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Order Structure of Symbolic Assertion Objects
October 1994 (vol. 6 no. 5)
pp. 830-835

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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Index Terms:
knowledge representation; order structure; symbolic assertion objects; symbolic objects; data analysis driven formalism; propositional calculus; duality intension; assertion objects; lattice theory; Galois connection; multiple-valued data
P. Brito, "Order Structure of Symbolic Assertion Objects," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 830-835, Oct. 1994, doi:10.1109/69.317710
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