Instead of a narrow but deep model, we propose using a broad but shallow one; one which can be used to compare theories on a grand scale. With this level of modelling, we believe that even in the limited false belief test, we can help to clarify the similarities and differences between some of the grand scale theories in the field.

The false belief test

The false belief test has its origins in Premack and Woodruff's (1978) experiment to determine whether or not chimpanzees could reason about one another's mental states - whether or not they had a "theory of mind", another term for common-sense psychology. Unfortunately, there was a methodological problem with this experiment; their chimpanzee subject, Sarah, could use her own beliefs rather than reasoning about another's, because the two were identical. To prove that Sarah was really able to reason about another's beliefs, they had to show that Sarah could still predict another's behaviour when her beliefs were different from that other's - that is, when the other had beliefs which Sarah believed to be false.

Following these problems with Premack and Woodruff's experiment, Wimmer and Perner (1983) devised a false belief test, which evaluated a (human) subject's to ascribe definite but false beliefs to another. Baron-Cohen et al. (1985) later simplified Wimmer and Perner's test so they could compare autistic, Down's syndrome, and normal children at different ages. Baron-Cohen et al.'s simplified false belief test is shown in figure 1.

Figure 1. Baron-Cohen et al.'s (1985) false belief test

Baron-Cohen et al.'s false belief test is presented as a simple story. There are two puppets, Sally and Anne. Sally has a marble, which she keeps in a basket. Then Sally leaves the room, and while she is away Anne takes the marble out of the basket and hides it in the box. Sally comes back into the room. The child subject is then asked the question: "where will Sally look for her marble?" Older children say that she will look in the basket, because although they know the marble is in the box, they know that Sally doesn't know it has been moved from the basket, and they can distinguish Sally's (false) belief from their own (true) belief. Younger children, on the other hand, and autistic children, do not distinguish between the two. They simply say that Sally will look in the box. The false belief test, therefore, explores the change that happens as common-sense psychology develops.

Baron-Cohen et al.'s theory was that a failure in the development of common-sense psychology might be responsible for autism, and the results from their experiment (and others which followed) certainly seemed to bear that out. As a result, there has been a focus of interdisciplinary research which has led to a number of different hypotheses about the nature and development processes involved in common-sense psychology.

Figure 2 shows a model for one possible theory of common-sense psychology, Leslie's 'decoupler' model. At the heart of Leslie's model is a manipulator that is capable of pretence - of decoupling beliefs from one context and applying them in another. It is this that makes reasoning about false beliefs possible, because a child can use this decoupling mechanism to separate someone else's beliefs into a different context from their own.

Figure 2. Leslie's (1987) 'decoupler' model

Given this simple theory of common-sense psychology, we will now turn to the cognitive model, and show how Leslie's 'decoupler' model can be represented in a model. But first, a few words on the modelling environment that we'll be using.

The modelling environment

Before we can build the models adequately, we need a representation language that is strong enough to do the physical and psychological reasoning required. In practice, the psychological parts of the model require the ability to reason about different contexts, distinguishing one agent's false beliefs from another agent's true beliefs. Something like a modal logic, therefore, is going to be required (Leslie, 1988, makes a direct comparison between the requirements for common-sense psychology and the properties of modal logics).

The model we present borrows this from McCarthy's (McCarthy & Hayes, 1969) 'situation calculus', where the effects of an event are described as a consequence relation between one state and another. At the core of McCarthy's calculus is a special function result, which represents the effects of an action on a situation by returning a new, modified, situation. The function result(p, s, s), where p is a person, s is an action, and s is a situation, has a value which is a new situation representing the effects of p doing s in s. For example:

This says that if marble is inside something that isn't box in situation s, the effect of alison putting marble in box is a new situation t such that marble is no longer where it was (in X), but is now inside box.

The full situation calculus is more powerful and more complicated than this implies, but this subset of it is sufficient for the purposes of this model, and further, it doesn't need the heavy inference machinery that a complete modal logic would. The situation calculus, then, is strong enough for the model, fairly easy to use computationally, yet it retains the referential properties of modal logics (McCarthy & Hayes, 1969).

The model implements a modified subset of the situation calculus in a Prolog-like language embedded in Common Lisp. Apart from the Lisp-like syntax, there is only one significant difference from standard Prolog - variables are normally prefixed with a ? question mark, but output variables in a clause head are prefixed with a ^ caret. ?value and ^value refer to the same variable.

Modelling Leslie's 'decoupler'

The base model for the false belief test comprises a number of separate modules. There include;

• a physical environment model,
• a basic physical reasoning module,
• a basic psychological reasoning module, and
• a script for the false belief test.

The Physical Environment Model

The first part of the modelling environment is a physical environment model which implements an event-driven simulation environment. As objects are physically m Úoved from one place to another events are generated and passed to all objects equipped with sufficient perceptual apparatus to be aware of them.

The Physical Reasoning Module

Even in the false belief test, physical reasoning is needed. The basic physical reasoning module is shown in figure 3. This implements the rules that Alison (as we'll call the subject in the false belief test) uses to make predictions about what happens as a result of physical actions and events.

Figure 3. The basic physical reasoning module

As far as physical reasoning is concerned, only three result actions are of interest. First, people can see an object being put into a container. Second, people can see an object being taken out of a container. And third, if a person enters a room, they can see all the objects (but not contained, or hidden, objects) within that room. All three of these actions serve to keep a person's model of the physical

The Psychological Reasoning Module

At the core of the model is a representation of one person's ability to reason about other people's mental states. This basic psychological reasoning module, corresponding to Leslie's theory of mind mechanism, is shown in figure 4. There are three result rules. The first rule is associated with perceived events; this is where the essence of psychological reasoning happens. The other two rules are associated with believes events, and are used for modelling the answering of questions; for this reason they print out an answer.

Figure 4. The basic psychological reasoning module

The first result rule uses the ascribe rule to keep all the notional worlds up to date with the perceived event. The ascribe rule implements the decoupler model in figure 2. It works like this. First, the those procedure is used to get all of ?self's beliefs out of the situation; this corresponds to ?self's notional world. Next, the requote procedure is used to raise all the expressions in the notional world, to create a new situation, ?situation2. Then, the rule passes this new situation to the interpreter, through the manipulator. The manipulator is played by the in-stance procedure, which 'pretends' to be in the right context to handle the given event. The interpreter is called by the nested call to the result procedure. Finally, the nested call to result returns a new situation, ?situation3, which is passed to requote again to restore its expression status in ?new-self-notional-world. This is then used to replace the old notional world in the situation, and the modified situation is returned.

Perhaps this will be clearer with a more concrete example. Imagine that we ask (result ?response sally (perceived sally (put-in marble box) ?S, ?NewS), in a situation ?S. Because this is a perceived event, the first result rule will be applied, calling ascribe. The those and require procedures are used to go through the situation ?S, decoupling all the relations (believes sally ?X) and generating a new situation ?S'. Then the model applies the physical reasoning rules in this new situation ?S', to generate an updated phys ical situation ?R'. The second requote call goes through ?R' to restore its quotation status to normal, and returns ?R. Finally, ?R is used to replace all Sally's beliefs in ?S, and the final situation returned in ?NewS.

The Script for the False Belief Test

The final component of the model is a script for the false belief test. This is shown in figure 5. There are two parts to this script. First, there are a serious actions which corresponds more or less to the movements of the characters in Baron-Coh 1en et al.'s story, shown in figure 1. Second, there are a number of questions; these are the kind of questions that an experimenter might ask a subject after acting out the scenario. It is the answers to these questions which reveal whether or not, or how, the child passes the false belief test.

Figure 5. Actions and questions for the false belief test

So far, we have described a basic version of the theory of mind mechanism, a version which successfully models the passing of the false belief test. With this in place, we can now begin to compare this with some of the alternatives. In this paper, we will only look at three alternative theories of common-sense psychology, the simulation theory, the copy theory, and the situation theory.

Comparing models 1: the simulation theory

The first alternative theory to be compared against Leslie's is the 'simulation theory', which is typified by a 'role taking' or 'perspective taking' approach. Gordon illustrates this by saying that "Smith believes that Dewey won the election" should be read as "let's do a Smith simulation. Ready? Dewey won the election" (Gordon, 1986, original emphasis).

According to the simulation theory, young children are simply unable to take other people's points of view. This can be modelled by dividing the main perceive rule into two - one for self, and one for others. In young children, the perceive rule for self functions as before, but the perceive rule for others does nothing. This is shown in figure 6.

Figure 6. Rules for the simulation theory (first version)

When run, this seems to fail the false belief test correctly in that Alison doesn't give answers at all for either Sally or Anne; before Alison can pass the test she needs to acquire the ability to simulate, or take the role of, other people. This corresponds to the development of a simulation ability: "before internalising this system, the child would simply be unable to predict or explain human action [but] after internalising the system the child could deal indifferently with actions caused by true beliefs and actions caused by false beliefs" (Gordon, 1986). This is why the kind of failure in the simulation theory is interesting; Alison simply fails to give answers for either Sally or Anne, because she failed to take their roles properly.

The second stage in the model, then, is the complete simulation rule, which implements a role taking strategy through the in-self primitive. This primitive has the effect of temporarily pretending to be a different self, and then handling the whole event in that context instead. It is this replacement second rule that allows Alison to pass the false belief test. The replacement rule which models this strategy is shown in figure 7.

Figure 7. Replacement rule for the simulation theory

There are a number of important conclusions to be drawn from this idea. First, in the simulation theory the behaviour involved in ascribing mentality to oneself is different from that involved in ascribing mentality to others. This contrasts with the theory of mind mechanism described earlier, where there is no difference between first person and third person ascription. This is shown by the rules' sensitivity to the self relation, which shows that there is an egocentricity involved in the simulation theory. The second point to note is that, in practice, the behaviour of this system is the same as that of the basic psychological reasoning module shown in figure 4, because the replacement second rule combines with the first to behave just as if there was a single rule using the ascribe action, a rule identical to the first result rule in figure 4. This is in accord with Perner's (1994) suggestion that, in practice, the difference between a theory and a simulation may be at worst one of emphasis.

Comparing models 2: the copy theory

The second model I'll compare against Leslie's theory of mind mechanism is Chandler's 'copy theory'. Chandler and Boyes describe younger children as behaving "as though they believe objects to transmit, in a direct-line-of-sight fashion, faint copies of themselves which actively assault and impress themselves upon anyone who happens in the path of such 'objective' knowledge" (Chandler and Boyes, 1982). They argue that this is the precursor to a complete theory of mind such as Leslie's, and therefore I'll only show the version which fails the false belief test - a version which passed the test would be identical to the complete model in figure 4.

From the complete model of the theory of mind mechanism corresponding to an adult theory of mind, we can modify the psychological reasoning module slightly to represent a child with a copy theory of belief. The main point of the copy theory is, in effect, that instead of ascribing beliefs to others, a 'copy' of one's own beliefs is used instead. Instead of building different notional worlds for Sally and Anne, both use the same, a copy of Alison's.

According to the copy theory, children simply do not ascribe real beliefs to others. This is shown by the modified result rules in figure 8, which replace the result rule in figure 4 so that beliefs are only ascribed to oneself. Note that these result rules are identical to the first (before full theory of mind) version of the simulation theory in figure 6. This is to be expected - Chandler's theory is an account of how children escape the kind of egocentricity that marks a simulation theory. But this is not the whole story in the copy theory; when children are asked about other people's beliefs, they answer by drawing on their own. For this, we also need to change the result rules for the believes relation; these are the rules which model how the child answers the kind of questions used in the false belief test. These changes are also shown in figure 8. Both the question rules are changed from figure 3 by using the self relation to find and use one's own beliefs, rather than anybody else's, to answer the given question. Because of this dependence on the self relation, this model shows that the copy theory, like the simulation theory, has an implicit (if rather better hidden) egocentricity.

Figure 8. Rules for the copy theory

There are more complex variations on the copy theory; for instance, Wellman (1990) argues that younger children have a copy theory of belief, but not of desires. This is outside the scope of this model because desire psychology isn't yet part of the modelling environment - this is an area for future work. But while the copy theory works to the extent that, when run, it correctly fails the false belief test, the model is quite radically different from an adult theory of mind, and it does seem to require a developmental jump of significant magnitude. All the egocentricity of the rules in figure 8 must be lost, and the child needs to learn to extend notional worlds to other people. This matches all the empirical evidence that is against a copy theory; Perner (1991) has argued convincingly that experiments involving inference from parts to wholes show that the evidence is against children having a copy theory at any age. Even so, this is something which could, in principle, be investigated further quite easily with this modelling approach.

Comparing models 3: the situation theory

The third reference comparison I'll make against the theory of mind mechanism is Perner's (1991) 'situation theory'. Perner's theory is substantially different from those presented so far because he draws a hard distinction between real and non-real situations, or contexts. The notional world an agent has of itself has a unique status. This is not mirrored in the basic psychological reasoning module in figure 3.

Perner argues that the reason younger children don't pass the false belief test is because the child subject applies the verbal form of questions incorrectly to the situation corresponding to reality, not to the non-real situation which has been played out by the puppets. According to the situation theory, unlike the copy theory, young children do have notional worlds, but they are not so good at understanding that a real question can apply to a non-real situation. Perner uses this distinction to explain why children who fail the false belief test are still capable of sophisticated notional world reasoning, such as that required by Zaitchik's (1990) 'false photograph' test.

Figure 9 shows the rules for the first version of the situation theory model - the version which models a child who cannot yet pass the false belief test. Note that the main result rule has been split into two: one for self and one for others. Superficially, this might look like egocentricity again, but this time the only difference between them is in the status they assign to different notional worlds, knows for self, and believes for others. Initially, as shown by the modified answer rules in figure 10, children can only link verbal questions to the world for self beliefs - the notional world with the status knows. Other notional worlds can and do exist, though; it is just that they cannot be accessed through verbal questions.

Figure 9. Ascription rules for the situation theory

Figure 10. Answer rules for the situation theory

Perner claims that the principal change in children between the ages of two and a half and four is the acquisition of a representation theory, which allows them to recognise that questions can refer not to reality, but to worlds or situations that are represented - that is, worlds or theories with the believes predicate. This corresponds to the child's development from a situation theorist into a representation theorist, shown in the modified rules in figure 11.

Figure 11. Changes from the situation theory to the representation theory

Perner argues that this change isn't a radical overturning of the existing theory - the kind of radical change that makes the copy theory implausible. Instead, he suggests that the change that happens is a "theory extension" (Perner, 1991), a relatively minor change to the existing theory. This character if theory extension is important to any developmental account of common-sense psychology, because the empirical evidence is that common-sense psychology develops gradually, not in big jumps (Carey, 1985).

Discussion

These models highlight several of the most important features of the common-sense psychology that underlies the false belief test, and show that these features can be emphasised by models that represent the different and competing theories in this field. Of the models presented, the one that seems to work best in this modelling framework is Perner's 'situation theory' model. The principal reason for this is that the apparent distance between passing and failing the false belief test is much smaller. For both the simulation theory and for Chandler's 'copy theory' there must be a radical development to the ascription of notional worlds. Perner's model clearly shows the character of theory extension which he suggests should be expected of a theory which matches the empirical psychological data on the development of these theories (Carey, 1985).

The simulation theory is quite similar to the version of Leslie's theory of mind mechanism that we have used as a base model - but both it and Chandler's copy theory show an apparent egocentricity. In practice, as I've argued, there are good reasons for supposing that in any real common-sense psychology, both theory and simulation aspects will be required and, therefore, a simulation theory will actually be complementary to, rather than alternative to, the models presented here (Perner, 1994). However, most of the people who have argued for a simulation theory have argued for it as an alternative to something like Leslie's 'decoupler' theory of mind mechanism, and therefore don't give much thought to how a simulation theory and a theory of mind mechanism might be combined in practice. But there is a twist to the simulation model; although it shows an apparent egocentricity, it can actually be functionally identical to Leslie's 'decoupler' model. This further backs up the arguments that the distinction between a theory and a simulation is one of interpretation rather than a real difference in behaviour (Perner, 1994).

It is, of course, possible to pursue this strategy still further developing models of some of the other models of common-sense psychology. Unfortunately, for an accurate model many of these require more complex models of perceptual apparatus (e.g. Baron-Cohen's, 1995, shared attention mechanism), or more complete models of common-sense psychology (e.g. Wellman's, 1990, simple-desire psychology) than have yet been developed within this framework. Even so, as a first attempt at the problem, the technique does seem to back up the existing points and arguments remarkably well, and to clarify the distinctions between the models which have been developed so far. And apart from anything else, at least within this limited scenario, it seems to work!

The usefulness of the modelling approach as a tool for studying common-sense psychology is a topic which deserves fuller discussion than is possible here. Even so, we believe that these models show cognitive modelling can help in this area.

Figure 12. Trace output from the different models

References

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