  Logical rules, both transferable and explainable, are widely used as weakly
supervised signals for many downstream tasks such as named entity tagging. To
reduce the human effort of writing rules, previous researchers adopt an
iterative approach to automatically learn logical rules from several seed
rules. However, obtaining more seed rules can only be accomplished by extra
human annotation with heavy costs. Limited by the size and quality of the seed
rules, the model performance of previous systems is bounded. In this paper, we
develop a novel framework STREAM to distill task-specific logical rules from
large pre-trained models. Specifically, we borrow recent prompt-based language
models as the knowledge expert to yield initial seed rules, and based on the
formed high-quality instance pool that acts as an intermediary role, we keep
teaching the expert to fit our task and learning task-specific logical rules.
Experiments on three public named entity tagging benchmarks demonstrate the
effectiveness of our proposed framework. With several predefined prompt
templates, our system has gained significant improvements over previous
state-of-the-art methods.
