Interactive Error Correction in Implicative Theories

TL;DR

This paper explores methods for interactively detecting and correcting errors in implicative theories derived from binary data, using Formal Concept Analysis to improve accuracy efficiently.

Contribution

It introduces two interactive error detection approaches based on Formal Concept Analysis, one using minimal implication bases and the other enabling polynomial-time error checking.

Findings

Both methods effectively identify errors in implicative theories.

The polynomial-time approach allows real-time error correction.

Computer experiments demonstrate practical applicability.

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.