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Machine teaching is an algorithmic framework for teaching a target hypothesisvia a sequence of examples or demonstrations. We investigate machine teachingfor temporal logic formulas -- a novel and expressive hypothesis class amenableto time-related task specifications. In the context of teaching temporal logicformulas, an exhaustive search even for a myopic solution takes exponentialtime (with respect to the time span of the task). We propose an efficientapproach for teaching parametric linear temporal logic formulas. Concretely, wederive a necessary condition for the minimal time length of a demonstration toeliminate a set of hypotheses. Utilizing this condition, we propose a myopicteaching algorithm by solving a sequence of integer programming problems. Wefurther show that, under two notions of teaching complexity, the proposedalgorithm has near-optimal performance. The results strictly generalize theprevious results on teaching preference-based version space learners. Weevaluate our algorithm extensively under a variety of learner types (i.e.,learners with different preference models) and interactive protocols (e.g.,batched and adaptive). The results show that the proposed algorithms canefficiently teach a given target temporal logic formula under various settings,and that there are significant gains of teaching efficacy when the teacheradapts to the learner's current hypotheses or uses oracles.

Adaptive Teaching of Temporal Logic Formulas to Learners with Preferences