Constructing Proofs in Symmetric Networks

Part of Advances in Neural Information Processing Systems 4 (NIPS 1991)

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Gadi Pinkus


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. The network is inherently fault tolerant and can cope with inconsistency and nonmonotonicity.