AGM Postulates

Where $K$ is a belief state, $K*A$ represents the set of beliefs resulting from revising $K$ with new belief $A$.

• $(K*1)$ $K*A$ is closed under logical consequence.
• $(K*2)$ $A$ belongs to $K*A$.
• $(K*3)$ $K*A$ is a subset of the logical closure of $K \cup \{A\}$.
• $(K*4)$ If $\neg A$ does not belong to $K$, then the closure of $K \cup \{A\}$ is a subset of $K*A$.
• $(K*5)$ If $K*A$ is logically inconsistent, then either $K$ is inconsistent, or $A$ is.
• $(K*6)$ If $A$ and $B$ are logically equivalent, then K*A = K*B.
• $(K*7)$ $K*(A \amp B)$ is a subset of the logical closure of $K*A \cup \{B\}$.
• $(K*8)$ If $\neg B$ does not belong to $K*A$, then the logical closure of $K*A \cup B$ is a subset of $K*(A \amp B)$.