A filter corresponding to an antichain in a poset is the set of all elements of the poset that are greater than at least one element from the antichain. For example, let us consider the tree in Figure 3. A filter corresponding to the antichain A " tC 1 , C 5 , C 8 u is the set of all subsumers of all elements from the antichain, i.e. F ilpAq " tC 1 C 15 u. The filter corresponding to the antichain B " tC 1 , C 7 , C 9 u is the set F ilpBq " tC 1 C 9 u. The intersection F ilpAq X F ilpBq and the resulting set of minimal elements are F ilpAq X F ilpBq ,
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