Constructing Proofs in Symmetric Networks

This paper considers the problem of expressing predicate calculus in con(cid:173) nectionist networks that are based on energy minimization. Given a first(cid:173) order-logic knowledge base and a bound k, a symmetric network is con(cid:173) structed (like a Boltzman machine or a Hopfield network) that searches for a proof for a given query. If a resolution-based proof of length no longer than k exists, then the global minima of the energy function that is associated with the network represent such proofs. The network that is generated is of size cubic in the bound k and linear in the knowledge size. There are no restrictions on the type of logic formulas that can be represented.