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Detection-based semantics does not differentiate between event detection and event occurrence and has been used for detecting events in most of the active systems that support Event-Condition-Action rules. However, this is a limitation for many applications that require interval-based semantics. In this article, we formalize the detection of Snoop (an event specification language) event operators using interval-based semantics (termed SnoopIB) in various event consumption modes. We show how events are detected using event detection graphs, and present a few representative algorithms to detect SnoopIB operators and comment on their implementation in the context of Sentinel-an active object-oriented DBMS.