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Belief spaces as sets of propositions

Abstract It is common in the knowledge representation literature for a belief space to be considered to be a set of sentences. Some implications of this stance are examined, and an alternative view, that belief spaces are sets of propositions is developed, and found to be an improvement. This latter view requires that propositions be accepted as entities in the domain of discourse of languages of thought, which, it is argued, accords with commonsense usage. In exchange, the semantics of nested belief expressions is simplified, and certain problems caused by the sentential view are avoided.