 This operator is called the “intuitionistic implication”, because of the similarity between its semantics and the one of the implication operator in Kripke’s semantics for intuitionistic logic (Kripke 1965). Its interpretation in terms of belief is quite straightforward: if the assignments in \(X\) represent the states of thing that some agent believes possible, then a subset \(Y\) of \(X\) may represent the result of a belief update in which the agent rejects some previously believed possible states of thing, and \(\phi \rightarrow \psi\) states than any such update that would cause \(\phi\) to hold would also cause \(\psi\) to hold. From this standpoint, this is a very natural concept which permits us to describe predictions about how such an agent’s overall belief state would react to belief updates.