There is a well known interplay between the study of algebraic varieties and propositional calculus of various logics. Prime examples of this are boolean algebras and classical logic, and Heyting algebras and intuitionistic logic. After the class of Heyting algebras was generalized to the semi-Heyting algebras by H. Sankappanavar in [San08], its logic counterpart was developed by one of us in [...

We introduce a numerical measure on sets of partitions of finite sets that is linked to the Goodman-Kruskal association index commonly used in statistics. This measure allows us to define a metric on such partions used for constructing decision trees. Experimental results suggest that by replacing the usual splitting criterion used in C4.5 by a metric criterion based on the Goodman-Kruskal coef...