Abstract
Decision implication is an important form of knowledge representation and acquisition in Formal Concept Analysis. Decision implication reduces the redundancy of knowledge extracted from data. However, decision implication cannot extract negative information from data, so there is information loss in decision implication. This paper introduces negative attributes to decision implication and proposes mixed decision implication, enabling decision implication to extract negative knowledge from data and to represent richer decision knowledge. This paper studies the logical systems of mixed decision implications. The semantical system of mixed decision implications is constructed to represent and deduce sound mixed decision implications and avoid contradictory mixed decision implications. In the syntactical system, Mixed Augmentation and Mixed Combination are introduced and the soundness, completeness and non-redundancy of these two inference rules are proved.
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