  With good explanatory power and controllability, rule-based methods play an
important role in many tasks such as knowledge reasoning and decision support.
However, existing studies primarily focused on learning chain-like rules, which
limit their semantic expressions and accurate prediction abilities. As a
result, chain-like rules usually fire on the incorrect grounding values,
producing inaccurate or even erroneous reasoning results. In this paper, we
propose the concept of tree-like rules on knowledge graphs to expand the
application scope and improve the reasoning ability of rule-based methods.
Meanwhile, we propose an effective framework for refining chain-like rules into
tree-like rules. Experimental comparisons on four public datasets show that the
proposed framework can easily adapt to other chain-like rule induction methods
and the refined tree-like rules consistently achieve better performances than
chain-like rules on link prediction. The data and code of this paper can be
available at https://anonymous.4open.science/r/tree-rule-E3CD/.
