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One response, advocated for the Scientist AI programme, is to ask only counterfactual questions, evaluated as if the answer had no influence. We observe that such answers tend to become irrelevant the moment they are learned, precisely because their premise is then false. We therefore explore a self-referential alternative in which the oracle reports not a single probability but a credal set that is simultaneously unbiased and self-consistent with the consequences of being learned. The naive self-consistency requirement is satisfied by too many sets (including the useless answer $[0,1]$), so the problem is to single out a canonical, nontrivial member. We do so with the Knaster--Tarski fixed-point theorem on the complete lattice of clos","title":"Unbiased Canonical Set-Valued Oracles Via Lattice Theory","url":"https://arxiv.org/abs/2606.26418","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.26418v1 Announce Type: new \nAbstract: A non-agentic \"oracle\" AI that estimates probabilities of future events faces a self-reference problem: once its answer is learned and acted upon, it can change the very probability it was asked to report. One response, advocated for the Scientist AI programme, is to ask only counterfactual questions, evaluated as if the answer had no influence. We observe that such answers tend to become irrelevant the moment they are learned, precisely because their premise is then false. We therefore explore a self-referential alternative in which the oracle reports not a single probability but a credal set that is simultaneously unbiased and self-consistent with the consequences of being learned. The naive self-consistency requirement is satisfied by too many sets (including the useless answer $[0,1]$), so the problem is to single out a canonical, nontrivial member. 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