False all the k-related worlds the result follows

Usefulness 3§14

Let us now consider some more examples in which our interval arithmetic approach can be shown to be useful and valid. We begin with a simple example. Suppose we have two relational fluents P, and Q, and that we know P is true or we know Q is true:

Proof. The proof is straightforward: We don’t know P if in at least one of the K-related worlds P is false.

So, if P is false in all the K-related worlds the result follows. We just have to be careful that there are any

Proof.

Knows′(¬P, s)