  Many AI applications rely on knowledge encoded in a locigal knowledge base
(KB). The most essential benefit of such logical KBs is the opportunity to
perform automatic reasoning which however requires a KB to meet some minimal
quality criteria such as consistency. Without adequate tool assistance, the
task of resolving such violated quality criteria in a KB can be extremely hard,
especially when the problematic KB is large and complex. To this end,
interactive KB debuggers have been introduced which ask a user queries whether
certain statements must or must not hold in the intended domain. The given
answers help to gradually restrict the search space for KB repairs.
  Existing interactive debuggers often rely on a pool-based strategy for query
computation. A pool of query candidates is precomputed, from which the best
candidate according to some query quality criterion is selected to be shown to
the user. This often leads to the generation of many unnecessary query
candidates and thus to a high number of expensive calls to logical reasoning
services. We tackle this issue by an in-depth mathematical analysis of diverse
real-valued active learning query selection measures in order to determine
qualitative criteria that make a query favorable. These criteria are the key to
devising efficient heuristic query search methods. The proposed methods enable
for the first time a completely reasoner-free query generation for interactive
KB debugging while at the same time guaranteeing optimality conditions, e.g.
minimal cardinality or best understandability for the user, of the generated
query that existing methods cannot realize.
  Further, we study different relations between active learning measures. The
obtained picture gives a hint about which measures are more favorable in which
situation or which measures always lead to the same outcomes, based on given
types of queries.
