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We argue for a new inference-based analysis of belief attribution in which the embedded proposition is inferable from, but need not directly identify, an underlying belief of the subject’s. The analysis accounts for attributions of belief in necessary truths and falsities, overcoming a major difficulty facing Hintikka (1962), and goes beyond Cresswell & von Stechow (1982) in accounting for intuitively valid inferable belief attributions. The analysis is based on a novel subjective I-semantics in which extensions depend dually on extension conditions assigned by a judge, and on the judge’s beliefs about what satisfies those conditions. The interpretation of believe uses syntactic inference over logical formulas, with premises deriving from beliefs of both the attributor and the attributee, and the conclusion derived from the clause embedded under believe. Unlike nearly all prior analyses of belief attribution since Hintikka, our proposal makes no commitment to possible worlds while generating de dicto, de re, de qualitate, de translato and other interpretations, with the only formal semantic ambiguity deriving from what gets raised out of the embedded clause.