Contingent planning models a robot that must achieve a goal in a partially observable environment with non-deterministic actions. A solution for this problem is generated by searching in the space of belief states, where a belief state is a set of possible world states. However, if there is an unavoidable dead-end state, the robot will fail to accomplish his task. In this work, rather than limiting a contingent planning task to the agent's actions and observations, we model a planning agent that is able to proactively resort to humans for help in order to complete tasks that would be unsolvable otherwise. Our aim is to develop a symbiotic autonomous agent, that is, an agent that, proactively and autonomously, asks for human help when needed. We formalize this problem and propose an extension of a translation technique to convert the contingent planning problem with human help into a non-deterministic fully observable planning problem that can be solved by an off-the-shelf efficient FOND planner.
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The purpose of this paper is to investigate the extension problem for the category of commutative hypergroups. In fact, by applying the new notion of a field of compact subhypergroups, sufficiently many extensions can be established, and among them splitting extensions can be characterized. Moreover, the duality of extensions will be studied via duality of fields of hypergroups. The method of extension via fields of hypergroups yields the construction of Pontryagin hypergroups which do not arise from group-theoretic objects.
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