How does an object level ontology appear in the lattice of theories?
Since it is represented by an IFF theory, an unpopulated object level ontology will appear as the closure of the theory, which is one element in the lattice of theories that is based at its underlying first order language. Since it is represented by an IFF logic, a populated object level ontology will appear as a path in the lattice of theories. One end of the path (the bottom end) will be located at the theory of the component model of the logic, and the other end of the path (the top end) will be located at the closure of the component theory of the logic.
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