Beyond associative memories: Logics and variables in connectionist models

Abstract

This paper demonstrates the role of connectionist (neural network) models in reasoning beyond that of an associative memory. First it is shown that there is a connection between propositional logics and the weighted-sum computation customarily used in connectionist models. Specifically, the weighted-sum computation can handle Horn clause logic and Shoham's logic as special cases. Second, it is shown how variables can be incorporated into connectionist models to enhance their representational power. Solutions to the connectionist variable binding problem are devised to enable connectionist networks to handle variables and dynamic bindings in reasoning. A new model, the discrete neuron formalism, which is an extension of the weighted-sum models, is employed for dealing with the variable binding problem. Formal definitions are presented, and examples are analyzed in detail.