Efforts towards endowing robots with the ability to speak have benefited from recent advancements in natural language processing, in particular large language models. However, current language models are not fully incremental, as their processing is inherently monotonic and thus lack the ability to revise their interpretations or output in light of newer observations. This monotonicity has important implications for the development of dialogue systems for human--robot interaction. In this paper, we review the literature on interactive systems that operate incrementally (i.e., at the word level or below it). We motivate the need for incremental systems, survey incremental modeling of important aspects of dialogue like speech recognition and language generation. Primary focus is on the part of the system that makes decisions, known as the dialogue manager. We find that there is very little research on incremental dialogue management, offer some requirements for practical incremental dialogue management, and the implications of incremental dialogue for embodied, robotic platforms in the age of large language models.
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