  Despite the superior performance of large language models to generate natural
language texts, it is hard to generate texts with correct logic according to a
given task, due to the difficulties for neural models to capture implied rules
from free-form texts. In this paper, we propose a novel graph-based language
model, Logical-GLM, to infuse logic into language models for more valid text
generation and interpretability. Specifically, we first capture information
from natural language instructions and construct logical bayes graphs that
generally describe domains. Next, we generate logical skeletons to guide
language model training, infusing domain knowledge into language models.
Finally, we alternately optimize the searching policy of graphs and language
models until convergence. The experimental results show that Logical-GLM is
both effective and efficient compared with traditional language models, despite
using smaller-scale training data and fewer parameters. Our approach can
generate instructional texts with more correct logic owing to the internalized
domain knowledge. Moreover, the usage of logical graphs reflects the inner
mechanism of the language models, which improves the interpretability of
black-box models.
