Exploring the Symbolic/Subsymbolic Continuum: A Case Study of RAAM

It is di cult to clearly de ne the symbolic and subsymbolic paradigms; each is usually described by its tendencies rather than any one de nitive property. Symbolic processing is generally characterized by hard-coded, explicit rules operating on discrete, static tokens, while subsymbolic processing is associated with learned, fuzzy constraints a ecting continuous, distributed representations. In addition, programming languages such as Lisp and mechanisms such as Turing machines are typically associated with the symbolic paradigm, while connectionism is frequently associated with the subsymbolic paradigm. Debates contrasting the two paradigms sometimes center on these mechanisms, for example comparing the capabilities of Turing machines with those of connectionist networks (see Adams, Aizawa, and Fuller in this volume). However, connectionist networks can be proven to be computationally equivalent to the abstract notion of Turing machines [Franklin and Garzon, 1990]. Therefore the computational mechanism is not the crucial issue in separating the symbolic and subsymbolic paradigms. What then is the crucial issue? We believe there are three major issues which distinguish the symbolic paradigm from the subsymbolic paradigm: (1) the type of representations; (2) the style of composition; and (3) the functional characteristics. We have summarized the key elements of these di erences between the two paradigms in Table 1. However, most cognitive science and classical arti cial intelligence (AI) models cannot be completely characterized as either purely symbolic or purely subsymbolic using these criteria. Instead, most models fall somewhere in between the two extremes, or in the so-called \Gap." For this reason, it seems appropriate to view the paradigms as de ning two opposite corners of a three-dimensional continuum as shown in