Decision implications: a logical point of view

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.