  Attribute exploration has been investigated in several studies, with
particular emphasis on the algorithmic aspects of this knowledge acquisition
method. In its basic version the method itself is rather simple and
transparent. But when background knowledge and partially described
counter-examples are admitted, it gets more difficult. Here we discuss this
case in an abstract, somewhat "axiomatic" setting, providing a terminology that
clarifies the abstract strategy of the method rather than its algorithmic
implementation.
