Abatements are, supposedly, additions made to a coat of arms to indicate dishonorable behavior on the part of the bearer.
Sir Christopher Lynch-Robinson, Intelligible Heraldry (1967), lists 7 cases: lying, boasting, sloth in war, drunkeness, killing a prisoner who has yielded, seduction or rape, revoking a challenge. He adds: "There is the argument that you cannot equitably have good conduct marks without bad conduct marks ...there is no reason why the minor peccadilloes ... should not have been recorded until by some deed of valour he wiped out the stain on his escutcheon."
He cites to Guillim's A Display of Heraldry and Vulson de la Colombiere's La Science Héroïque, plus Shelden Treatise on Titles of Honor.
G. Leigh's Accedence of Armory (1562) lists the abatements as:
These abatements appear to be a pure fiction (albeit a fairly old one). Here are a few quotes from reliable writers:
Guillim, Display of Heraldrie, viii. sect.1. 31 (1611): "An Abatement is an accidentall mark annexed to coat-armour denoting some vngentleman-like, dishonorable, or disloiall demeanour qualitie or staine in the bearer whereby the dignitie of the coate-armour is greatly abased."
Chambers Cyclopaedia (1751), s.v.: "It is a little controverted among authors, whether heraldry allows of any such things as regular abatements..The last editor of Guillim discards the whole notion of Abatements as a chimaera."
Charles Boutell, English Heraldry (1883), p.213: "Abatement is a term which was unknown until it made its appearance in certain heraldic writings of the 16th century, when it was used to denote such marks or devices as, by the writers in question, were held to be the reverse of honourable Augmentation-Augmentations of dishonour indeed, tokens of degradation. True Heraldry refuses to recognise all such pretended abatements, for the simple reason that, if they could exist at all, they would be in direct antagonism to its nature, its principles, and its entire course of action. Honourable itself, Heraldry can give expression only to what conveys honour, and it records and commemorates only what is to be honoured and held in esteem. All the devices of Heraldry, accordingly, in their various degrees, are "Tokens of Honour;" and "Arms," if they attest anything whatever, "are the testimony of some noble action." The very idea of an heraldic Abatement implies, if not a complete ignorance, certainly a thorough misconception of the character and office of heraldry. Even if Heraldry were to attempt to stigmatise what is, and what ought to be esteemed, dishonourable, who would voluntarily accept insignia of disgrace, and charge and display them upon his Shield, and transmit them to his descendants? And the believers in Abatement must hold that Heraldry can exert no compulsory legislative power, which might command a man to blazon his own disgrace, and force him to exhibit and to retain, and also to bequeath, any such blazonry. A belief in heraldic Abatement, however, is by no means singular or rare. [Boutell cites the case of the muzzle on the bear, badge of the Beauchamps, and the argument made by some that it is an abatement that should be removed.] [...] neither at Warwick nor elsewhere is there such a thing as "Abatement" in English heraldry."
Parker, A Glossary of terms Used in Heraldry (1894): "Abatements, sometimes called Rebatements, are marks of disgrace attached to arms on account of some dishonourable act of the bearer. They are shewn by pieces of different shapes being to all appearance cut out of, or off from, the shield; their shapes and positions are represented by the following varieties, which are nine in number, and must be either sanguine or tenné, which the old writers call "staynande colours," otherwise they are no abatements but honourable charges, viz.-
As the use of arms is not compulsory, a bearer would of course rather relinquish them than publish his own disgrace by bearing them abated. Abatements such ass the above exist only in systems of heraldry, and no instance of their actual use is on record: but under the several headings diagrams will be found explaining the meaning of the terms which are used by heraldic writers.
Broken chevrons, and beasts turned towards the sinister, are supposed by some heraldic writers to have been given as abatements.
"And Edward the Third of England ordained two of six stars which a gentleman had in his arms to be effaced, because he had sold a seaport of which he was made governor." [According to Sir George Mackenzie, in allusion to Aymery of Pavia, a Lombard, governor of Calais in 1349, who bore azure four mullets or.]
There is another mark of disgrace which is due only to the traitor: it consists in debasing or reversing the entire coat."
Woodward, A Treatise on Heraldry (1895), p.676: "Abatements. Certain marks of disgrace invented by the old heralds, but which naturally never came into use. Menetrier [a 17th c. French heraldist] justly calls them "sottises Anglaises." The marks of illegitimacy are the only abatements in use."
A.C. Fox-Davies, A Complete Guide to Heraldry (1909): "The subject of abatements is one of those pleasant little insanities which have done so much to the detriment of heraldry. One, and one only, can be said to have had the slightest foundation in fact; that was the entire reversal of the escutcheon in the ceremony of degradation following upon attainder for high treason. Even this, however, was temporary, for a man forfeited his arms entirely by attainder. [...] But that any person should have been supposed to have been willing to make use of arms carrying an abatement is preposterous, and no instance of such usage is known. Rather would a man decline to bear arms at all; and that any one should have imagined the existence of a person willing to advertise himself as a drunkard or an adulterer, with variations in the latter case according to the personailty of his partner in guilt, is idiotic in the extreme."
Guy Cadogan Rothery, Concise Encyclopaedia of Heraldry (1915, repr. 1985): "Abatement, or Rebatement. Mark of dishonour invented by certain writers and intended to be used in debruising coats by arms. As a matter of fact the only abatements ever adopted were those relating to illegitimacy of birth."
Boutell's Heraldry (1950, rev. C.W. Scott-Giles), p.123: "Marks of bastardy have sometimes been called abatements, because they abate the status of the arms to the extent of showing that their owner is not in the legitimate line of succession. It should be noted that the word abatement is not used as implying dishonour. There is no such thing as a mark of dishonour in heraldry."
Woodcock and Robinson, The Oxford Guide to Heraldry (1988), p.68: "In contrast [to the nine augmentations of honor] there are also nine abatements of honour which could be added to arms by the Court of Chivalry for base behavior. As no examples exist of arms with such abatements, at best they are a theoretical punishment to discourage armigers from dishonourable acts."
Thus, abatements seem to me a perfect specimen of the what Gheusi called the work of idle heraldists, inventing rules which neither describe nor influence actual practice.
Scottish heraldry may be the only exception. In Scots Heraldry, Innes of Learney mentions abatements in marital situations (p.153, footnote 3): "The law of arms provides for abating the arms of an adulterer by two gussets sanguine, and where the bearing of arms is necessary this, and one gusset (they will be close-gussts) for non-adulterous divorcees, are, at least in Patents, applied in the case of divorcees."
In French blazon, diffamé is the term used to denote an animal whose tail is cut off (defamed in English). Literally, it means "deprived or its reputation" (fama=reputation in Latin). It is also said of arms which have been altered, by the removal of an element or the addition of a dishonorable element, to signify loss of honor. One example often cited is that of Jean d'Avesnes who, having insulted his mother Marguerite countess of Flanders in the presence of king Louis IX, purportedly saw his arms diffamées, and the lion was made morné, that is, without teeth or claws. It is taken by writers to be a mark of infamy, but it is found in several Briton coats, and also used as a canting device for the family de Mornay.
A lion with its tail between its hind legs is termed "couard" (coward), and may also be a mark of infamy.
I do not know for sure, of course, but my guess is that the concept of abatement is typical of the decay in which heraldry entered after the 16th century, at a time when the medieval world disappeared and heraldry ceased to be a natural, organic element of society. The 16th and 17th centuries saw many attempts to hijack heraldry and endow it with meaning it never had, in particular restricting it to the nobility, or regulating its usage by the sovereign, and turning it into some semantic of honor. In truth, a coat of arms could at times be used to signify marks of honor (the use of royal augmentations being an example), but those were not very frequent (and rather rare in English heraldry). One spoke of one's coat of arms as a source of pride and honor, but just as well, one spoke of one's name in the same way. A name, and a coat of arms, were made honorable by those who bore them, but they were so only in relation to the individuals and families they were associated with; of their own, they never mean anything honorable.
The fact that Enlgish heraldry invented such a bureaucratic system of abatements is also a reflection of the change that heraldry underwent in that country, when Henry VIII and later the Stuarts regulated it. Only in a country where the law, and a set of government officials, determined who could use arms and who couldn't, could such a system be dreamed of. To believe one instant in abatements requires the belief that the bearing of arms can not only be prohibited, but also forced. Only England and Scotland ever had anything approaching the legal institutions requisite for the implementation of abatements. Even then, British writers on heraldry are clearly under no illusions in the matter.