The ability to generate explanations of perceived events and of one's own actions is of central importance to how we make sense of the world. When modeling explanation generation, one common tactic used by cognitive systems is to construct a linkage of previously created causee ect pairs. But where do such cause-e ect pairs come from in the rst place, and how can they be created automatically by cognitive systems? In this paper, we discuss the development of causal representations in children, by analyzing the literature surrounding a Piagetian experiment, and show how the conditions making cause-e ect pair creation possible can start to be modeled using a combination of feature-extraction techniques and the structured knowledge representation in the hybrid cognitive architecture CLARION. We create a task in PAGI World for learning causality, and make this task available for download.
Faced with some unfamiliar event, an agent1 will attempt to make sense of it
by constructing an explanation, even if the explanation that ultimately gets
accepted is not entirely coherent. Generating explanations is also important to
arti cial cognitive systems, particularly those that need to communicate with
other humans, for example, to present rationales for its own actions.
1 In this paper, `agent' will refer to any actor (arti cial or natural) capable of cognitive
thought, `cognitive system' will refer to any system that attempts to model cognitive
phenomena, and `cognitive architecture' will refer to full cognitive systems (such as
CLARION) satisfying the de nition of cognitive systems in [
Previous work (e.g., [
In this paper, we attempt to understand how the sort of cause-e ect pairs that are used in explanation generation can be created in an autonomous agent, in a psychologically plausible way. Section 2 reviews some literature on the emergence of causality in children, focusing on a classical Piagetian experiment we will call the oating task. We then describe a task, implemented in the simulation environment PAGI World, for testing abilities that underly the autonomous creation of cause-e ect pairs, along with an algorithm to perform this task, implemented in the cognitive architecture CLARION (Section 3). Section 4 discusses future work and concludes. 2
If we are to understand how cause-e ect pairs can be created automatically by a cognitive system, it would be very helpful to understand how the ability to reason causally develops in humans. We will start with a particularly relevant Piagetian experiment. 2.1
In one of Jean Piaget's early works, The Child's Conception of Physical Causality, Piaget introduced a task to elicit clues from children as to how they generate explanations. In what we will refer to here as the oating task, Piaget presents a series of objects to a child (e.g., a wooden boat, a pin, a pebble, and so on) and asks the child to predict whether or not the object (the candidate oating object) would oat. The child makes his prediction, explaining his or her reasoning when possible, and then the object is placed in the water. The child watches whether or not his prediction was correct, and then is asked to explain why the object did or did not oat.
Piaget found that the responses given by children seemed to be roughly categorizable into four stages. These stages are to be seen as continuously changing behavioral phenomena, meant to describe general trends noticed in subjects' explanations. In the rst stage, explanations are characterized by \animistic and moral reasons," e.g. a boat will oat \because they must always lie on the water," or a piece of glass will sink \because it's not allowed to put glass on the water" [17, p.136]. Piaget described stage-1 explanations as moral because they seemed to him to imply a sense of social obligation on the part of the inanimate objects, as opposed to adherence to some natural law.
In the second stage, starting at about 5 years of age, we see the appearance of dynamism, or the invocation of an abstract force in explanations. Children explain that boats oat because they're heavy, big, or because the \water is strong." However, they apply their explanations in inconsistent or contradictory ways. Compare this to the third stage (starting at about 5 or 6 years), where children instead tend to use the explanation that boats are light, rather than heavy. The di erence here, according to Piaget, is subtle but important: oating is no longer explained by an appeal to a simple property of the candidate oating object. Rather, the lake \produces an upward- owing current which sustains the lighter [ oating] body." In other words, oating is understood to be a property that emerges out of an interaction necessitated by both properties of the lake and properties of the candidate oating object.
Finally, in the fourth stage (starting at about age 9, but parts of which are seen as early as ages 6{8), we start to see reasoning taking into account multiple properties of an object simultaneously. By referring to the hollow-ness of the boat, for example, children relate the boat's volume to its weight. Furthermore, whereas in stage 3 properties of the candidate oating object like light-ness or heavy-ness are no longer regarded by the child to be absolute, internal properties. Instead, they are seen as properties that only hold relative to something else (in this case a corresponding volume of water). 2.2
Piaget's work is extremely voluminous, spanning almost 60 years, and careful
scholars have noted evolutions in Piaget's thought that at times puts the younger
Piaget against the older [
For example, the description of stages that we reiterated in Section 2.1 is
exemplary of the type of stage-based development that critics are quick to claim
is virtually useless, since the scienti c consensus is that \cognitive changes are
gradual and cumulative" [
That being said, it is not the goal of this paper to mount a full-scale defense of the Piagetian body of literature. Although it cannot be denied that some of Piaget's theories are incompatible with, and need to be re ned by, more recent work in developmental psychology, let it su ce to point out that the critics of Piaget are overzealous in indiscriminately discarding the entirety of his work, especially the almost 60 years of qualitative observations of children's behavior. Even if one were to ignore all of Piaget's proposed explanations for developmental mechanisms, his observations remain a fertile ground for cognitive modelers, as they provide at the very least a set of expected behaviors of children of di erent ages when faced with very speci c tasks. We described some of these behaviors in Section 2.1, and the current paper intends to model them. 3
The CLARION cognitive architecture [
The present paper can be considered another in that sequence. As
mentioned earlier, the previous model of explanation [
In CLARION's NACS, localist chunks corresponding to outputs can be placed
on the top level, and microfeatures corresponding to inputs and hidden nodes
can be placed on the bottom level. In Section 3.2, we set up the NACS in this
way, and apply a feature selection algorithm to the oating task. First, we turn
to a description of our computational simulation of the oating task.
PAGI World [
PAGI World is easy to learn and use, thanks to design choices that we hope will encourage researchers to make use of PAGI World. Because it can be run on almost any operating system and controlled using almost any programming language, PAGI World provides a platform for cognitive architectures of all types (particularly those which claim to be general-purpose) to compare their performance on the exact same tasks.
Piagetian experiments are somewhat di cult to model computationally for two important reasons: First, they often rely on objects that need to move in a physically realistic way, and it is nontrivial for researchers to program su ciently realistic simulations for every model they create; second, assessing agents in Piagetian experiments makes heavy use of explanatory dialogue, that is, the experimenter must be able to ask questions about the task and the subject must be able to answer them. Although this second di culty is one that is still beyond the reach of AI researchers, the rst di culty is handled quite nicely by PAGI World, since PAGI World has the ability to simulate water and create objects that oat or do not oat in it.
Thus, for all of the reasons discussed above, PAGI World is an ideal choice for hosting the Piagetian oating task. In our implementation, PAGI guy is positioned below a tank of water. An object with a randomly generated volume and weight is created, and appears in the middle of the tank, where it then either oats to the top, sinks to the bottom, or stays relatively motionless (Figure 1). After a few seconds, this object disappears and the process repeats. This allows PAGI guy to collect data about what it observes, so that we can later ask questions. In this section we demonstrate that a simple feature selection algorithm can be implemented in CLARION, by using a network that takes in low-level microfeatures and outputs a prediction as to whether an object will oat, sink, or remain stationary. Feature selection is an inherent property of backpropagation, in the sense that as backpropagation updates weights, certain nodes (which can correspond to features) will have higher weights connected to them than others.
CLARION is designed to work with low-level distributed networks that can be trained with backpropagation. We started by creating a network consisting of ve inputs, all microfeatures in the bottom level of CLARION's NACS: mass, volume, and three microfeatures for color (red, green, blue). Each input can be activated by a value between 1 and 255. Three outputs are created, each of them implemented as a chunk in the top level of the NACS: oat, sink, and stationary. We also create ve additional microfeatures h1; :::; h5, to serve as the hidden layer of the network.
Feature selection proceeds as follows. We collected sensory data from instances of the oating task in PAGI World, where an object of randomized color, mass, and weight appears in the middle of the tank and oats, sinks, or remains stationary. Each instance of an object appearing in the oating task is recorded and called an example. The input features are then individually isolated; that is, we only activate one feature at a time, allow the activation to propagate up to the hidden microfeatures (h1; :::; h5), and further up to the output chunks, and the output chunk with the highest activation is taken to be the `prediction' of this particular instance. We repeat this for n examples; weights are updated using backpropagation after every example. One successful run-through of all n examples is called an epoch. We then execute another epoch, runing through the same n examples again.
After e epochs, we evaluate the average error on the same n examples that the network was trained on. Note that this di ers greatly from standard machinelearning practice: generally a test data set is used that is non-overlapping with the training data set. However, we are not necessarily interested in getting the correct prediction; we are interested in modeling the reasoning of the child in a way that is psychologically plausible. It is psychologically plausible that a child would use a limited set of examples from his memory to validate hypotheses or features, and it is less plausible that a child would run through a set of thousands of training examples rst.
In any case, the evaluation of error on the n examples gives us an error rate for the feature that was isolated. We can then repeat this entire process with the other features, obtaining an error rate for each feature. The feature that had the lowest error rate is taken to be the winner of this iteration. (Originally, we also recorded the feature that had the second-lowest error rate, but because the results were so overwhelmingly in favor of mass and volume (a color-related feature was selected less than once per 1000 iterations), we only present the data here for the lowest error rate.) The feature-selection algorithm is laid out in a more convenient form in Algorithm 1.
The iterations were repeated 1000 times per experiment. We carried out this experiment six times, for three di erent values of n (n 2 f5; 10; 20g) and two di erent values of e (e 2 f2; 20g). Figure 2 shows the value of n on the x-axis, and the number of times (out of 1000 iterations) some particular feature was chosen as having the lowest error rate on the y-axis.
The values of n we chose for each experiment were intentionally very small. It seems implausible that children carrying out the oating experiment would actually be trained using hundreds of instances before they output their predictions. Therefore, we kept n very low in order to see what results emerged. As it turns out, the results match our intuitions: using our feature-selection algorithm settles extremely quickly on either the mass or volume features, and the only growth we see as n and e are increased is a slowly growing gap between the amount of times mass is chosen and the amount of times volume is chosen (a gap which was larger for 20 epochs than it was for 2 epochs).
The fact that even tiny values of n and e identify mass and volume as the most relevant features is consistent with the idea that, in line with Piaget's suspicions, the growth allowing the more complex explanations of stage-2 and later reasoning is a growth in the complexity of the representations themselves|that is, new nodes (corresponding to new concepts) might be created to represent abstract ideas such as density, water-current, and higher-level features constructed out of the lower-level ones used in our experiments. 4
This paper presents a task designed to closely model the Piagetian oating task,
and then shows how the behaviors of stage-1 children can be explained as feature
selection over simple representations in the CLARION cognitive architecture.
Future work will attempt to explain the sequence of behaviors shown by Piaget
in the oating task. For example, the ability to consider multiple properties at
once (which appears in stage-3 children) may be explained using a template
structure designed to group properties together. Likewise, the shift from
singleplace predicates to relations seen in stage 4 might be explained by a stabilization
of the property groupings and the emergence of two-place predicates (a similar
strategy is used in the DORA model [
Another series of tasks, highly relevant to the study of the development of
causality in children, may be interesting to examine using the model developed in
this paper. These are the series of \collision" tasks [
The backpropagation used in this paper for feature selection is one of many
ways CLARION can select features. In the future, as we tackle more complex
tasks, we can make use of, e.g., principal component analysis (PCA) or sparse
autoencoders [
Causality, of course, is an immensely complex and well-studied topic, and early steps such as those taken in this paper can only hope to scratch the surface. Future work will expand the philosophical, psychological, and historical perspectives on the notion of causality and how it relates to explanation generation.2 5
This work was funded by O ce of Naval Research (ONR) grant number N000141310342. 2 The oating task presented in this paper is available for download, along with PAGI World, at the website: We encourage researchers to test their particular cognitive architectures or systems on this and other tasks, and report their results. genre=article\&doi=10.1080/0951508042000286721\&magic=crossref| |D404A21C5BB053405B1A640AFFD44AE3 21. Sun, R., Peterson, T.: Autonomous Learning of Sequential Tasks: Experiments and Analyses. IEEE Transactions on Neural Networks 9(6), 1217{1234 (November 1998) 22. Sun, R., Zhang, X.: Accounting for Similarity-Based Reasoning within a Cognitive Architecture. In: Proceedings of the 26th Annual Conference of the Cognitive Science Society. Lawrence Erlbaum Associates (2004)