Biomedical ontologies are typically structured in a biaxial way, reflecting both a taxonomic and a mereological order. Common examples such as the Gene Ontology and the Unified Medical Language System (UMLS) excel in terms of coverage but lack an adequate semantics of the mereological relations they incorporate. This shortcoming is particularly evident as far as the (non-)mandatory existence of parts for their wholes is concerned, on the one hand, and the propagation of properties across part-whole hierarchies, on the other hand. We provide a formal specification of the semantic foundations of mereology in the biomedical domain that is closely linked to the paradigm of description logics. In essence, we here propose to emulate mereological reasoning by taxonomic reasoning. In an attempt to capture much of the shared intuition underlying merelogical reasoning in the biomedical domain, we distinguish for each mereologically relevant concept four different classes of parts and wholes which allow for the expression of five different propagation patterns.