A formal framework for characterizing querying algorithms

Algorithmic procedures have been devised for constructing a knowledge space by querying experts. The queries submitted to the expert consist of assertions that are to be accepted or rejected. The present paper provides a characterization of the algorithms that may be used to draw inferences from previously collected answers. It is based on the notion of a closure on the set of all assertions, and its extension to a set containing for each assertion a positive and a negative instance, representing acceptance and rejection, respectively. The developed characterization emphasizes the significance of the well-known QUERY and PS-QUERY procedures. Potential applications of the presented results in contexts other than knowledge space theory are pointed out.