Could anyone answer this question, please?
If someone apologize, and you reply "Well... I appreciate your mentioning it."
I'm going to have a presentation about apology response strategies, there is an apology respone strategies Rejection, and Thanking is a sub-strategy under rejection for example "Er thank for apologizing anyway."
I want to ask you can "Well... I appreciate your mentioning it." be ranked as thanking sub-strategy.

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It could either be sub-strategy for thanking or rejection. A lot will depend on the tone & tenor of the person thanking and the gestures made, if any. What is said & done afterwards is also significant.

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It could also be classed as a rejection sub-strategy. If you said, 'Well... I appreciate your mentioning it, but I'm still not happy about what you did', you are rejecting the apology. It depends what you say afterwards.

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Yes as word goes, precisely it is thanking sub strategy but if you are angry or upset then figuratively it may mean the other way round. Generally you can take it for granted that it comes under thanking strategy

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Yes. Anyone could.