Knowledge organization systems (KOS) can use different types of hierarchical relations: broader generic (BTG), broader partitive (BTP), and broader instantial (BTI). The latest ISO standard on thesauri (ISO 25964) has formalized these relations in a corresponding OWL ontology (De Smedt et al., ISO 25964 part 1: thesauri for information retrieval: RDF/OWL vocabulary, extension of SKOS and SKOS-XL. http://purl.org/iso25964/skos-thes, 2013) and expressed them as properties: broaderGeneric, broaderPartitive, and broaderInstantial, respectively. These relations are used in actual thesaurus data. The compositionality of these types of hierarchical relations has not been investigated systematically yet. They all contribute to the general broader (BT) thesaurus relation and its transitive generalization broader transitive defined in the SKOS model for representing KOS. But specialized relationship types cannot be arbitrarily combined to produce new statements that have the same semantic precision, leading to cases where inference of broader transitive relationships may be misleading. We define Extended properties (BTGE, BTPE, BTIE) and analyze which compositions of the original “one-step” properties and the Extended properties are appropriate. This enables providing the new properties with valuable semantics usable, e.g., for fine-grained information retrieval purposes. In addition, we relax some of the constraints assigned to the ISO properties, namely the fact that hierarchical relationships apply to SKOS concepts only. This allows us to apply them to the Getty Art and Architecture Thesaurus (AAT), where they are also used for non-concepts (facets, hierarchy names, guide terms). In this paper, we present extensive examples derived from the recent publication of AAT as linked open data.