  Multi-hop logical reasoning on knowledge graphs is a pivotal task in natural
language processing, with numerous approaches aiming to answer First-Order
Logic (FOL) queries. Recent geometry (e.g., box, cone) and probability (e.g.,
beta distribution)-based methodologies have effectively addressed complex FOL
queries. However, a common challenge across these methods lies in determining
accurate geometric bounds or probability parameters for these queries. The
challenge arises because existing methods rely on linear sequential operations
within their computation graphs, overlooking the logical structure of the query
and the relation-induced information that can be gleaned from the relations of
the query, which we call the context of the query. To address the problem, we
propose a model-agnostic methodology that enhances the effectiveness of
existing multi-hop logical reasoning approaches by fully integrating the
context of the FOL query graph. Our approach distinctively discerns (1) the
structural context inherent to the query structure and (2) the relation-induced
context unique to each node in the query graph as delineated in the
corresponding knowledge graph. This dual-context paradigm helps nodes within a
query graph attain refined internal representations throughout the multi-hop
reasoning steps. Through experiments on two datasets, our method consistently
enhances the three multi-hop reasoning foundation models, achieving performance
improvements of up to 19.5%. Our code is available at
https://github.com/kjh9503/caqr.
