### Artificial IntelligenceAIMA Exercises

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?
1. FC will infer the literal $Q(A)$.
2. FC will infer the literal $P(B)$.
3. If FC has failed to infer a given literal, then it is not entailed by the KB.
4. BC will return ${true}$ given the query $P(B)$.
5. If BC does not return ${true}$ given a query literal, then it is not entailed by the KB.

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?
1. FC will infer the literal $Q(A)$.
2. FC will infer the literal $P(B)$.
3. If FC has failed to infer a given literal, then it is not entailed by the KB.
4. BC will return ${true}$ given the query $P(B)$.
5. If BC does not return ${true}$ given a query literal, then it is not entailed by the KB.

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