On the Compilation of Stratified Belief Bases under Linear and Possibilistic Logic Policies

Developing efficient approaches for reasoning under inconsistency is an important issue in many applications. Several methods have been proposed to compile, possibly inconsistent, weighted or stratified bases. This paper focuses on the well-known linear order and possibilistic logic strategies. It provides a way for compiling a stratified belief base in order to be able to process inference from it in polynomial time. The resulting extra compilation cost is very low. In particular, the number of additional variables, that are added to original stratified bases, corresponds exactly to the number of priority levels existing in the base. Moreover, our compilation approach allows an efficient computation of weighted possibilistic conclusions and possibilistic conditioning.