As used in this chapter:
(A) "Cost" or "costs" includes compensation, damages, and expenses that are incident to an improvement covered by this chapter and all items of cost described in division (B) of section 133.15 of the Revised Code that are incident to an improvement covered by this chapter.
(B) "Public obligations" has the same meaning as in section 133.01 of the Revised Code.
(C) "Road" includes any state or county road or part of any state or county road, or any state or county road and any municipal corporation street, or part of a road or street of those types, which form a continuous road improvement.