New Semantics for Quantitative Possibility Theory

New semantics for numerical values given to possibility measures are provided. For epistemic possibilities, the new approach is based on the semantics of the transferable belief model, itself based on betting odds interpreted in a less drastic way than what subjective probabilities presupposes. It is shown that the least informative among the belief structures that are compatible with prescribed betting rates is nested, i.e. corresponds to a possibility measure. It is also proved that the idempotent conjunctive combination of two possibility measures corresponds to the hypercautious conjunctive combination of the belief functions induced by the possibility measures. This view differs from the subjective semantics first proposed by Giles and relying on upper and lower probability induced by non-exchangeable bets. For objective possibility degrees, the semantics is based on the most informative possibilistic approximation of a probability measure derived from a histogram. The motivati...

• Type: Conference
• Year: 2001
• Where: ECSQARU
• Authors: Didier Dubois, Henri Prade, Philippe Smets
• Keywords: Automated Reasoning, ECSQARU 2001, Possibility Measures, Possibility Measures Corresponds, Semantics