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 \(K*(A \amp B)\).