Rule acquisition is one of the main purposes in the analysis of formal decision contexts. Up to now, there have been several types of rules in formal decision contexts such as decision rules, decision implications, and granular rules, which can be viewed as ∧‐rules since all of them have the following form: “if conditions 1,2, …, and m hold, then decisions hold.” In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward two new types of rules which are called ∨‐rules and ∨‐∧ mixed rules based on formal, object‐oriented, and property‐oriented concept lattices. Moreover, a comparison of ∨‐rules, ∨‐∧ mixed rules, and ∧‐rules is made from the perspectives of inclusion and inference relationships. Finally, some real examples and numerical experiments are conducted to compare the proposed rule acquisition algorithms with the existing one in terms of the running efficiency.