Modelling supra-classical logic in a Boltzmann neural network: I representation

Abstract

Abstract This paper looks at the representation of supra-classical, non-monotonic (SCNM) logic by an artificial neural network. It identifies the features of defeasiblity in this logic related to inference in the context of common-sense reasoning. It considers the machine characteristics that make a representation possible, with reference to previous literature. We describe a theoretical environment for investigating the representation and provide experimental evidence confirming that a Boltzmann machine is a suitable network representation. A Boltzmann machine can learn an input distribution corresponding to a preference relation and explicitly retrieve appropriate model states, constituting one-to-many mappings, entailed by the uncertain information contained in a premiss. The place of the Boltzmann machine in knowledge representation is discussed. In future papers, this neural network model of SCNM logic will serve as an experimental gateway for exploration of typicality and belief revision.