Connectionist approaches to the modeling of cognitive processes have often been attacked on the grounds that they do not employ compositionally structured representations (e.g.,Fodor & Pylyshyn 1988). But what exactly is compositional structure, and how does such structure contribute to cognitive processing? This paper clarifies these questions by distinguishing two different styles of compositionality, one characteristic of connectionist modeling and the other essential to mainstream symbolic or "Classical" approaches. Given this distinction,it is clear that connectionist models can employ compositionally structured representations while remaining, both conceptually and in practice, quite distinct from the Classical approach;moreover, it can be shown that certain central aspects of cognition, such as its systematicity,are at least in principle amenable to Connectionist explanation.

Several connectionist models have been supplying non-classical explanations to the challenge of explaining systematicity, i.e.. structure sensitive processes, without merely being implementations of classical architectures. However, lately the challenge has been extended to include learning related issues. It has been claimed that when these issues are taken into account, only a restricted form of systematicity could be claimed by the connectionist models put forward so far. In this paper we investigate this issue further, and supply a model and results that satisfies even the revised challenge.

This paper challenges the widely accepted claim that "classical" cognitive architectures can explain the systematicity of cognition (Fodor & Pylyshyn, 1988). There are plausible ways of rendering more precise the systematicity hypothesis (as standardly formulated) in which it is entailed by classical architectures, and other plausible ways in which it is not. Therefore, it is not a determinate issue whether systematicity is entailed, and hence explained, by classical architectures. The general argument is illustrated in a particular domain, the systematicity of deductive inference. In the case of the capacity to carry out the inference modus tollens, the systematicity hypothesis can be made precise in two ways, one entailed by classical architectures, another which is not. Further, the latter, but not the former, accurately describes the actual empirical phenomenon. Put another way, the clumps that these deductive inference capacities come in are not the clumps that are entailed by classical architectures. Therefore, in this area at least, systematicity considerations count against the classical conception of cognitive architecture.