Modelling Common-Sense Psychology and the False Belief Test
Knowledge Media Institute and Department of Psychology
Walton Hall, Milton Keynes, MK7 6AA, UK
+44 1908 653169
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.
Common-sense psychology, theory of mind, false belief test, cognitive
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,
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
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
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
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
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. 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)
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
Figure 11. Changes from the situation theory to the representation
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).
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
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
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