There are a wide variety of applications that either require or assume the existence of some underlying definition of “interestingness.” However, interests vary from user to user, from situation to situation, and from one time to another. This diversity of interests cannot be captured through a single definition. In this paper, we propose a framework called Full Interestingness Programs (FIPs) that form a subclass of the Hybrid Knowledge Base Paradigm of Lu, Nerode and Subrahmanian. FIPs may be built “on top” of any query language whatsoever. Using FIPs, interests may be easily expressed and captured, and used on an application-specific basis using an application-independent FIP-evaluator. In this paper, we provide a formal semantics for FIPs, as well as techniques for processing requests (queries) to FIPs. University of Maryland Technical Report CS-TR-3817 and UMIACS-TR-97-57, July 25, 1997.