Shared Multi-Space Representation for Neural-Symbolic Reasoning

This paper presents a new neural-symbolic reasoning approach based on a sharing of neural multi-space representation for coded fractions of first-order logic. A multi-space is the union of spaces with different dimensions, each one for a different set of distinct features. In our case, we model the distinct aspects of logical formulae as separated spaces attached with vectors of importance weights of distinct sizes. This representation is our approach to tackle the neural network’s propositional fixation that has defied the community to obtain robust and sound neural-symbolic learning and reasoning, but presenting practical useful performance. Expecting to achieve better results, we innovated the neuron structure by allowing one neuron to have more than one output, making it possible to share influences while propagating them across many neural spaces. Similarity measure between symbol code indexes defines the neighborhood of a neuron, and learning happens through unification which propagates the weights. Such propagation represents the substitution of variables across the clauses involved, reflecting the resolution principle. In this way, the network will learn about patterns of refutation, reducing the search space by identifying a region containing ground clauses with the same logical importance.