First of all, absolutely do not accept any payment from the logger as it may be construed as payment of damages for the wrongful act. Instead, please contact your local Illinois Department of Natural Resources Conservation Police Officer (CPO) in order to file a formal complaint of wrongful tree cutting (i.e., timber theft). Please work with your local Conservation Police Officer to determine which course of action you should take--the CPO will likely recommend that you work with an IDNR district forester or a professional consulting forester to determine the approximate volume and value of the trees wrongfully cut.
Here in Illinois, we have an Illinois Compiled Statute, listed under Civil Liabilities, that is entitled: (740 ILCS 185/) Wrongful Tree Cutting Act.
Fortunately, the victims of wrongful tree cutting here in Illinois have several options of recourse when it comes to timber theft/trespass. Part of this Act states that the offended party shall be awarded “treble stump damages” — in other words, the individual who illegally cut your trees shall pay the offended party three times the appraised value of the timber that was wrongfully cut.
The entire Act can be found here: http://www.ilga.gov/legislation/ilcs/ilcs3.asp?ActID=2060&ChapAct=740%26nbsp%3BILCS%26nbsp%3B185%2F&ChapterID=57&ChapterName=CIVIL+LIABILITIES&ActName=Wrongful+Tree+Cutting+Act.
Illinois DNR Office of Law Enforcement http://dnr.state.il.us/law3/
Please Note: The "Wrongful Tree Cutting Act" is intended for forestry-related acts of wrongful tree cutting (i.e., timber trespass), not wrongful tree cutting or vandalism with regard to ornamental/landscape trees. Unfortunately, I know of several instances where this law has been misinterpreted by Illinois lawyers and judges in cases involving landscape or ornamental trees--this is not the intent of 740 ILCS 185. The only such exception I can think of relating to a situation involving a landscape/yard tree is the deliberate theft of a high-value black walnut tree from someone's yard.