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Abstract

Hierarchies abound to help us organize our world. A hierarchy places items into a general order, where more 'general' is also more 'abstract'. The etymology of hierarchy is grounded in notions of religious and social rank. This article, after a historical review, focuses on knowledge systems, an interloper of the term hierarchy since at least the 1800s. Hierarchies in knowledge systems include taxonomies, classification systems, or thesauri in information science, and systems for representing information and knowledge to computers, notably ontologies and knowledge representation languages. Hierarchies are the logical underpinning of inference and reasoning in these systems, as well as the scaffolding for classification and inheritance. Hierarchies in knowledge systems express subsumption relations that have flexible variants, which we can represent algorithmically, and thus computationally. This article dissects that variability, leading to a proposed typology of hierarchies useful to knowledge systems. The article argues through a perspective informed by Charles Peirce that natural hierarchies are real, can be logically determined, and are the appropriate basis for knowledge systems. Description logics and semantic language standards reflect this perspective, importantly through their open-world logic and vocabularies for generalized subsumption hierarchies. Recent research suggests possible mechanisms for the emergence of natural hierarchies.