An implication or connotation: the meaning suggested by words or expressions beyond their literal content.
その発言には批判の含意があると受け取られた。
That remark was interpreted as having an implied criticism.
文章全体の含意を慎重に読み取ることが大切だ。
It's important to carefully read and interpret the overall implications of the text.
言葉の表面的意味と含意は必ずしも一致しない。
The surface meaning of words and their implications do not always match.
In logic: (material) implication; a relation where one proposition logically entails another (material conditional).
命題Aが命題Bを含意するとは、Aが真ならばBも真であることを意味する（マテリアル含意）。
That proposition A implies proposition B means that if A is true then B is also true (material implication).
数学の証明では、含意関係を厳密に扱う必要がある。
In mathematical proofs, implication relations must be treated rigorously.