Mutual implications and granularity

This paper illustrates a technique for discovering mutual implications among hierarchically structured data. Such a technique may be applied to both knowledge and data bases. If the hierarchical structure makes it possible to define granularity levels, mutual implications can be evaluated at any level. Results can be quantitative (i.e. a degree in the range [0, 1]) or qualitative (i.e. a label taken from a user-defined set). If the ground data do not represent a mapping among individuals, i.e. the level of information granularity is not the highest, a local approximation based on T-Norms can be used. The process of implication discovery allows one to derive inference rules for expert systems and to detect default values. In addition, it might be successfully used by sophisticated machine learning algorithms.