Question $10$

Consider the BCP$-$rule as described in $9\mathrm{.}2\mathrm{.}7.$

$($i$)$ Explain why it is not possible to syntactically check whether two arbitrary concept descriptions

in NNF are complements of one another. Give an example to illustrate your explanation.

$($ii$)$ Prove that the BCP$-$rule preserves the satisfiability of the assertions in the current node, at least

for $n=1.$