A Description Logic for Analogical Reasoning

TL;DR

This paper introduces a novel approach to analogical reasoning within description logic ontologies, addressing limitations of existing formalizations and enabling inference patterns like rule translation and extrapolation.

Contribution

It proposes an alternative semantics for analogical reasoning in description logics, filling a gap in formal methods for explainable AI.

Findings

Identifies limitations of standard analogical formalization in description logics.

Introduces a semantics based on bijective feature mappings.

Demonstrates inference patterns such as rule translation and extrapolation.

Abstract

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more widespread adoption. To mitigate this issue, we present a mechanism to infer plausible missing knowledge, which relies on reasoning by analogy. To the best of our knowledge, this is the first paper that studies analogical reasoning within the setting of description logic ontologies. After showing that the standard formalisation of analogical proportion has important limitations in this setting, we introduce an alternative semantics based on bijective mappings between sets of features. We then analyse the properties of analogies under the proposed semantics, and show among others how it enables two plausible inference patterns: rule translation and rule extrapolation.