A Lexicographic Inference for Partially Preordered Belief Bases
Sadok Ben Yahia, Salem Benferhat, Sylvain Lagrue, O. Papini · 2015
Coherence-based approaches are quite popular to reason un-der inconsistency. Most of them are defined with respect to totally preordered belief bases such as the lexicographic inference which is known to have desirable properties from theoretical, practical and psychological points of view. How-ever, partially preordered belief bases offer much more flex-ibility to represent efficiently incomplete knowledge and to avoid comparing unrelated pieces of information. In this pa-per, we propose a lexicographic inference for partially pre-ordered belief bases that extends the classical one. On one hand, we define a natural inference relation which consists in applying classical lexicographic inference from all compat-ible totally preordered belief bases. On the other hand, we propose a novel cardinality-based preorder between consis-tent subbases. This cardinality-based preorder can be indif-ferently applied on partially or totally preordered belief bases. Then, applying classical inference on the preferred consistent subbases, according to this preorder, provides another lex-icographic inference relation for partially preordered belief bases. Interestingly enough, we show that these two infer-ence relations are equivalent. Lastly, a semantic characteriza-tion of these two equivalent definitions is provided.