A property of the Kripke semantics for intuitionistic logic such that:

• • if $\phi$ is true at $w$ and $wR{w}^{\prime }$, then $\phi$ is true at $w^{\prime }$ as well

where $w$ and $w^{\prime }$ are possible worlds and $R$ is the binary accessibility relation. This property has a natural reading when the possible worlds of the Kripke semantics are interpreted as states of knowledge and the accessibility relation is interpreted as progression between stages in the course of an investigation. Heredity then captures the thesis that investigation only yields new information, i.e., no information is lost during an investigation.