Embedding Vector Differences Can Be Aligned With Uncertain Intensional Logic Differences

TL;DR

This paper demonstrates that differences between embedding vectors can approximate intensional logic differences in hypergraph nodes, suggesting a new way to connect vector algebra with uncertain logical reasoning for knowledge representation.

Contribution

It introduces a novel alignment between embedding vector differences and intensional logic differences, bridging vector operations with uncertain logical inference in knowledge graphs.

Findings

Vector differences can approximate intensional logic differences.

Embedding vector algebra can guide uncertain logical inference.

Potential for a functorial mapping between logic and vector space.

Abstract

The DeepWalk algorithm is used to assign embedding vectors to nodes in the Atomspace weighted, labeled hypergraph that is used to represent knowledge in the OpenCog AGI system, in the context of an application to probabilistic inference regarding the causes of longevity based on data from biological ontologies and genomic analyses. It is shown that vector difference operations between embedding vectors are, in appropriate conditions, approximately alignable with "intensional difference" operations between the hypergraph nodes corresponding to the embedding vectors. This relationship hints at a broader functorial mapping between uncertain intensional logic and vector arithmetic, and opens the door for using embedding vector algebra to guide intensional inference control.