If the knowledge base is empty, then interpretations are unconstrained and can
be defined to cause mischief. The only set subsumed by the empty set is the
empty set. Any interpretation mapping Doctor to the empty set and Surgeon and
Woman to non-empty, non-disjoint sets (so that their intersection is non-empty)
results in
And Surgeon Woman \(\sqsubseteq\) Doctor
subsuming a non-empty set in an empty set, which doesn’t work.
This page last modified on 2006 January 24.