Numerical Representations of Acceptance
This work aims to provide a more general setting for belief revision in logic and AI, building on existing frameworks like AGM theory, but it appears incremental as it extends known concepts without major breakthroughs.
The paper investigates acceptance functions, a subclass of uncertainty measures that capture the idea of accepting propositions based on confidence comparisons, and establishes their general properties. It finds that necessity measures align with this view while probability and belief functions generally do not.
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 Gardenfors) must be closed under logical consequence, it is also required that the separate acceptance o 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 estabilished. The motivation behind this work is the investigation of a setting for belief revision more general than the one proposed by Alchourron, Gardenfors and Makinson, in connection with the notion of conditioning.