ABSTRACT
The primary interest of this chapter is in understanding how systems which are described in a symbolic specification style may be implemented using a connectionist architecture. As a focus of attention, techniques have been developed for compiling Horn clauses into a connectionist network. This offers significant practical benefits but also forces limitations on the scope of the compiled system. Executable symbolic specifications are (in the right hands) effective for describing systems and are comparatively easy for designers to understand. However, they normally require extra machinery, in the form of an interpreter or theorem proving system in order to be executed. For many applications (particularly when the system is to be implemented in hardware) such extra mechanisms are both inefficient and structurally complex. Connectionist systems, on the other hand, use structurally simple components, may provide very fast inference and have no need of a separate interpreter, but are difficult to use directly for specification because of the mass of connections between elements. By providing automatic translation from symbolic to connectionist representations, one should be able to cancel out the deficiencies of each style whilst retaining the advantages of both. Unfortunately, this type of compilation is not straightforward; since an interpreter has to be merged into the connectionist networks, the compilation process has to take into account not only the Horn clauses themselves but also the strategy, which is intended to be used for drawing inferences from them. It also appears that some fundamental aspects of symbolic inference are difficult to translate directly into a connectionist framework. In particular, it has proved to be difficult to provide a full translation of term unification (in the style of common Horn clause languages like Prolog) and this has, in turn, placed awkward limitations on the forms of inferences which could be supported. The purpose of this chapter is to propose a localist network architecture which removes some of these fundamental limitations, resulting in a connectionist system which extends expressive power in achieving symbolic inference.
