The meaning of a concept in use is shaped by the situation, task, goals, and prior knowledge. For example, a request to make a poster "visually appealing for a five-year-old" might evoke bright colors and cartoon imagery for one collaborator, but less text, bold shapes, and visual simplicity for another. We call such task-relevant differences conceptual misalignment. We introduce Alignment Games, a framework for making these differences visible and repairable during human-AI interaction. Drawing on theories of situated conceptualization, we characterize task-specific conceptual frames in terms of relevant attributes, values, relations, constraints, and priorities. We then define alignment moves that intervene on the situation, the reasoning used to interpret it, or the resulting frame. Through examples from educational content generation, creative coding, and argumentative writing, we show how these moves can be composed into repair sequences and derive design principles for supporting task-sufficient conceptual alignment at runtime.

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