We show several representation theorems for explanatory reasoning based on cumulative models. An explanatory process is given by a binary relation £ between formulas in a propositional language where the intended meaning of α £ γ is "γ is a preferred explanation of α". To each cumulative model E (a variation of those studied by Kraus, Lehmann and Magidor) is associated an explanatory relation £ E . We show results of the following type: An explanatory relation £ satisfies certain logical postulates iff it coincides with £ E for some cumulative model E of the appropriate type.

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