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potato comments on Timeless Decision Theory and Meta-Circular Decision Theory - Less Wrong
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Quick stupid question: what does "A[]->O" stand for? specifically "[]->"? Is that a material implication? Should I read it as "P(O|A is the output of this computation and rest of universe)"?
(edit): could someone please help with this?
I suck at symbolic logic or computer logic or whatever so I'm commenting in the hope that someone else sees my comment and answers your question.
It means "If A were true, then O would be true." Note that this is a counterfactual statement.
I could be wrong about this, but I believe the arrow is intended to indicate a functional mapping, and the [] is some noise about types. So: The probability that (this computation yields a lambda mapping A to O) given (rest of universe).
It would be nice if someone weighed in with something more definitive. Various reference materials, along with search tools such as Google and Symbolhound, are not particularly helpful.