R.I. Gen. Laws § 34-10-12: Payment for previously constructed fence.

Whenever the whole or more than one-half (½) of any partition fence shall have been made by the proprietor or possessor of the land on one side of the fence, the proprietor or possessor of the land adjoining, when he or she improves the land, shall pay to the proprietor or possessor who made the fence the value of so much of the fence erected as the fence may exceed one-half (½) of the fence on the whole line; and in case of his or her refusal so to do, the value shall be ascertained by any fence viewer of the town where the land is situated, on application to him or her for that purpose.