Closure and Justification
John Hawthorne has some nice arguments for the view that knowledge is closed under known implication. I don't know much about knowledge, but it seems to me that there is a good reason to believe that at least justification -- and hence presumably also justified true believe -- is not so closed. The reason is this:
E is some evidence, H and S are alternative and incompatible hypotheses. (Obvious examples are skeptical scenarios, like E = visual evidence of a zebra, H = there is a zebra, S = there is a mule disguised as a zebra.) E strongly supports H: It raises its probability of truth from about 0.3 to about 0.9. And H implies Not-S. Yet E does not raise the probability of Not-S. On the contrary, it raises the probability of S.
Let "S(p)" abbreviate "p is strongly supported by the availble evidence". The picture shows that
S(p) and S(p -> q) does not imply S(q);
S(p & q) does not imply S(p); (let p=-S, q=H)
S(p) does not imply S(p v q); (let p=H, q=-S).