Attribute Exploration with Background Implications and Exceptions

Implications between attributes can represent knowledge about objects in a speciied context. This knowledge representation is especially useful when it is not possible to list all speciied objects. Attribute exploration is a tool of formal concept analysis that supports the acquisition of this knowledge. For a speciied context this interactive procedure determines a minimal list of valid implications between attributes of this context together with a list of objects which are counterexamples for all implications not valid in the context. This paper describes how the exploration can be modiied such that it determines a minimal set of implications that lls the gap between previously given implications (called background implications) and all valid implications. The list of implications can be simpliied further if exceptions are allowed for the implications.