Comparing and Weakening Possibilistic Knowledge Bases

Weighted logics are important tools for reasoning under uncertain knowledge. A weighted knowledge base is a set of weighted formulas of the form (φi, αi) where φi is a propositional formula and αi is the certainty degree associated with φi. This paper addresses two issues in the possibility theory framework: i) how to compare two weighted knowledge bases with respect to their information contents? and ii) how to syntactically define the concept of forgetting variables? We show that comparing knowledge bases is the counterpart of the concept of the specificity relation defined between possibility distributions.