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A hyperidentity is a second order universal formula, i.e., a universal formula from the second order language (in the sense of A. Church and A.I. Mal'tsev). The hyperidentities of the variety of weakly idempotent lattices are completely characterized in this paper. The existence of a finite base of hyperidentities for this variety is proved as a consequence.
We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that ensures that no non-Shannon inequalities exist. It is demonstrated...
In this paper, we propose a new efficient data reduction algorithm through combining lattice with rough set. On the basis of lattice learning, the algorithm applies the concept of attribute reduction in the theory of rough sets and calculates the importance degree of attributes automatically by a density based approach. Under acceptable classification precision and complexity, it reduces row and column...
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