Representation theorems for explanatory reasoning based on cumulative models

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.