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Assistive shared-control robots have the potential to transform the lives of millions of people afflicted with severe motor impairments. The usefulness of shared-control robots typically relies on the underlying autonomy's ability to infer the user's needs and intentions, and the ability to do so unambiguously is often a limiting factor for providing appropriate assistance confidently and accurately. The contributions of this paper are four-fold. First, we introduce the idea of intent disambiguation via control mode selection, and present a mathematical formalism for the same. Second, we develop a control mode selection algorithm which selects the control mode in which the user-initiated motion helps the autonomy to maximally disambiguate user intent. Third, we present a pilot study with eight subjects to evaluate the efficacy of the disambiguation algorithm. Our results suggest that the disambiguation system (a) helps to significantly reduce task effort, as measured by number of button presses, and (b) is of greater utility for more limited control interfaces and more complex tasks. We also observe that (c) subjects demonstrated a wide range of disambiguation request behaviors, with the common thread of concentrating requests early in the execution. As our last contribution, we introduce a novel field-theoretic approach to intent inference inspired by dynamic field theory that works in tandem with the disambiguation scheme.