Numerical Representations of Acceptance
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Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of acceptance, what we call acceptance functions. Due to the monotonicity property of confidence measures, the acceptance of a proposition entails the acceptance of any of its logical consequences. In agreement with the idea that a belief set (in the sense of Giirdenfors) must be closed under logical consequence, it is also required that the separate acceptance of two propositions entail the acceptance of their conjunction. Necessity (and possibility) measures agree with this view of acceptance while probability and belief functions generally do not. General properties of acceptance functions are established. The motivation behind this work is the investigation of a setting for belief revision more general than the one proposed by Alchourr6n, Giirdenfors and Makinson, in connection with the notion of conditioning.
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