Penn et al. present an encompassing argument on why nonhumans are not able to reason relationally. Their point is well made, yet they fail to adequately address the basis of performance in the relation-like reasoning tasks in which animals do succeed, such as same-different learning (Young & Wasserman Reference Young and Wasserman1997), match to sample, and primitive grammatical learning (T. Q. Gentner et al. Reference Gentner, Fenn, Margoliash and Nusbaum2006; Hauser & Weiss Reference Hauser and Weiss2002). Although these tasks do not necessarily require a relational reasoning system, they are instances of relational responding. If animals do not possess a perceptual symbol system, how do they respond relationally?
We offer an explanation for the ability of animals in the form of a computational model that learns to respond to categories defined by relations by making structured comparisons to concrete examples stored in memory. The model, BRIDGES (Building Relations through Instance Driven Gradient Error Shifting), provides an account of how animals (and people) learn to respond relationally. The model does not posit elaborate processes or representations.
BRIDGES combines two popular approaches to cognition, exemplar-based category learning (Kruschke Reference Kruschke1992) and structure mapping theory (D. Gentner Reference Gentner1983). Exemplar-based models store every experienced stimulus in memory. When a novel stimulus is encountered, the similarity between the stimulus and each stored exemplar is calculated. The novel item is assigned to the category whose members have the highest summed similarity. A learning process adjusts the attention allocated to the various stimulus dimensions, which affects the model's notion of similarity. For instance, if small red stimuli and big red stimuli belong to category A, and small blue stimuli and big blue stimuli belong to category B, the model will learn to weight color more than size.
Structure mapping theory expands on this notion of similarity. The similarity between two scenes is determined by aligning the objects and relations present within one scene with the objects and relations in the other scene (Markman & Gentner Reference Markman and Gentner1993). The quality of the alignment determines similarity.
BRIDGES extends the notion of similarity used in exemplar models to an attention-weighted form of structure mapping theory. This allows relational similarity, the degree to which mapped objects play the same role in their corresponding relations (Jones & Love Reference Jones and Love2007), to play a variable role in the alignment process. Attention can shift between the features (e.g., red) and the relations (e.g., redder). This allows for abstraction away from the features and toward the relations, but only so far as the statistics of the environment warrant. Attention is updated according to a supervised or unsupervised gradient descent algorithm. The result is that BRIDGES is able to learn to respond differentially to the presence of relations, but that responding is still affected by the features of the stimuli.
BRIDGES has successfully simulated (Tomlinson & Love Reference Tomlinson, Love, Gil and Mooney2006) relational responding in a number of situations, including same-different learning in pigeons (Young & Wasserman Reference Young and Wasserman1997) and infant grammar learning (Marcus et al. Reference Marcus, Vijayan, Bandi and Vishton1999). Like the participants in these experiments, BRIDGES generalizes to presentations of the relations with novel objects. Also, these relations are still clouded by the featural similarity of the individual stimuli since attention shifting is rarely complete. BRIDGES's operation is consistent with observed relational shifts (from concrete to abstract) in children and experts (Chi et al. Reference Chi, Feltovich and Glaser1981; Gentner & Rattermann Reference Gentner, Rattermann, Gelman and Byrnes1991).
In contrast to BRIDGES, Penn et al. explain the match-to-sample tasks and same-different learning as a result of entropy detection (see Young et al. Reference Young, Ellefson and Wasserman2003), which does not require a relational competency. Entropy explanations and BRIDGES both do equally well in accounting for a number of phenomena. However, BRIDGES is distinguished from an entropy explanation by its sensitivity to experienced examples (i.e. attention does not fully shift to relations). In support of BRIDGES, Gibson and Wasserman (Reference Gibson and Wasserman2004) found that pigeons adjust their responding when the featural similarity of the test arrays is put at odds with the relational similarity of the arrays.
BRIDGES suggests that animals and humans at various stages of development can be understood as lying along a continuum. When modeling the simple behavior of animals or infants, attention shifting is rarely complete and a representation with only simple features and a type-token relation is sufficient. The type-token relationship assumes that the individual is able to recognize objects present in the input as members of a larger category. In other words, when pigeons are presented with an array of shapes, they are able to represent the squares as members of an abstract type, square. In contrast, when modeling more complex behavior, in children or adults, a representation using other relations (e.g., cause) or high-order relations (i.e., relations between relations) is often required. Additionally, attention shifting occurs faster and is more complete. BRIDGES provides a tool to talk about these and other differences in a quantitative way.
Animals might not be able to succeed at complex relational reasoning tasks, but they can compare current examples to previous examples in a structured way, and from this respond in a manner consistent with an understanding of abstract relations. BRIDGES is a computational model of how this relation-like behavior can be learned. By comparing concrete examples of the relations in a structured manner, one can learn to respond in a manner consistent with the relations, without true abstract knowledge.
