Which of the following statements are true ?

(A) A sentence α entails another sentence β  if β is true in few worlds where α is true.

(B) Forward chaining and backward chaining are very natural reasoning algorithms for knowledge bases in Horn form.

(C) Sound inference algorithms derive all sentences that are entailed.

(D) Propositional logic does not scale to environments of unbounded size.

Choose the correct answer from the options given below:

The correct answer is option 4.

Key Points

The relationship of entailment between sentences is crucial to our understanding of reasoning. A sentence α entails another sentence β if β is true in all world where α  is true. Equivalent definitions include the validity of the sentence α⇒β and the unsatisfiability of sentence α∧¬β.

Hence statement I is False.

For information bases in Horn form True, forward and backward chaining is rather normal reasoning algorithms. These are very natural algorithms that run in linear time.

Hence statement II is True.

Both sentences that are entailed False are derived by sound inference algorithms (it is complete not sound) If only sentences entailed by Knowledge Base are derived, the inference algorithm is sound.

Hence statement III is False.

Propositional logic does not scale to unbounded conditions. That is right. Propositional logic is relatively efficient for certain tasks within an agent, but it does not scale to unbounded environments because it lacks the descriptive capacity to deal concisely with time, space, and universal patterns of object relationships.

Hence statement IV is True.

∴ Hence the correct answer is (B) and (D) only.