Which of the following statements are true? (A) A sentence 𝛼 entails another…

Final answer: The two true statements are the one about forward/backward chaining for Horn knowledge bases and the one about propositional logic not scaling to unbounded environments.

• Statement: "A sentence α entails another sentence β if β is true in few worlds where α is true" — False. Entailment means β must be true in all models/worlds where α is true, not just a few.

• Statement: "Forward chaining and backward chaining are very natural reasoning algorithms for knowledge bases in Horn form" — True. Horn clauses support efficient forward-chaining (data-driven) and goal-directed backward-chaining; both are standard and practical for Horn KBs.

• Statement: "Sound inference algorithms derive all sentences that are entailed" — False. Soundness guarantees that any derived sentence is indeed entailed; the property of deriving every entailed sentence is called completeness.

• Statement: "Propositional logic does not scale to environments of unbounded size" — True. Propositional logic requires a separate proposition for each ground fact; for domains that can grow without bound, this propositionalization is not scalable and first-order representations are needed.

Therefore the correct choice picks the two true statements: the one about forward/backward chaining for Horn knowledge bases and the one about propositional logic not scaling to unbounded environments.