We will argue that the systems developed so far constitutes a solid foundation for a full-fledged cognitive system. We will point out a number of problems with the architecture and sketch how the perceptual system can be extended to handle more modalities and representations at various levels of generalization.

The expectancy network introduced in chapter 5 can be used as the starting point for the internal environment which is the corner-stone of planning and problem solving. When internal categories are formed for recurrent expectations, chunkin becomes possible, which in turn allows planning at different levels of specificity. All these extensions require that the creature uses multi-modal representations however, and this will be the first topic of this chapter.

Olfaction

This view of olfaction is easily reconciled with the model of optimal approach behavior presented in chapter 4. Such a behavior consists of the two phases orientation and approach. To use realistic smell signals, an animal would have to divide its behavior into successive phases of the olfactory based orientation toward the goal, and the approach behavior. The approach behavior could possibly be blind in this case, that is, it could consist of locomotion straight ahead. Alternatively, it could be controlled by dead-reckoning (see Gallistel 1990).

Another point to mention about real olfactory sensors is that they have varying degree of specificity (Shepherd 1991). Some sensors react to very few chemical substances while others fire for a much broader range of inputs. As we have already seen in relation to perceptual categorization in chapter 7, nodes with larger specificity should have a larger influence on later processing stages than nodes with lesser specificity. In section 9.3 below, this will be formulated as a general principle.

The Somatic Senses

The collision sensor was included to handle cases where the whiskers do not react, but this is not a particularly good solution. Since the collision sensor does not give any directional information, the best the creature can do when it reacts is to turn at random. A much better system would use many more whiskers or other tactile sensors everywhere on the body. Since the spatial pattern of activation would inform the creature of where an obstacle is and how large it is, a much more efficient avoidance behavior could be constructed. In some animals, such as the snake, it is even possible to let the avoidance behavior be calculated locally in the spinal cord using lateral inhibition (Hirose 1993).

The representation used in the tactile sensors can be considered as a representation by place (Martin 1991). This means that a node has the same meaning each time it fires. The signal from the whisker on the left means that there is something touching on the left. The intensity of the signal directly codes for the intensity of the touch and the signal always has the same meaning. There is no message coded in the signal other than intensity, which means that no decoding is necessary.

A second property of the somatic representation is that it is spatiotopic, that is, arranged according to the spatial location of the sensors. Sensors that are close to each other on the body are represented by nodes that are physically close in the brain (Kandel and Jessel 1991). We used this property in the construction of many of the reactive behaviors described in chapter 4. Again, the resolution is very low since the creature can only distinguish between left and right. A better spatial resolution would make many tasks much simpler. This property will be considered again below in relation to orienting behavior and multisensory mappings.

In most animals, the spatiotopic representation does not directly tell the animal where in space an object is located since this also depends on how the different parts of its body are positioned at a certain time. The representation is in local body coordinates and it appears sensible that this representation should somehow be converted into a global egocentric coordinate system in many cases.

Vision

The first is that it works at almost any range. It can be used to recognize an obstacle long before the creature comes into contact with it. The same is true about the identification of goals, landmarks and other cues. The inclusion of vision makes all these processes simpler and more effective once the visual image has been analysed. The analysis of the visual image itself is however a far from trivial problem, and this is why this modality has not been considered above.

The second property of vision which is of importance in this context is that it is spatiotopic in a way similar to the somatic representations. For vision, however, the representation is arranged according to the location on the retina and not the body. This type of representation is usually called retinotopic (Martin 1991). Like the somatic senses, the coordinate system used in the visual representation is a function of the orientation of various parts of the body, most notably the position of the head and the eyes. To calculate the location of a visual cue in egocentric, or even allocentric, coordinates, some form of coordinate transformation is necessary. Andersen and Zipser (1990) have proposed a computational model of how this process may be implemented in the posterior parietal cortex.

It appears that the mammalian brain solves this problem by dissociating the calculation of spatial location from the identification of a visual cue (Mishkin, Ungerleider and Macko 1983). By centering the cue on the fovea, the brain does not generally require that the representation is translation invariant. As a consequence, the calculation of spatial location can be made without reference to the actual cue. Only the vergence angles between the eyes and the position of the head need to enter the calculation. This makes it much simpler to use a spatiotopic representation for the location of a cue.

Orientation movements can, thus, be made with respect to the representation of the location of a cue without involving the representation of the cue in itself. That is, orientation movements will automatically be generalized to all visual cues. It seems that some similar mechanism must operate for the somato-sensory modalities, but we are not aware of any empirical evidence that either supports or contradicts this idea.

The third property of the visual system which fits nicely with the model presented above is its organization as parallel visual control systems (Goldberg, Eggers and Gouras 1991). The visual system is equipped with behavior modules, possibly involving the whole body, which perform some specific visual behavior such as a saccade movement, smooth pursuit or a visual orienting reaction. In smooth pursuit, the eyes track a moving object to keep it fixed on the fovea. This is, thus, a form of approach movement as it was defined in chapter 4. The visual orienting reaction is, of course, just another kind of orienting reaction that also fits well within the framework presented in chapter 4. Like the behavior modules presented above, the visual behaviors can be used by different engagement modules for varying purposes.

Multi-Modal Interaction

The important property of multi-modal representations is that information from one modality can be transformed into another. By touching an object, we can imagine how it looks, and by looking at it, we can imagine how it would feel to touch, and even what sound it would make when we touch it or if we would drop it on the floor. How this sort of transformation is performed is not very well known except in the case of orienting movements, so we will concentrate on this type of multi-modal interaction.

In the case of the orienting reaction, the different modalities interact through the use of a common spatiotopic code (Stein and Meredith 1993). Since it is only the location of an object that is important for an orienting movement, all modalities can easily be mapped onto this common spatial code (see Balkenius 1995). It does not matter whether an input comes from the visual, auditory or somato-sensory system since each of these modalities contains information about the location of a stimulus, and it is only the location that needs to be represented in the orienting system.

The main problem solved by the orienting system is to choose which stimulus to attend to when many are simultaneously present (Johnston and Dark 1986). This could be done by competition using the choice mechanisms presented in chapter 3. In this choice, the intensity of a stimulus together with a count of the number of modalities involved determine which stimulus will be chosen. The choice can potentially be biased by expectations about the current situations generated by an expectancy network as described in chapters 5 and 8. One role of the expectancy network is, thus, to habituate the orienting reaction to stimuli that have already been attended to (see also section 7.4).

Submodalities and Perceptual Dimensions

Another type of submodality that is required in vision is the representation of stimuli at different scales (Witkin 1983). This kind of submodality also exists in the olfactory system (Shepherd 1991). The result of these submodalities is that every stimulus will be represented at different levels of specificity even before any categorization takes place. A node with high specificity will react to very few stimuli while nodes with lower specificity will react to a larger set of stimuli. It is possible to consider each submodality as a dimension along which every stimulus is categorized. We will call the representation in all submodalities taken together the sensory schema. This is shown in figure 9.2.1.

Figure 9.2.1 The distributed sensory schema consists of the collection of representations in all modalities. Each modality is divided into a number of dimensions or submodalities that may represents the stimulus properties in different scale-spaces or levels of specificity.

The sensory schema is a collection of signals that are all active when the sensors of the creature are directed toward a specific stimulus. To discuss such schema we need to distinguish between stimuli external to the creature, and the sensory schema they activate, which is internal. Sometimes, these two aspects of a stimulus are referred to as the distal and proximal stimulus respectively (Gray 1975).

The conclusion that can be drawn from this section is that it is necessary to consider all stimuli as configurations of the representations in all the individual modalities. It is, thus, too simplified to consider the signals entering the cognitive system as representations of individual stimuli as we have done in the previous chapters. The representation of a conditioned stimulus, CSi, must be replaced with the sensory schema ai it activates in all the sensory modalities. This will make the mechanisms for categorization and association much richer as well as allowing for generalization (see Balkenius 1994c).

In chapter 5, we introduced the problem of negative patterning (see figure 5.5.3). In this situation, the conjunction of two sensory cues, say, S0 and S1, should produce different predictions of the environment than each of the cues taken together. This requires that a configurational category is created for the combined stimulus, S0€S1. It is also necessary that the expectations from the configurational category can compensate for those from the individual stimuli. As we saw in chapter 7, expectancy learning could automatically generate the required associations.

Making the transition from stimulus cues to sensory schemata requires that all stimuli are handled as configurational. Given a sensory system with two modalities A and B, a single stimulus, S, will activate one or more representations in each modality. Let the representation in modality A be called a, and the representation in modality B be called b. The representation of S will then be the conjunction of the representations in the two modalities, that is, a€b. This representation must obviously be treated in the same way as the configurational stimuli were treated above. The initial predictions made from the stimulus representation will handle each modality independently until expectations are not met. In this case, a new category will be created which will represent the sensory schema a€b (see the simulation in figure 7.2.5). This second-order category will be denoted by ca€b.

Let us consider a concrete example where stimulus S0 consists of a blue circle. We will assume that this stimulus is analyzed in the two visual submodalities for shape and color. The signals from the shape system will represent that the stimulus is round and the signals from the color system will represent the color blue. Let us further assume that the presentations of blue shapes or round shapes have always been followed by a high pitch tone, called S1.

When presenting a round shape, the shape representation will cause the expectancy system to predict that the high pitch tone, S1, will follow. This prediction will also be made independently from the color representation, when a blue shape is presented. If the expectation is not fulfilled, say, if the presentation of the blue circle is followed instead by a low tone, called S2, a mismatch occurs. The predictions made from the sensory schema BLUE€ROUND was incorrect. This will cause a new category to be created that lets a specific node react every time a round blue shape is presented (see section 7.2). This category, that we may call cBLUE€ROUND, will subsequently predict both the non-occurence of the high pitch tone, S1, and the presentation of the low pitch tone, S2, as shown in figure 9.3.1.

Figure 9.3.1 Category formation as the result of negative patterning between different submodalities. The presentation of a blue circle predicts a low pitch tone, S2, although all other shapes that are either round or blue predict a high pitch tone, S1. This will cause a second-order category to be created that represents this specific exception.

Note that the second-order category is more specific than the nodes coding for the individual submodalities. The level of specificity will increase with the number of submodalities that must occur together for the category to match. With more specific categories, the predictions made can also be more specific. This is, thus, an example of a learned scale hierarchy. Also remember that we are still talking about neural activity patterns although the example is beginning to look like an attribute-value structure.

This is an example of category formation by specialization (Charniak and McDermott 1985). Another possible type of category formation is categorization by generalization. In this case, a set of specific categories learn the same expectations. Two stimuli, S0 and S1, activate the perceptual schemata a and b respectively. Assume that each of these schemata is independently associated with a category node, g, which already exists in the system. Since both a and b can activate g on its own, it seems appropriate to consider this category as a generalization of a and b.

Figure 9.3.2 Categorization by generalization is handled by an associative process. No new category need to be created in this case.

A fairly simple extension of the mechanisms we have described earlier in this book would, thus, handle categorization based on both specialization and generalization. New categories are only created during specialization which is natural since generalization assimilates the new instance to a category that already exists.

Temporal Expectations

(Equation 9.4.4)

Using this type of representation, predictions over longer periods of time could only be made using avalanches started by a sensory cue or by secondary conditioning (see chapter 5). In a more general system, predictions must be made over arbitrary periods of time. It is not sufficient to represent that the presentation of Si at time t will predict the presentation of Sj at time t+1. A more useful expectation would represent, not only that Sj will follow Si, but also when. Representations of this type would look the following way,

(Equation 9.4.5)

Here, Dij is a parameter that is specific for each pair of stimuli. A further extension would replace the single parameter Dij with a function of time that assigns a probability to the statement Si(t)ÆSj(t+d) for each value on d. This function can be represented either directly, or as a set of parameters.

One way to parametrize the representation is to represent the prediction as an interval [Dij-xij, Dij+xij] around a mean value represented by Dij. This requires, of course, that S0 has preceded S1 at least once. If it has not, the values of Dij and xij have no meaning, and this suggests that we should also represent the certainty of both Dij and xij. This certainty, cij, should be zero initially, and increase as the estimates of Dij and xij improve. This is not sufficient, however.

To know whether Si really predicts Sj, we need to weigh it against the probability that Sj is present without being preceded by Si. If, for instance, Sj is always present, Si has obviously no predictive power and there should be no association between Si and Sj. A similar effect occurs in latent inhibition experiments where the presentation of a CS on its own retards the subsequent development of an association with an US (Mackintosh 1983). In this case, the pre-exposure to the CS makes the probability that the US will follow smaller than if the CS had never been presented before. This suggests that latent inhibition can be explained with a mechanism that estimates the probability of occurance of each stimulus and compares it with the probability of each CS-US pair (Gallistel 1990).

Balkenius (1992) has presented a neural network architecture that is able to extract the amount of information one node transmits about the state of another. Although it was not recognized in that paper, the proposed network model solves the problem of latent inhibition in the case of simultaneous conditioning. However, the model is not easily extended to temporal predictions, and this is what is required for a useful internal environment.

An extended creature will, thus, need to form predictions that are based on transferred information and not on temporal contiguity. These predictions must code both when a stimulus is likely to follow another and with what certainty this prediction is made. As in the case of categorization, these predictions must also be made for distributed schemata and not for local stimulus representations, since it is necessary to represent predictions from one submodality to another.

Working Memory

This memory can be seen as a generalization of the working memory for novel foods introduced in chapter 5. In that simple working memory, only the sickness sensor could recall the stored memory. For a more general working memory, any sufficiently specific subschema from any modality should recall the entire sensory schema with which it was stored. For example, the activation of a place representation will read out the expectations of the stimulus that will be perceived at that location. In the same way, the activation of some other sensory property will read out the location at which that property can be found (figure 9.4.1).

Figure 9.4.1 The expectancy network equipped with a temporary working memory for binding of sensory representations. The general expectations in the expectancy network are enhanced with specific predictions in the working memory.

Content addressable memories have been much studied within the neural network literature and there are many models to choose from (see, for example, Hinton and Andersson 1981, Kohonen 1984, and section 3.3). In many respects, the working memory has many of the properties of the expectancy network presented in chapter 5. One may conceive of the working memories as a collection of expectations formed by simultaneous conditioning. The problems associated with negative patterning will also show up in the working memory, which means that it too will require a categorization mechanism. These problems are so severe here that it would be possible to form categories of all new schemata even without checking whether it is required or not (Rolls 1990). Since it is required that working memories are very specific, high-order categories will always be needed.

In fact, if the working memory, categorizes each novel stimuli into a unique category in this way, it could also potentially generate a learning signal that could start the creation of higher-order categories in much the same way as the recruitment mechanism in chapter 7.

There are also a number of differences compared to the expectancy network. Since the working memory stores individual stimuli rather that general contingencies, it is appropriate for this type of conditioning to be based on temporal contiguity rather than transferred information. There is also no need for an extinction mechanism. Like in the case of smell aversion, the memories could fade away gradually until they are extinguished on their own accord.

The inclusion of a working memory may potentially solve the so called binding problem (Hinton, McClelland and Rumelhart 1986). It can be stated as follows. If sensory processing is segregated into finer and finer submodalities represented at different locations, how does the brain know which sensory properties belong to the same stimulus? The solution we suggest is to bind sensory features together, by associating them with the spatial location at which the stimulus occurs, and store the combined schema in the working memory. In support of this idea, it has been shown that location is a more reliable cue for recall from memory than, for example, color or shape (Johnston and Dark 1986, see also Mishkin, Ungerleider and Macko 1983).

The expectations stored in this working memory must be treated as expectations both of the present and the future. If stimulus S is present at location L when the memory is stored, the working memory must enforce the expectation that this is still the case as long as the memory lasts. When this type of association has been generalized within the expectancy network, it could form the basis for the idea of object permanence (Flavell 1985). An object is a perceptual schema which has the property that it predicts itself to be present in the future. This corresponds to the expectation that a collection of some certain stimulus properties will be present at some external location in the future.

In the radial maze discussed in section 2.8, something like the kind of working memory sketched here would be required. Simply including a working memory does not solve the problem, however. There are still a number of questions that must be answered. For example, it is not clear how the animal knows how to use its memory in the way required by the task. Nor is it apparent how it recognizes what task it is supposed to perform in the first place.

Consequences of Actions

The recurrent expectations used in chapter 8 to select the shortest path to a goal can be seen as a slightly simpler version of this system. Since we assumed that the creature would only use an approach strategy to reach the goal, it was possible to ignore the consequences of actions. The only consequence of importance to an approach behavior is that a stimulus becomes closer than it was before. It was, thus, possible to 'plan' using only sensory information. With the introduction of the type of expectations described here, it will be possible to use all types of behaviors in look-ahead choice. The recurrent expectations described in chapter 8 were of the S-S' kind. With the addition of the efference copies, these associations are extended to the more general S-R-S' type (see sections 2.7 and 2.15).

Note that the efference copies used to predict the consequences of actions are very similar to the recurrent expectations discussed in chapter 8. It may even be possible that the same pathway can handle both types of signals. Recall that the same expectancy network can be used both to produce conditioned behavior and for sensory expectations. By introducing scale-hierarchies also in time (Albus 1991), planning at different levels of specificity is also made possible (see also Newell 1990).

Figure 9.4.2 Predicting consequences of actions by associating efference copies of motor commands with subsequent sensory schemata.

Chunking

Figure 9.4.3 Chunking by recurrent recategorization

Once the higher-order categories have been formed, they will enter into simple associations within the expectancy network as if they were of second order. Thus, it is not necessary for a sensory schema to be propagated through the recurrent connection n times to activate an already established nth-order category. One iteration will always suffice (figure 9.4.3).

We suggest that a recurrent recategorization of this type may lie behind the process that is commonly referred to as chunking (Newell 1990). If the expectancy network can construct temporal prediction of the kind discussed above, temporal as well as spatial chunking can be handled by the same mechanism. The idea behind chunking is, thus, very simple. Getting the dynamics right is however a far from trivial task.

An alternative to this architecture is to use a fixed number of categorization modules connected in series. This is the approach taken, for example, in the multilayer perceptron (Rumelhart, Hinton and Williams 1986). Since the order of categorization is fixed, the dynamics is much simpler than for recurrent recategorization. Its abilities are more restricted, however.

When a creature has the ability to form accurate temporal predictions both from its sensory inputs and from the actions it performs, it will have the basis for an internal environment. It can potentially shut off its sensors and effectors and behave in this internal environment instead of externally. With the introduction of a working memory, the creature will be able to change this environment in much the same way as it can change the external environment. Using the chunking ability, the internal environment can also be handled at different levels of specificity. In the next section, we will describe how the internal environment can be used for planning and problem solving.

Figure 9.5.1 A functional hierarchy.

Figure 9.5.1 shows an agent architecture proposed by Balkenius (1993, see also Gärdenfors and Balkenius 1993). In this architecture, the three functional levels described in section 3.2 are thought of as distinct subsystems that are coordinated by a central motivational system. The lowest layer controls the fundamental reactive behavior. This system equips the agent with a set of elementary abilities that are used as a basis for more complex behaviors. An intermediate adaptation layer controls behavior based on expected rewards. This level is based on reinforcement learning which generates internal incentives that can override the external signals to the reactive level. The top layer learns about the consequences of various actions in the environment. This knowledge can later be used as the internal environment where actions can be tested before they are performed externally.

The upper two layers are similar to the DYNA architecture proposed by Sutton (1992, see also Peng and Williams 1993) and can be used for planning and problem solving. In such processes, the top layer plays a role similar to the world model in traditional AI systems. However, this model is never essential for the behavior of the agent. If this layer is removed, the agent can still learn any behavior in the world given sufficient training. The important aspect of this level is that its representations of the world are detached (Gärdenfors 1995), that is, they are not confined to here and now, but can be used independently of the current perceptual situation.

By depending on the already existing systems, a planning ability is the result of adding a single functional layer (see figure 3.2.8). We have an example of a true system property that cannot be localized in one specific module of the agent. With the model system, the agent can be engaged in planning, but this module does not plan in itself. The result of the planning process is to adapt the reactive system to the internal environment, rather than to produce a fixed program to execute (compare Lyons, Hendriks and Mehta 1991).

The architecture presented here is in many respects similar to the one presented by Gulz (1991). Planning is considered as internal simulation of external behavior. Instead of using the external world to generate new sensory information, actions are performed in an internal model. The different actions are simulated in this model, and a new sensory input is generated internally. In this view, the internal model is not independent of the agent itself. It is a module which can generate the sensory information which would be the result if the agent had performed the corresponding action externally.

The internal model is used very differently compared to the models used within the symbol processing paradigm. The model is not a description of the world. As far as our agent is concerned, the internal model is a world. However, to be successful, this internal world must be parallel to the external world. Planning can be seen as behavior in this internal world instead of the external world (Balkenius 1993, see also Gärdenfors 1992, and Gärdenfors and Balkenius 1993). The only difference between a search in the internal world and actions performed externallyd is that all actions can be undone as well as taking much less time to perform. The plan constructed from behavior in the internal world is in no way different from the paths learned from externally tested action sequences. The same mechanisms are used, and the plan is represented and executed in the same way as a behavior that has been practiced in the external world.

The plans constructed using the internal environment are also very different from classical plans. A useful view of the type of plans constructed by this architecture are as resources and not as programs (Payton 1990). Horswill and Stein (1995) have suggested that robot control systems can be classified according to their commitment to generated plans. In this scheme, classical AI systems have a high degree of commitment. When the plan has been constructed, it is executed from the first step to the last. On the other hand, the plans constructed by the architecture described here have a minimal degree of commitment, since plans are used reactively. It may even be questionable to call the changes to the reinforcement system plans since they are not explicitly represented as a such.

When the abilities suggested in this chapter have been included in the architecture, the dynamics generated internally will parallel that between the creature and its environment (compare section 4.2). It is interesting to note that the dynamical concepts introduced in chapter 4 can be used to describe both the dynamics between the organism and the environment, and the internal operation of a neural system. For example, the planning of an approach behavior would correspond to the convergence to an attractor within the artificial neural network controlling the creature. If such a mapping can be done in general, it would allow a dynamical view of cognition on all process levels. Goal-directed thought could, thus, be seen as internally performed goal-directed behavior.

In the first case, planning is used to speed up learning of S-R associations by silently rehearsing stored copies of previous experiences. In this type of planning, no generalization is required in the internal environment. This is essentially the type of learning used within the DYNA framework (Sutton 1992). Stored experiences are selected at random and used to train a reinforcement leaning module. Since planning of this type is not at all goal-directed, there is no guarantee that the trained experiences will be relevant to the creature.

In the second type of planning, some form of goal-direction is involved. Such planning requires that the internal environment can be used for generalization. If the behavior that leads to the goal is already known planning is unnecessary. If it is unknown, planning is impossible. Planning, thus, requires a situation that is somewhere in between. That is, a new situation to which old knowledge can be applied.

Gulz (1991) distinguishes between two other types of planning. The first type is called immediate planning and is produced when the approach of a specific goal is obstructed. The planning that it generates is directed toward this specific goal. For instance, an unexpected encounter with an obstacle that is hard to overcome could generate immediate planning behavior.

The second type of planning is called anticipatory. Such planning does not relate to the current engagement of the creature. Instead, it is caused by simulated needs. The creature anticipates that it will become hungry tomorrow and plans its day accordingly.

There is an obvious similarity between the situation in which the orienting reaction is executed and the situations in which immediate planning could be activated. In both cases, something unexpected happens in the environment and in both cases ongoing behavior must be inhibited. This suggests that this type of planning is closely connected to emotional states. The prototypical emotion activating immediate planning is, thus, frustration caused by omission of an expected reward or by an unexpected obstacle.

Anticipatory planning, on the other hand, is not caused by any external event. It must, thus, compete with other engagements through the motivational system. This is the role of the anticipatory drive introduced in chapter 6.

There is, thus, a clear connection between emotion and immediate planning and motivation and anticipatory planning. Depending on the type of emotion or on the type of simulated motivation, we can identify different modes of planning. Different types of planning are caused by immediate punishment or frustration and by their anticipated counterparts. On the positive side, these modes are less clear, allthough one may possibly identify daydreaming with planning motivated by anticipated reward.

First, it is necessary that the creature uses distributed representations at multiple scales and of many modalities to be able to generalize from one situation to another. This problem is addressed by adding more sensors and more sensory processing to the creature.

Second, the categorization mechanism described in chapter 5 must be extended to handle these distributed representations. The main problem here is to devise a matching criterion that generates new categories at the right times. With an incorrect matching rule, too many categories will be formed. While the mechanism described in chapter 7 can learn any expectancy, this is often done at the cost of a large number of unnecessary category nodes. For a more economical system, a more advanced mechanism for category creation is needed.

Third, the internal environment puts some non-trivial requirements on to the expectancy network. It must somehow represent both which stimulus will follow another, as well as when, and with what certainty. The need for a representation of the consequences of actions and for hierarchical chunking makes this problem even more complex. This is an area for future research.

None of the above problems appear impossible to solve, however, and in restricted cases, they all have simple solutions. Given that these problems are solved more generally, we have shown that some complex cognitive abilities will become possible. It should be clear that these systems are natural extensions of the mechanisms we have already developed.