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Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society

By: Michael G. Shafto; Pat Langley | Book details

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Page 614
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Systematicity: Psychological evidence with connectionist implications
Steven Phillips
Information Science Division
Electrotechnical Laboratory
1-1-4 Umezono, Tsukuba, 305, Japan
stevep@etl.go.jp
Graeme S. Halford
Department of Psychology
The University of Queensland
Brisbane, 4072, Australia
gsh@psy,uq.edu.au

Abstract
At root, the systematicity debate over classical versus connectionist explanations for cognitive architecture turns on quantifying the degree to which human cognition is systematic. We introduce into the debate recent psychological data that provides strong support for the purely structure-based generalizations claimed by Fodor and Pylyshyn ( 1988). We then show, via simulation, that two widely used connectionist models (feedforward and simple recurrent networks) do not capture the same degree of generalization as human subjects. However, we show that this limitation is overcome by tensor networks that support relational processing.
Distribution of cognitive behaviour
In the search for the essential components of cognitive architecture researchers have looked for concepts, phenomena and principles that help reduce potential candidates to, ultimately, a single architecture that explains cognitive behaviour. Systematicity is one such concept.Systematicity is the property whereby cognitive capacities are grouped on the basis of common structure. For example, the ability to infer that "John went to the store" given that "John and Mary went to the store", extends to other structurally related inferences such as "Mary went to the store" given that "Mary and John went to the store". These two inferences share the common structure "P and Q implies P".The concept of systematicity was introduced by Fodor and Pylyshyn ( 1988) to differentiate two candidate cognitive architectures: classical (symbol based) and connectionist (vector based) on the basis of their distribution of behaviours. In brief, their argument is that:
Human cognitive behaviour is grouped on the basis of common structure (e.g., from above, it is not the case that one can do the first inference, but not the second).
Classical architectures capture this grouping of behaviours by positing structure sensitive processes.
Connectionist architectures, by specifying context- sensitive (structure insensitive processes), distribute behaviour irrespective of structure.
Therefore, classical (symbol) systems are a better explanation for cognitive architecture, although connectionist architectures may provide suitable implementations of classical ones.

At issue here is not whether an architecture can ultimately exhibit all the observed stimulus-response behaviours, but how these behaviours are distributed over their available resources (e.g., learning trials). For example, an architecture based on simple associations requires two association steps (e.g., 1: A→B; 2: B→A) to support a bidirectional link between events A and B. By contrast, a relation based architecture only requires one step (e.g., R(A,B)), since bi(omni)directionality is built into relational operators ( Phillips, Halford, & Wilson, 1995). The two architectures, although supporting the same functionality, distribute that functionality differently. The relevant difference is that there are states of associative based architectures for which representations of events are accessible in one direction, but not the other (e.g., after step 1, but before step 2). If one only ever observes bidirectional behaviour then such observations would be support for the relation based architecture, and not the association based architecture, although the former could be implemented by the latter1.

Clearly, then, the root of the systematicity argument over cognitive architecture rests on the degree to which human cognition is systematic. Fodor and Pylyshyn take systematicity to be self-evident. Without recourse to specific data they claim, for example, that one can make inferences of the form PQ, PQ, if and only if one can make inferences of the form QP, QP. Subsequently, Hadley ( 1994) characterized systematicity as generalization to novel syntactic position, based on a review of language learning. Researchers have demonstrated networks supporting this definition of systematicity to various degrees ( Christiansen & Chater, 1994; Hadley & Hayward, 1994; Niklasson & van Gelder, 1994; Phillips, 1994). However, others2 question whether the empirical evidence supports this definition either way, given the difficulty of controlling subjects' background knowledge and observing what knowledge they have acquired in the course of an experiment. Furthermore,

____________________
1
Analogously, whereas the architectural components of a database system are typically provided by fourth-generation languages such as SQL, such languages may be implemented in third-generation languages such as C, or Pascal. The point is, of course, that the sorts of behaviours exhibit by "paper- based" information processing systems are better captured (modelled) by relational languages like SQL, rather than procedural languages like C.
2
Anonymous reviewer of Phillips (submitted).

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