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 φ was true, but now I know that φ is false.” 1 Product Update 1.1 Language and Models A belief epistemic model M is a tuple M = (W, {∼j: j ∈ G}, V, w0). 1. W is a set of possible worlds, called the states of the model.

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