And I forgot to mention one thing in the last post which is relevant. Gaifman, in his paper, states that if in we have that then . I’ll quickly show that that’s a theorem of my approach, and, indeed, any similar approach.

Suppose that . In that case, then, my approach has that , because the agent knows B is logically implied by A. If that’s the case, then:

With equality if and only if either (A is logically certain given X) or (B is also impossible when A is false, which means it’s logically equivalent to A). So maybe this was fairly obvious to you, but if it wasn’t, now you have *that* proof in your background list of proofs and theorems!

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