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As we become increasingly reliant on remote science platforms, the ability to autonomously and intelligently perform data collection becomes critical. In this paper we view these platforms as question-asking machines and introduce a paradigm based on the scientific method, which couples the processes of inference and inquiry to form a model-based learning cycle. Unlike modern autonomous instrumentation, the system is not programmed to collect data directly, but instead, is programmed to learn based on a set of models. Computationally, this learning cycle is implemented in software consisting of a Bayesian probability-based inference engine coupled to an entropy-based inquiry engine. Operationally, a given experiment is viewed as a question, whose relevance is computed using the inquiry calculus, which is a natural order-theoretic generalization of information theory. In simple cases, the relevance is proportional to the entropy. This data is then analyzed by the inference engine, which updates the state of knowledge of the instrument. This new state of knowledge is then used as a basis for future inquiry as the system continues to learn. This paper will introduce the learning methodology, describe its implementation in software, and demonstrate the process with a robotic explorer that autonomously and intelligently performs data collection to solve a search-and-characterize problem.