Can you solve the impossible day of the week logic puzzle?

Can you solve for the day of the week Abby was born? What about Barry? This is an incredible logic riddle.
van Ditmarsch, Hans, Michael Ian Hartley, Barteld Kooi, Jonathan Welton, and Joseph BW Yeo. "Cheryl's Birthday." arXiv preprint arXiv:1708.02654 (2017).
arxiv.org/pdf/...
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