A key challenge in abstraction-based verification and control under complex specifications such as Linear Temporal Logic (LTL) is that abstract models retain significantly less information than their original systems. This issue is especially true for continuous-time systems, where the system state trajectories are split into intervals of discrete actions, and satisfaction of atomic propositions is abstracted to a whole time interval. To tackle this challenge, this work introduces a novel translation from LTL specifications to \( AP \) -observation automata, a particular type of Büchi automata specifically designed for abstraction-based verification. Based on this automaton, we present a game-based verification algorithm played between the system and the environment, and an illustrative example for abstraction-based system verification under several LTL specifications.