The Structure of Implications on a Complete Brouwerian Lattice
Weicai Li, Feng Qin, Zhihong Yi · 2007
Investigate the set of all implications on a complete Brouwerian lattice. Define operators to endow these sets as monoid structure, which are also complete Brouwerian lattice. Then discuss the implication operators on a linear complete Brouwerian lattice, and propose a method to generate new implication operators. Moreover, the contra-positive symmetrization property of implication operators and the relation between two comparable implications on [0, 1] are studied.