Consider a version of the Blocks World with just three blocks - a, b, and c. The on relation is axiomatized below.
¬
on(a,a)
on(a,b)
¬
on(a,c)
¬
on(b,a)
¬
on(b,b)
on(b,c)
¬
on(c,a)
¬
on(c,b)
¬
on(c,c)
Let's suppose that the above relation is defined as follows. This is almost the same as in Section 7.7 except that we have replaced an occurrence of on with above.
A sentence φ is consistent with a set Δ of sentences if and only if there is a truth assignment that satisfies all of the sentences in Δ ∪ {φ}. Say whether each of the following sentences is consistent with the sentences about on and above shown above. Be careful. It's tricky.
