 In hard information terms, (A1) states that hard information is closed under (known) implications. Since the first conjunct states that all states accessible by \(\alpha\) are \(\phi\) states, \(\alpha\) possesses the hard information that \(\phi\), hence \(\alpha\) also possesses the hard information that \(\psi\). (A2) states that if \(\phi\) holds in the set of all models, then \(\alpha\) possesses the hard information that \(\phi\). In other words, (A2) states that all tautologies are known/hard stored by the agent, and (A1) states that \(\alpha\) knows the logical consequences of all propositions that \(\alpha\) knows (be they tautologies or otherwise). That is, the axioms state that the agent is logical omniscient, or an ideal reasoner, a property of agents that we will return to in detail in the sections  below.[1] 