Full Idea
Free logic is an unusual example of a non-classical logic which is first-order.
Clarification
First-order includes quantification over objects
Gist of Idea
Free logic is one of the few first-order non-classical logics
Source
Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], Pref)
Book Reference
Priest,Graham: 'Introduction to Non-Classical Logic' [CUP 2001], p.-9