A connectionist representation of first-order formulae with dynamic variable binding

The relationship between symbolicism and connectionism has been one of the major issues in recent Artificial Intelligence research. An increasing number of researchers from each side have tried to adopt desirable characteristics of the other. These efforts have produced a number of different strategies for interfacing connectionist and sym¬ bolic AI. One of them is connectionist symbol processing which attempts to replicate symbol processing functionalities using connectionist components.In this direction, this thesis develops a connectionist inference architecture which per¬ forms standard symbolic inference on a subclass of first-order predicate calculus. Our primary interest is in understanding how formulas which are described in a limited form of first-order predicate calculus may be implemented using a connectionist archi¬ tecture. Our chosen knowledge representation scheme is a subset of first-order Horn clause expressions which is a set of universally quantified expressions in first-order predicate calculus. As a focus of attention we are developing techniques for compiling first-order Horn clause expressions into a connectionist network. This offers practical benefits but also forces limitations on the scope of the compiled system, since we tire, in fact, merging an interpreter into the connectionist networks. The compilation process has to take into account not only first-order Horn clause expressions themselves but also the strategy which we intend to use for drawing inferences from them. Thus, this thesis explores the extent to which this type of a translation can build a connectionist inference model to accommodate desired symbolic inference.This work first involves constructing efficient connectionist mechanisms to represent basic symbol components, dynamic bindings, basic symbolic inference procedures, and devising a set of algorithms which automatically translates input descriptions to neural networks using the above connectionist mechanisms. These connectionist mechanisms are built by taking an existing temporal synchrony mechanism and extending it further to obtain desirable features to represent and manipulate basic symbol structures. The existing synchrony mechanism represents dynamic bindings very efficiently using tem¬ poral synchronous activity between neuron elements but it has fundamental limitations in supporting standard symbolic inference. The extension addresses these limitations.The ability of the connectionist inference model was tested using various types of first order Horn clause expressions. The results showed that the proposed connectionist in¬ ference model was able to encode significant sets of first order Horn clause expressions and replicated basic symbolic styles of inference in a connectionist manner. The system successfully demonstrated not only forward chaining but also backward chaining over the networks encoding the input expressions. The results, however, also showed that implementing a connectionist mechanism for full unification among groups of unifying arguments in rules, are encoding some types of rules, is difficult to achieve in a con¬ nectionist manner needs additional mechanisms. In addition, some difficult issues such as encoding rules having recursive definitions remained untouched