Which of the following statements is false w.r.t FOL inference Forward chaining in data log kb runs in polynomial time Entailment in a datalog KB is semi decidable Inference in FOL KB is semi decidable Backward chaining suffers from redundant inferences and infinite loops

To determine which statement is false with respect to First-Order Logic (FOL) inference, let's analyze each statement: 1. **Forward chaining in a Datalog KB runs in polynomial time**: This statement is generally true. Forward chaining is a method of reasoning that can be implemented efficiently, and for Datalog, which is a subset of FOL, it can be done in polynomial time. 2. **Entailment in a Datalog KB is semi-decidable**: This statement is true. Entailment in Datalog is semi-decidable because if a query is entailed by the knowledge base, there is a procedure that can confirm this, but if it is not entailed, the procedure may run indefinitely. 3. **Inference in FOL KB is semi-decidable**: This statement is true. Inference in general First-Order Logic is semi-decidable, meaning that there is an algorithm that can confirm if a statement is provable, but if it is not provable, the algorithm may not terminate. 4. **Backward chaining suffers from redundant inferences and infinite loops**: This statement is true. Backward chaining can indeed suffer from redundant inferences if the same goals are pursued multiple times, and it can also enter infinite loops if there are cyclic dependencies in the rules. Based on this analysis, all statements except the first one are true. Therefore, the false statement is: **Forward chaining in a Datalog KB runs in polynomial time.** This statement is actually true, so the correct answer is that none of the statements provided are false. However, if you are looking for a statement that could be misleading or misinterpreted, it would be the first one, as it might not hold in all contexts outside of Datalog or under certain conditions.