A definition from Webster's 1828 dictionary:

SEMI-PELA'GIAN, n.In ecclesiastical history, the Semi-pelagians are persons who retain some tincture of the doctrines of pelagius. See Pelagianism. They hold that God has not by predestination dispensed his grace to one more than another; that Christ died to all men; that the grace purchased by Christ and necessary to salvation, is offered to all men; that man, before he receives grace, is capable of faith and holy desires; and that man being born free, is capable of accepting grace, or of resisting its influences.