かねる: difficulty judging and a tactful refusal
Express difficulty making a judgment or accepting a request. Distinguish this from lacking an ability, asking someone to wait, and the risk expression かねない.
Saying a request is difficult to accept
そのご要望はお受けしかねます。 politely declines a request by saying it is difficult to accept. Despite the indirect wording, it can be an actual refusal, not a promise of imminent approval.
Add かねる to the masu-stem. 答える becomes 答えかねる, and 判断する becomes 判断しかねる. The polite ending is かねます.
Insufficient information for a judgment
この情報だけでは判断しかねます。 means that a judgment is difficult with this information alone. It identifies insufficient evidence or information, not a complete lack of personal capacity to judge.
It does not promise a definite decision if the listener simply waits longer. Check この情報だけでは and any further explanation to identify the missing conditions or next steps.
Inability differs from possible risk
泳げません。 directly expresses an inability to swim. Rather than changing every inability into a form such as 泳ぎかねます, check whether the context involves difficulty with a request, decision, or judgment.
判断しかねます expresses difficulty judging, while 誤解を招きかねません warns of possible misunderstanding. Adding a negative to かねる does not automatically produce an affirmative statement of ability.
Quick check: Does こちらではお答えしかねます。 promise that an answer will definitely be provided here?
Show the answer and why
No. It politely declines by saying that an answer cannot be provided by this side. It does not promise an actual answer or one at a later time.