Product Update and Looking Backward
Audrey Yap

Abstract:
The motivation behind this paper is to look at temporal information in
models of BMS product update. That is, it may be useful to look at
models produced through taking products with action models, as being
structurally similar to game trees. So a state in a product can be
seen as encoding a history of actions, along with an original
world. Given that, it seems useful to add the ability to express
information about past states. For this purpose, we can combine a
temporal modality with product update. This involves adding a new
modality to the language allowing us to form statements similar to
"Before you did $c$, I didn't know whether $\phi$ was true, but now I
know that $\phi$ is false."

Keywords: Baltag-Moss-Solecki;  product update;  action models;  games