Through Artificial intelligence, are we expecting action based intelligence? or it is BI first then AI?
How AI is relevant in solving problems like Cyber Security?
AI is a tool (and is not the first step in smart technology) like excel. Business intelligence is a collection of all the output of all applications/tools, coupled with decision making ability to optimize and evolve a business. BI can be augmented with AI (most "AI" is not really AI and VCs are exhausted hearing pitches about it that are inaccurate). BI can make AI better. However, if an idiot builds the AI, you will have IAI. Your question about AI and cyber security needs more framing. What problem in cyber security are you referencing?
Artificial Intelligence: This subject deals with Logic, Reasoning, Graph Traversing/Mining etc. It deals with automatic ways of reasoning and reaching to a conclusion by computers. Some of the algorithms of this domain are BFS, DFS, A*, Djikstra, Best First, Backtracking etc.
Business Intelligence: This field is even more business goal focused than Data Mining. There is no algorithm for this rather it is a skill of converting raw data to useful information for the business. Data sources could be internet search, internal business sources, web click data, customer feedback data etc.