Analogical Reasoning Within a Conceptual Hyperspace

TL;DR

This paper introduces a neuro-symbolic approach combining hyperdimensional computing and Conceptual Spaces Theory to perform analogical reasoning, providing a concrete architecture and preliminary experimental validation in a toy domain.

Contribution

It operationalizes Conceptual Spaces Theory using hyperdimensional computing, enabling analogical inference beyond traditional predicate-based methods.

Findings

Successfully performed category-based analogical reasoning

Enabled property-based analogical reasoning

Demonstrated feasibility with preliminary toy domain experiments

Abstract

We propose an approach to analogical inference that marries the neuro-symbolic computational power of complex-sampled hyperdimensional computing (HDC) with Conceptual Spaces Theory (CST), a promising theory of semantic meaning. CST sketches, at an abstract level, approaches to analogical inference that go beyond the standard predicate-based structure mapping theories. But it does not describe how such an approach can be operationalized. We propose a concrete HDC-based architecture that computes several types of analogy classified by CST. We present preliminary proof-of-concept experimental results within a toy domain and describe how it can perform category-based and property-based analogical reasoning.