Exercise 9.6 [subsumption-lattice-exercise]

Consider the subsumption lattices shown in Figure subsumption-lattice-figure (page subsumption-lattice-figure).

1. Construct the lattice for the sentence ${Employs}({Mother}({John}),{Father}({Richard}))$.

2. Construct the lattice for the sentence ${Employs}({IBM},y)$ (“Everyone works for IBM”). Remember to include every kind of query that unifies with the sentence.

3. Assume that indexes each sentence under every node in its subsumption lattice. Explain how should work when some of these sentences contain variables; use as examples the sentences in (a) and (b) and the query ${Employs}(x,{Father}(x))$.