Imprecise beliefs: a tiny introduction

davidad has posted to the AI Alignment Forum a technical framework arguing that standard probability distributions fail to capture the full range of beliefs a reasoner needs. The piece, prompted by a challenge from fellow researcher Richard Ngo, identifies specific gaps: probability distributions can't formally express independence between variables, or the conditional probability structures that reasoning requires. davidad proposes defining beliefs as mathematical functionals and demonstrates how several existing frameworks in AI safety and statistics—credal sets, infra-Bayesian reasoning, and others—all fit within this unified model.

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