A Unified View of Consequence Relation, Belief Revision and Conditional Logic

The notion of minimality is widely used in three different areas of Artificial Intelligence: nonmonotonic reasoning, belief revision, and conditional reasoning. However, it is difficult for the readers of the literature in these areas to perceive the similarities clearly, because each formalization in those areas uses its own language sometimes without referring to other formalizations. We define ordered structures and families of ordered structures as the common ingredient of the semantics of all the works above. We also define the logics for ordered structures and families. We present a uniform view of how minimality is used in these three areas, and shed light on deep reciprocal relations among different approaches of the areas by using the ordered structures and the families of ordered structures.