Successful conversations require speakers to align on the meaning of concepts, a challenging but crucial task for human-robot interaction. Understanding the process of establishing such alignment is hindered by competing interpretations of the term and isolated, unidirectional investigations of its design space. This paper argues for a design-centric understanding of conceptual alignment as a bidirectional and co-constructive process. We introduce a taxonomy that characterizes conceptual alignment dialogues along what triggers its initiation and what level(s) of conceptual understanding it concerns. We further present a dialogue act schema as an operational tool that captures the interactional moves through which alignment is achieved. Together, these contributions provide a structured foundation for analyzing, comparing, and designing conceptual alignment in human-robot interaction.

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