How was Pelagianism originally formally defined? The terms "Pelagianism" and "Semipelagianism" are often used in polemical contexts, but what was specifically anathematized by the church when the Pelagian heresy was originally condemned?
The Council of Carthage (418) was called to address the issue of Pelagius and the charges against him that Jerome and Augustine had brought, as well as Donatus and his own heresy. The council drew up eight canons, condemning a heresy it ascribed to Pelagius. This has become known as Pelagianism.
From the anathemas in the first eight canons of the Council of Carthage, we can deduce the following points of Pelagian doctrine, all of which were condemned at the council:

Grace is not completely necessary for obedience (Canons 3-5)
People are not born sinful (Canon 2)
Death is natural and inevitable, not in any sense a result of sin (Canon 1)
Christians need not call themselves &quot;sinners,&quot; or ask for forgiveness, except out of humility (Canons 6-8)

The following summary of Pelagianism from B.B. Warfield in The Plan of Salvation [PDF] therefore seems apt:

[The Pelagians] built up a complete autosoteric system. On the one side this system was protected by the denial of any &quot;fall&quot; suffered by mankind in its first head, and accordingly of any entail of evil, whether of sin or mere weakness, derived from its past history. Every man is born in the same condition in which Adam was created; and every man continues throughout life in the same condition in which he is born. By his fall Adam at most has set us a bad example, which, however, we need not follow unless we choose; and our past sins, while of course we may be called to account for them and must endure righteous punishment on their account, cannot in any way abridge or contract our inherent power of doing what is right. ...  At any moment he chooses, therefore, any man can cease all sinning and from that instant onward be and continue perfect. ...
The Pelagian scheme therefore embraces the following points. God has endowed man with an inalienable freedom of will, by virtue of which he is fully able to do all that can be required of him. To this great gift God has added the gifts of the law and the gospel to illuminate the way of righteousness and to persuade man to walk in it; and even the gift of Christ to supply an expiation for past sins for all who will do righteousness, and especially to set a good example. Those who, under these inducements and in the power of their ineradicable freedom, turn from their sins and do righteousness, will be accepted by the righteous God and rewarded according to their deeds.

According to Warfield in the same document, while Pelagianism ascribed to man &quot;the whole of salvation,&quot; Semipelagianism ascribed to man &quot;the initiation of salvation,&quot; which the Second Council of Orange (529) condemned. However, Warfield (a Calvinist) laments that the council denied the &quot;certain efficacy&quot; or &quot;irresistibility&quot; of saving grace, which he and many others believe to have been a cardinal doctrine of Augustine's in his fight against Pelagius.
The blogger Turretinfan provides a helpful summary of Warfield's summary. Note that what he refers to as the &quot;sufficiency&quot; of grace is simply what Warfield calls &quot;certain efficacy&quot; or &quot;irresistibility&quot;:

In the set of definitions by Warfield:
Pelagianism [condemned at the Council of Carthage] Denies:

The sufficiency of grace;
The necessity of initial grace; and
The general necessity of grace.

Semi-Pelagianism [condemned at the Council of Orange] Denies:

The sufficiency of grace; and
The necessity of initial grace.

Semi-semi-Pelagianism [condemned by Calvinists] Denies:

The sufficiency of grace.