That's what I said :-)   

What is necessary is that the relationships be subsumed under a parent relationship, and that that parent relationship be transitive.  In controlled vocabularies, these semantics  are provided by "the Hierarchical Relationship" (aka Broader Term, or BT).  

There are sub-relations of BT for  species/genus (BTG), individual/species (BTI), and part/whole (BTP). 

a BTI b ^ b BTG c ->  a BTI c 

a BTG b ^ a BTG c ->  a BTG c 

a BTP b ^ b BTP c ->  a BTP c 

a BTI b -> a BT b

a BTG b -> a BT b

a BTP b -> a BT b 

Where a, b,  and c are intentional concepts.

 If [a] is entity to which the concept a refers, 

a BTI b -> Individual([a]) ^ Collection([b]) ^ isa([a],[b]) 

a BTG b -> Collection([a]) ^ Collection([b]) ^ genls([a],[b]) 

a BTP b -> Collection([a]) ^ Collection([b]) ^ partTypes([b],[a])

where partTypes([b],[a]) means that every intact [b] has at least one part that is an [a]. 

Part-hood is considered transitive (see e.g. Croft & Cruse (2004). Cognitive Linguistics, where Cruse reverses his position in Cruse (1986). Lexical Semantics.  Both books CUP).   

[Whilst we're talking CUP, Murphy (2008). Semantic Relations and the Lexicon. makes a fairly good case for treating hypero/hypo-nymy as being non lexical in nature.] 

It's not strictly necessary that the relationships be one-to-many (if scheme is poly-hierarchic, a value may be aggregated under more than one category.  How values are distributed amongst the aggregates is application specific (e.g. du assigns the entire size of a multiply linked file to a single, unspecifed  parent;  an equally valid semantics would have been  to divide the size equally amongst all the different parents within the scope of an execution; it would also be meaningful  to divide by the total number of links to the file. 

Simon