Beyond associative memories: Logics and variables in connectionist models

This paper demonstrates the role of connectionist (neural network) models in reasoning beyond that of an associative memory. First we show that there is a connection between propositional logics and the weighted-sum computation customarily used in connectionist models. Speci cally, the weighted-sum computation can handle Horn clause logic and Shoham's logic as special cases. Secondly, we show how variables can be incorporated into connectionist models to enhance their representational power. We devise solutions to the connectionist variable binding problem to enable connectioninst networks to handle variables and dynamic bindings in reasoning. A new model, the Discrete Neuron formalism, is employed for dealing with the variable binding problem, which is an extension of the weighted-sum models. Formal de nitions are presented, and examples are analyzed in details. ACKNOWLEDGEMENTS I wish to thank Dave Waltz, James Pustejovsky, and Tim Hickey (all of Brandeis University) for many discussions. I also want to acknowledge Honeywell SSDC for the support during the revision of this paper. Finally I wish to thank the reviewer and the editor for their detailed comments. 2