ASAI link are used to deliver the ANI/CLID to applications. ASAI interfaces to the G3 through a MAPD card and typically connects to a Computer Telephone Integration (CTI) server. There are quite a number of different software packages that can connect to ASAI. For instance, Avaya has CVLAN/TSAPI and Envox has CT Connect (previously Intel NetMerge).
The ASAI link doesn't give you access to a "table" on the Definity. Instead, it sends a messages with information about a call when certain events (e.g., a call being offered to an agent) occur.
Hope this helps.