The logic intrinsic meaning of "interest"

Hi,
[interest]

1. (text)Sport doesn’t hold much interest for my family.

[the logic intrinsic meaning of “for” and “interest”]:
(rephrased)Sport doesn’t hold much force towards my family, that causes someone to pay / give attention.

1. (text)That’s of no interest to me.

[the logic intrinsic meaning of “is of”, “to”]:
(rephrased)That identifies no interest towards me. = In that I am not interested.

1. (text) Can I interest you in this book?

[the logic intrinsic meaning of “in”]:
(rephrased) Can this book be of the thing in which I interest you?

The logic intrinsic way could I have used instead of text?
Thank you for your help.