Reasoning with partially ordered information in a possibilistic logic framework

In many applications, the reliability relation associated with available information is only partially defined, while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge. Partial pre-orders offer more flexibility than total pre-orders to represent incomplete knowledge. Possibilistic logic, which is an extension of classical logic, deals with totally ordered information. It offers a natural qualitative framework for handling uncertain information. Priorities are encoded by means of weighted formulas, where weights are lower bounds of necessity measures. This paper proposes an extension of Possibilistic logic for dealing with partially ordered pieces of knowledge. We show that there are two different ways to define a possibilistic logic machinery which both extend the standard one.