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Two problems for the knowledge level in cognitive architectures

Before delving into our case study, it is necessary to introduce the current context of the problem that we are going to analyze. In a recent article I co-authored with Christian Lebiere (one of the main ACT-R developers) and Alessandro Oltramari, entitled “The knowledge level in cognitive architectures: Current limitations and possible developments” (Lieto, Lebiere, and Oltramari, 2018), we pointed out how Cognitive Architectures, in order to play an epistemological and explanatory role, in regards to their knowledge processing capabilities, had to face two main issues: the limited size and the homogeneous typology of the encoded and processed knowledge. These two problems emerged from a knowledge level analysis (d la Newell) of the capabilities of such systems. In particular, we pointed out how - concerning the size problem - the

knowledge embedded and processed in such architectures is usually very limited, ad-hoc built, domain specific, or based on the specific tasks they have to deal with. Thus, every evaluation of the artificial systems relying upon them, is necessarily task-specific and do not involve not even the minimum part of the full spectrum of processes involved in the human cognition when the “knowledge” comes to play a role. As a consequence, the structural mechanisms that the CAs implement concerning knowledge processing tasks (e.g., that ones of retrieval, learning, reasoning, etc.) can be only loosely evaluated, and compared w.r.t. that ones used by humans in similar knowledge-intensive situations.

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In other words, we posited that, from an epistemological perspective, the explanatory power of their computational simulation was strongly affected. In reference to the problem of the “homogeneous typology” of the encoded knowledge, on the other hand, we pointed out that the current versions of the cognitive architectures did not consider some important theoretical and experimental results coming from Cognitive Science concerning the nature of the different types of conceptual representations and the different types of reasoning and categorization procedures associated with such representations. In Cognitive Science, indeed, different theories have been developed about how humans organize, reason, and retrieve conceptual information. The oldest one, known as “classical” or Aristotelian theory, states that concepts - the building blocks of our knowledge infrastructure - can be simply represented in terms of sets of necessary and sufficient conditions (and this is completely true, for instance, in mathematical concepts: e.g., an EQUILATERAL TRIANGLE can be classically defined as a regular polygon with three corners and three sides). In the mid-1970s, however, the previously mentioned experimental results from Rosch demonstrated its inadequacy for ordinary - or commonsense - concepts, which cannot be described in terms of necessary and sufficient traits. In particular, Rosch’s results indicated that conceptual knowledge is organized in our minds in terms of prototypes. Since then, different theories of concepts have been proposed to explain different representational and reasoning aspects concerning the typicality or, in other terms, the commonsense effect. The most important one, in addition to the prototype theory, is the so-called “exemplar theory”.[1]

Prototype and exemplar approaches, however, present significant differences. Prototype theory posits that knowledge about categories is stored in terms of some representation of the best instances in the category. For example, the concept “BIRD” should coincide with a representation of a prototypical bird (e.g., a robin). In the simpler versions of this approach, prototypes are represented as (possibly weighted) lists of features. This kind of representational assumption is strictly coupled with a specific categorization procedure known as prototypical reasoning. An example of such a reasoning strategy is the following - let us assume that we have to categorize a stimulus with the following features: “it has fur, it woofs, and it wags its tail”. The result of a prototype-based categorization would be “dog”, since these cues are associated with the prototype of dog. According to the exemplar view, on the other hand, a given category is mentally represented as a set of specific exemplars explicitly stored in memory: the mental representation of the concept “BIRD” is the set of the representations of (some of) the birds we have encountered during our lifetime. Also, the exemplars-based representational assumption is coupled with a specific categorization procedure. In particular, this theory posits that when we have to categorize a given stimulus, the similarity comparison is done not with “prototypes” but with the exemplars-representations that are available in our memory. For example: if an exemplar corresponding to the stimulus being categorized is available in our long-term memory, it is acknowledged that humans classify the stimulus by evaluating its similarity with regard to the exemplar, rather than with regard to the prototype associated with the underlying concepts. For example, a penguin is rather dissimilar from the prototype of a bird. However, if we already know an exemplar of penguin, and if we know that it is an instance of bird, it is easier for us to classify a new penguin as a bird with regard to a categorization process based on the similarity to the prototype of that category. This type of commonsense categorization is known in literature as “exemplars-based categorization” (and in this case the exemplar is favoured with regard to the prototype because of the phenomenon known as old-item effect).

As these examples show, prototype and exemplars-based theories make different assumptions about both the type of representations involved in categorization and the corresponding reasoning procedures leading to a given output. In particular, prototype models intend to capture only some central, and cognitively founded, aspects of the features of a concept, while the exemplars models represent in toto the particular knowledge of a certain entity. Concerning the categorization process, on the other hand, the decision of whether a target belongs to some category depends, for both prototype-based and exemplars-based cases, on the result of a similarity comparison computed between prototypical or exemplars representations and target representations. Despite this common mechanism, however, in the prototype view the computation of similarity is usually assumed to be linear (a property that is shared by the target and the prototype increases the similarity between both, independently of whether other properties are shared by them) while, according to the exemplar view, it is assumed to be non-linear (a property that is shared by the target and the exemplar is considered relevant only if there are also other shared properties between the two representations). An additional difference among the two approaches concerns the different assumptions about how such representations are stored in memory. According to prototype theorists, we store in our long-term memory only some parameters that characterize the categories we represent. According to exemplar theorists, we form memories of many encountered category members and we use, by default, these memories in cognitive tasks. This difference impacts the memory costs as well. In fact, prototypes are more synthetic representations, and occupy less memory space, compared to exemplars. On the other hand, the process of creation of a prototype requires more time and cognitive effort, while the mere storage of knowledge about exemplars is more parsimonious and less consuming because no abstraction is needed. Table 4.2 shows a synthetic comparison of these two representational and reasoning models. Interestingly enough, although these approaches have been largely considered competing ones, several results suggest that human subjects may use, on different occasions, different representations to categorize concepts. In particular, the first psychological study supporting the idea of multi-process theory was done by Malt (1989). Her study aimed at investigating whether people categorize and learn categories according to exemplar approaches or prototype-based models and she used behavioural measures such as categorization probability and reaction time. Her results demonstrate that not all subjects retrieve exemplars to categorize. Some use exemplars, a few rely on prototypes, and others appeal to both exemplars and prototypes. A protocol analysis of subjects’ description of their categorization strategy confirms this interpretation. Malt writes (1989: 546-547):

Three said they used only general features if the category in classifying the new exemplars. Nine said they used only similarity to old exemplars, and eight said that they used a mixture of category features and similarity to old exemplars. If reports accurately reflect the strategies used, then the data are composed of responses involving several different decision processes.

TABLE 4.2 Prototype models vs exemplar models

Prototype models

Exemplar models

Memory storage

The prototype of each category is a sort of “average” description of all the exemplars experienced.

Many exemplars encountered are stored along with the category to which it belongs.

Memory costs

Not expensive. Prototypes are “synthetic” representations.

Expensive: the information concerning whole particular exemplars is stored.

Cognitive efforts

It is expensive to build the

prototype. More time is requested.

It is parsimonious to use the exemplars knowledge.

Decision rule for categorization

Linear.

Not linear.

Inferential

prediction

Not so good because it does not keep in memory all the traits.

Better in support predictions based on partial information.

Categorization

effects

Similarity degree based on typicality.

Old items advantage effect.

This finding suggests that people can use either prototypes or exemplars in categorization tasks, which is consistent with other well-known studies such as those by Smith et al. (1997) and Smith and Minda (1998), the latter of which had experiments carried out with artificial stimuli. Smith et al. (1997), in fact, found that the performances of half the subjects of their experiments were best fit by a prototype model, while the performances of the other half were best fit by an exemplar model. This suggests that people can learn at least two different types of concepts - prototypes and exemplars - and that they can follow at least two strategies of categorization. Smith and Minda (1998) replicated these findings. Additionally, they found that during the learning phase, subjects’ performances were best fitted by different models, suggesting that, when they learn to categorize artificial stimuli, subjects can switch from a strategy involving prototypes to a strategy involving exemplars. They also found that the learning path is influenced by the properties of the categories that subjects are presented with. For example, they show that categories with few, dissimilar members promoted the use of exemplar-based categorization strategies. Thus, psychological evidence suggests that we have at least two different mechanisms for categorizing. These mechanisms rely on different types of knowledge: prototypes and exemplars.

Such experimental evidence has led to the development of the so-called “heterogeneous hypothesis” about the nature of concepts. It hypothesizes that different types of conceptual representations exist (and may co-exist): prototypes, exemplars, classical representations, and so on (Lieto, 2014). All such representations, in this view, constitute different bodies of knowledge and contain different types of information associated with the same conceptual entity. Furthermore, each body of conceptual knowledge is distinguished by specific processes in which such representations are involved (e.g., in cognitive tasks like recognition, learning, categorization, etc.). In particular, prototypes and exemplars representations are associated with the possibility of dealing with typicality effects and non-monotonic strategies of reasoning and categorization, while classical representations (i.e., those based on necessary and/or sufficient conditions) are associated with a standard deductive mechanism of reasoning. Our human categorization capacity, therefore, is a direct consequence of having a heterogeneous set of representations for the same concepts and heterogeneous and integrated categorization strategies relying on prototypes, exemplars, and classical rule-based categorization (the latter one concerning the classical representations relying on necessary and sufficient conditions).

In the representational level of cognitive architectures, however, this heterogeneity is almost neglected. In general, despite the fact that some efforts have been made to implicitly address the presented problems, they are, as we will show next, not completely satisfactory for jointly solving both the mentioned limitations.

  • [1] For the sake of completeness, it is worth noting that there is another theory that tries to explainthe typicality effects phenomena, known as the “theory-theory” (Murphy, 2002). It adopts someform of a holistic point of view about concepts. According to some versions of theory-theories,concepts are analogous to theoretical terms in a scientific theory. For example, the concept“BIRD” is individuated by the role it plays in our mental theory of zoology. In other version ofthe approach, concepts themselves are identified with micro-theories of some sort. For example, the concept “BIRD” should be identified with a mentally represented micro-theory aboutbirds. With respect to the prototypes and exemplars theories, however, which rely on morerobust empirical data, the “theory-theory” approach is highly underspecified and more vaguelydefined. As a consequence, at present, its theoretical and computational treatment is more problematic and not considered here.
 
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