As membership can depend on the mode we are in, making a program use modal membership requires new tricks. Kripke's "Possible Worlds" semantics for Modal Logic give us one powerful tool to create a membership which can switch between modes without affecting computation elsewhere. It is a vivid demonstration of how expanding our logical toolbox expands what we can compute.
Useful previous videos include
* Membership with Uncertainty https://youtu.be/6b-QDMTGdbc?si=Rz9qo1MHdPxHgdvu
* Constructive Membership https://youtu.be/RyUJhiu5TvU?si=oI99MXXTyBtYTWXL
