It is widely accepted that cognition can be understood at multiple levels of analysis, but there are different claims about the nature of these levels (Broadbent Reference Broadbent1985; Marcus Reference Marcus2001; Rumelhart & McClelland Reference Rumelhart and McClelland1985; Smolensky Reference Smolensky1988). In Semantic Cognition (Reference Rogers and McClelland2004), Rogers & McClelland (R&M) appear to suggest that parallel distributed processing (PDP) approaches and structured approaches lead to proposals at the same level of analysis, and are therefore competitors. Like some previous researchers (Smolensky Reference Smolensky1988), we believe that these two paradigms are compatible, and that they aim for explanations at different levels of analysis.

Since R&M treat structured approaches as the competition, they naturally emphasize the problems they see with structured models of cognition. Among other criticisms, they suggest that structured approaches cannot capture typicality, exceptions, and the graded inferences that are characteristic of human learning (Semantic Cognition, p. 44); that there are few attempts to explain how taxonomic hierarchies might be acquired (pp. 13, 31); and that structured approaches do not explain why people make very different inferences when reasoning about different kinds of properties (e.g., “has cold blood” vs. “weighs ten tons,” p. 34).

If PDP approaches and structured approaches operate at different levels of analysis, then many phenomena (e.g., graded inferences and learning) will turn out to be compatible with both approaches. Some structured models suffer from the limitations described by R&M, but others do not. Models that combine probabilistic inference with structured representations allow for noise and exceptions, and are able to account for graded generalizations and typicality effects (Anderson Reference Anderson1991; Kemp & Tenenbaum Reference Kemp, Tenenbaum, Alterman and Kirsh2003; Tenenbaum Reference Tenenbaum, Solla, Leen and Muller2000). Combining probabilistic inference with structured representations also leads to a principled account of how these representations might be acquired, and there are probabilistic models that learn categories (Anderson Reference Anderson1991), taxonomic hierarchies (Kemp et al. Reference Kemp, Perfors, Tenenbaum, Forbus, Gentner and Regier2004), abstract schemata (Kemp et al. Reference Kemp, Goodman, Tenenbaum, McNamara and Trafton2007a), and logical theories (Kemp et al. Reference Kemp, Goodman, Tenenbaum, Platt, Koller, Singer and Roweis2008)

Structured approaches also help to explain how different kinds of knowledge support inferences about different kinds of properties. Shafto et al. (Reference Shafto, Kemp, Baraff, Coley, Tenenbaum, Bara, Barsalou and Bucciarelli2005) have shown that a probabilistic model that incorporates a taxonomic hierarchy accounts for inferences about taxonomic properties (e.g., “has sesamoid bones”), and that a model that relies on a structured representation of a food web predicts inferences about disease properties (e.g., “carries E. Spirus bacteria”). As R&M point out, allowing for multiple structured representations can raise some challenging problems, but none of these problems seems insurmountable. For example, there are models that learn multiple representations of the relationships between a set of categories (Shafto et al. Reference Shafto, Kemp, Mansinghka, Gordon, Tenenbaum, Sun and Miyake2006) and models of inductive reasoning that combine the knowledge embedded in multiple representations (Kemp et al. Reference Kemp, Shafto, Berke, Tenenbaum, Schölkopf, Platt and Hoffman2007b).

Although psychologists should ultimately aim to understand semantic cognition at multiple levels of analysis, it is useful to consider whether the current generation of structured models shows more or less promise than the current generation of PDP models. The community as a whole may pursue multiple approaches, but individuals will need to decide which of these approaches is most deserving of their time and attention. R&M provide a comprehensive description of the benefits that PDP approaches can provide, but there are two primary reasons why structured approaches appear more promising to us.

First, formalizing commonsense knowledge is a major challenge for models of semantic cognition. R&M suggest that structured models may be “too restrictive or constraining to capture the nuances of human knowledge of all sorts of things” (Semantic Cognition, p. 44). We are drawn toward the opposite conclusion, and feel that there are fundamental aspects of human knowledge that are naturally captured using structured representations but are difficult for current-generation PDP models to incorporate. Several examples can be found in the literature, but here we focus on two: standard PDP models do not provide a compositional system for building complex concepts out of simpler pieces (Fodor & Pylyshyn Reference Fodor and Pylyshyn1988) and find it difficult to discover abstract relational laws (Marcus Reference Marcus2001). The work of R&M appears to suffer from both of these limitations. First, it is not clear how the model will handle relations of several different arities (e.g., CAN[canary, fly], and CAN[cat, eat, canary]), or cases involving nested relations (e.g., CAUSE[EATS(canary, food), GROWS(canary)]). Second, it seems likely that the model will struggle to acquire abstract knowledge about relations: for instance, it is not clear whether the model can recognize that a relation (e.g., ISA[·,])) tends to be transitive, or that two relations (e.g., HAS[·,·] and POSSESSES[·,]) are near identical in meaning. Abstract knowledge of this sort should support inferences about novel categories: for example, given that a dax is a wug and a wug is a zav, a dax is likely to be a zav. Extensions of the R&M approach may be able to overcome many of the limitations we identified, and PDP models of relational learning and reasoning (Doumas et al. Reference Doumas, Hummel and Sandhofer2008; Shultz & Vogel Reference Shultz, Vogel, Forbus, Gentner and Regier2004) may help to show the way. At present, however, PDP models seem less successful at capturing complex systems of relational knowledge than models that rely on predicate logic as a representation language.

A second advantage of structured models is that they make more direct contact with previous psychological research on semantic cognition. As R&M suggest in their opening chapter (Semantic Cognition, Ch. 1), many psychologists who have written about categorization, the theory-theory, and related topics have seen the need for structured representations. To mention only one example, the work of Keil (Reference Keil1979) is motivated in part by the idea that categories are organized into taxonomic hierarchies, and Keil's approach can be directly converted into a structured model that helps to explain how taxonomic hierarchies are acquired and used for induction (Schmidt et al. Reference Schmidt, Kemp, Tenenbaum, Sun and Miyake2006). The work of R&M may encourage psychologists to develop new experiments and theories that explore the notion of distributed representations. At present, however, the most profitable interactions between computational approaches and psychological studies seem likely to be organized around structured models.

Predictions about the future of any discipline are notoriously unreliable, but we will venture two of them. First, researchers will eventually understand how structured semantic representations are instantiated in the brain. Second, deep insights at the neural level will only be possible once we have a deep understanding of the computations supported by structured semantic representations.