Interactive error correction in implicative theories

Abstract

Errors in implicative theories coming from binary data are studied. First, two classes of errors that may affect implicative theories are singled out. Two approaches for finding errors of these classes are proposed, both of them based on methods of Formal Concept Analysis. The first approach uses the cardinality minimal (canonical or Duquenne–Guigues) implication base. The construction of such a base is computationally intractable. Using an alternative approach one checks possible errors on the fly in polynomial time via computing closures of subsets of attributes. Both approaches are interactive, based on questions about the validity of certain implications. Results of computer experiments are presented and discussed. • Two classes of errors in binary data tables (formal contexts) are studied. • Finding errors based on computing an implication base leads to intractable solution. • Finding errors based on closure computation allows for a polynomial algorithm. • Finding errors in a data table row (object intent) is described and illustrated. • Experiments demonstrate the efficiency of finding errors via closure computation.