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Decision implications: a logical point of view

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Abstract

This paper serves to present the semantical and syntactical aspects of decision implications. In the semantical aspect, we will introduce the notions of “closure” and “unite closure”, representing the closure of condition attributes with respect to decision attributes and the closure with respect to the whole attribute set respectively. In the syntactical aspect, we form two deduction rules, namely Augmentation and Combination, and prove that they are complete with respect to the semantical aspect. Moreover, we describe an approach to obtain a decision context from a given set of decision implications, and show that the decision context obtained can produce the same set of decision implications.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the manuscript. The work is supported by National Natural Science Foundation of China (61303107, 61272095, 61175067, 41101440, 61202018), and Project Supported by National Science and Technology (2012BAH33B01).

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Authors and Affiliations

  1. School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, China

    Zhai Yanhui, Li Deyu & Qu Kaishe

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  1. Zhai Yanhui
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  2. Li Deyu
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  3. Qu Kaishe
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Correspondence to Zhai Yanhui.

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Yanhui, Z., Deyu, L. & Kaishe, Q. Decision implications: a logical point of view. Int. J. Mach. Learn. & Cyber. 5, 509–516 (2014). https://doi.org/10.1007/s13042-013-0204-2

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