#refutation

Question 1: Single choice

mediumAI-checkedKnowledge Representation & Reasoning

A knowledge base is a set of sentences $KB = \{P_1, \dots, P_n\}$ and $\alpha$ is a query. Which condition is equivalent to $KB \models \alpha$ ( $KB$ entails $\alpha$ )?

The set $KB \cup \{\alpha\}$ is jointly satisfiable1
The set $KB \cup \{\lnot\alpha\}$ is jointly satisfiable2
The set $KB \cup \{\lnot\alpha\}$ is jointly unsatisfiable3
The sentence $\alpha \to (P_1 \land \dots \land P_n)$ is a tautology4

Timed test