a hierarchy is an unambiguous lattice

Words are ambiguous because the same word is used in different contexts with different meanings.  We can pin down the meaning of a word, in a given context, by using a genus-differentia definition.  When we do that we can arrange our words into a genus-species hierarchy (often called a taxonomy).  If we merge two different contexts together, using the same word even though it has different meanings, we get a lattice (often called an ontology).

I very deliberately used the word "ontology".  It is a sad fact that many brilliant researchers in the field of Artificial Intelligence have used ontologies instead of taxonomies.  This AI research is the foundation of the current Semantic Web activity.

Enough abstractions.  Let me give you a very simple example.
Aristotle said: man is a rational animal.
Ms. Feminist said: You chauvinist pig! Women are people too.
Dr. AI said: OK, let's collect everything we know about "man".
From Aristotle, we know that:
    man is an animal
    man is rational
    man has sex = male or female
From Ms. Feminist, we know that
    person is an animal
    woman is a person with sex = female
    man is a person with sex = male
    woman is better than man
Now that we have all this information together, we can see that
    the genus of man is animal and person
    man is rational
    man has sex = male or female

Now I don't believe that any AI researcher is that naive.  But I do believe that many AI researchers have used ambiguous "definitions" of words in less obvious cases, while simultaneously proclaiming that it is "impossible" to define words.

That is why genus-differentia definitions are part of the KR language.
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Dick McCullough 
knowledge := man do identify od existent done
knowledge haspart list of proposition