Order structure of symbolic assertion objects

We study assertion objects that constitute a particular class of symbolic objects. Symbolic objects constitute a data analysis driven formalism, which can be compared to propositional calculus, but which is oriented toward the duality intension (characteristic properties) versus extension (set of all individuals verifying a given set of properties). The set of assertion objects is endowed with a partial order and a quasi-order. We focus on the property of completeness, which precisely expresses the duality intension-extension. The order structure of complete assertion objects is studied, using notions of lattice theory and Galois connection, and extending R. Wille´s work (1982) to multiple-valued data. Two results are then obtained for particular cases