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Notes -
Right - the view is not that one fails to believe that P if one fails to believe all logical consequences of P, but rather that one is normatively obliged to believe those consequences insofar as you are or can become aware of them. If Dave hasn't yet realised that the number in the corner of the Sudoku matrix is a 1, then that's not a mark against his relevant states not being beliefs. However, if Dave realises that the number in the corner of the matrix should be a 1 according to the rules of Sudoku but still asserts that it's not, that's a mark against the assertion being underpinned by something other than a belief (or by a different sort of belief in special cases - e.g., if John is filling in the puzzle with aesthetic considerations in mind, and doesn't care about the rules). The point here is that there are many, many cases where people are actually aware of logical or probabilistic consequences of things that they profess, yet fail to profess or act in accordance with those consequences, suggesting that the things they profess in the first instance aren't actually beliefs in the strict sense.
To be clear, I'm happy with the idea that everyone routinely fails to anticipate or consider even the immediate implications of most of the things they assert. All that matters for pinning down the belief/s-disposition distinction is that in the case of the former but not the latter, in the cases where people are aware of the implications, they should (and as a rule do) adopt and endorse them.
A nice case! That said, what you're giving me here is an instance where someone - in virtue of the evidence at their disposal - could quite reasonably and rationally fail to draw the logical consequence that someone with better evidence would draw. That's distinct from the kinds of failures that I take to be indicative of s-disposition instances, where even when people can follow through and endorse the implications, they're not disposed to do so.
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