Variable decision knowledge representation: A logical description

Decision-making is important in all science-based professions, where specialists apply their knowledge to making valuable decisions. In Formal Concept Analysis, decision-making problem is handled within decision contexts and in the form of decision implications. In this paper, we introduce the notion of variable decision implication to generalize decision implications and uncertain decision implications. We describe the semantic aspect of variable decision implications by defining the notions of follow, non-redundant, complete, etc., and provide the syntactical description by presenting three inference rules and proving their soundness and completeness. This paper also provides a re-explanation of deduction of associative rules, and should be regarded as a starting point for effectively reducing the size of associative rules.