Interactive Error Correction in Implicative Theories
This work addresses error correction in implicative theories, which is incremental as it builds on existing methods in Formal Concept Analysis.
The paper tackles the problem of errors in implicative theories from binary data by proposing two interactive approaches based on Formal Concept Analysis, one using a canonical base and another polynomial-time method, with results discussed from computer experiments.
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.