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Order structure of symbolic assertion objects

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1 Author(s)
Brito, P. ; Dept. de Matematica, Aveiro Univ., Portugal

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

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Knowledge and Data Engineering, IEEE Transactions on  (Volume:6 ,  Issue: 5 )