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On Compositionality of ISO 25964 Hierarchical Relationships (BTG, BTP, BTI)

Hierarchical relations are one of the most important relations in Knowledge Organization Systems (KOS). In view of the Linked Data scenario and vocabulary mappings, the logical grounding of relationships becomes increasingly important to ensure true interoperability. Considerable research is done in the field of subsumption and mereology in general, yet the compositionality of hierarchical relationships has not been investigated systematically so far. Compositionality matters with respect to transitive closure and inference in information retrieval vocabularies. It is a prerequisite for sensible search expansion, more specifically, search explosion over hierarchy chains. The exploration of compositionality of BTG, BTP, BTI, is a first step towards this end. Our analysis builds on examples from the Getty vocabularies (AAT, TGN, ULAN), considering all nine possible compositions of the three kinds of relationships. Among other conclusions we propose some extension of ISO hierarchical relationship properties.
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