A Logic of Attribute Containment

We present a logic of if-then rules such as "if all attributes of an object are among those from A then they are among those from B." The attributes can either be yes/no attributes, such as male and has all wheel drive, or graded attributes, such as red and good performance which apply to objects to certain grades. We assume an abstract nonnumeric framework in which the grades form a particular bounded partially ordered set equipped with aggregation operators. For such framework, we provide basic syntactic and semantic notions, describe complete non-redundant sets of the if-then rules, and a logic for reasoning with such dependencies with its ordinary-style and graded-style completeness.