This question considers Horn KBs, such as the following:
$$\begin{array}{l}
P(F(x)) {:;{\Rightarrow}:;}P(x)\
Q(x) {:;{\Rightarrow}:;}P(F(x))\
P(A)\
Q(B)
\end{array}$$ Let FC be a breadth-first forward-chaining algorithm that
repeatedly adds all consequences of currently satisfied rules; let BC be
a depth-first left-to-right backward-chaining algorithm that tries
clauses in the order given in the KB. Which of the following are true?
-
FC will infer the literal
$Q(A)$ . -
FC will infer the literal
$P(B)$ . -
If FC has failed to infer a given literal, then it is not entailed by the KB.
-
BC will return
${true}$ given the query$P(B)$ . -
If BC does not return
${true}$ given a query literal, then it is not entailed by the KB.