Reasoning with vectors: A continuous model for fast robust inference

This article describes the use of continuous vector space models for reasoning with a formal knowledge base. The practical significance of these models is that they support fast, approximate but robust inference and hypothesis generation, which is complementary to the slow, exact, but sometimes brittle behaviour of more traditional deduction engines such as theorem provers.

The article explains the way logical connectives can be used in semantic vector models, and summarizes the development of Predication-based Semantic Indexing, which involves the use of Vector Symbolic Architectures to represent the concepts and relationships from a knowledge base of subject-predicate-object triples. Experiments show that the use of continuous models for formal reasoning is not only possible, but already demonstrably effective for some recognized informatics tasks, and showing promise in other traditional problem areas. Examples described in this article include: predicting new uses for existing drugs in biomedical informatics; removing unwanted meanings from search results in information retrieval and concept navigation; type inference from attributes; comparing words based on their orthography; and representing tabular data, including modelling numerical values.

The algorithms and techniques described in this article are all publicly released and freely available in the Semantic Vectors open-source software package.¹