Lattice Theory Enables Unbiased Set-Valued AI Oracles.

The paper addresses a fundamental challenge for non-agentic AI oracles: how to provide unbiased predictions when the act of reporting an answer can inherently alter the probability of the event being predicted. Traditional counterfactual approaches, which assume no influence, often render the oracle's answer irrelevant once learned. Instead, this research proposes a novel self-referential alternative. The oracle reports not a single probability estimate, but rather a "credal set"—an interval of probabilities—that is simultaneously unbiased and self-consistent with the consequences of its own disclosure. This approach acknowledges and incorporates the oracle's influence on the future. To identify a canonical and useful credal set from the many possibilities, the authors employ the Knaster-Tarski fixed-point theorem within the complete lattice of closed credal sets. They define an isotone operator whose least fixed point yields this canonical answer. For binary events, this construction results in a clear interval, extending the concept from point estimates to a more robust, self-consistent range of probabilities.