Complexity and Cautiousness Results for Reasoning from Partially Preordered Belief Bases

Partially preordered belief bases are very convenient for an efficient representation of incomplete knowledge. They offer flexibility and avoid to compare unrelated pieces of information. A number of inference relations for reasoning from partially preordered belief bases have been proposed. This paper sheds light on the following approaches: the partial binary lexicographic inference, the compatible-based lexicographic inference, the democratic inference, the compatible-based inclusion inference, the strong possibilistic inference and the weak possibilistic inference. In particular, we propose to analyse these inference relations according to two key dimensions: the computational complexity and the cautiousness. It turns out that almost all the corresponding decision problems are located at most at the second level of the polynomial hierarchy. As for the cautiousness results, they genereally extend those obtained in the particular case of totally preordered belief bases.