Perelman & Olbrechts-Tyteca introduce the class of quasi-logical arguments as the first of the three categories of “association schemes” ([1958], p. 191), that is argument schemes. Quasi-logical arguments can be understood “by bringing them closer to formal thought, logical or mathematical. But a quasi-logical argument differs from a formal deduction in that it always presupposes adherence to non-formal theses, which alone allows the application of the argument” (Perelman 1977, p. 65)

Six schemes are more precisely analyzed, and these bear the same name as their logical counterparts:

Among the quasi-logical arguments, we shall first analyze those which depend on logical relations — contradiction, total or partial identity, transitivity; we shall then analyze those which depend on mathematical relations — the connection between the part and the whole, the smaller and the larger, and frequency. Many other relations could obviously be examined. (Perelman & Olbrechts-Tyteca [1958], p. 194)

Definitions are “typical of quasi-logical argumentation” (id., p. 214):

When they are not part of a formal system, and when they nevertheless claim to identify the definiens and the definiendum, we shall consider them a form of quasi-logical argumentation” (id., p. 210).

The “quasi-logical” label is symptomatic of the method of the Treatise, rejecting “logic” but constantly using it a contrario to define argumentation in general and in particular to characterize the “quasi-logical” super-category of argument schemes. The category includes all the argumentative strategies involving phenomena such as negation, scales, relations and definitional stereotypes. In fact, it is the system of language that is considered to be a quasi-logic.

The arguments in this category are defined by a common characteristic:

[Quasi-logical arguments] lay claim to a certain power of conviction, in the degree that they claim to be similar to the formal reasoning of logic or mathematics. Submitting these arguments to analysis, however, immediately reveals the differences between them and formal demonstrations, for only an effort of reduction or specification of a non-formal character makes it possible for these arguments to appear demonstrative. This is why we call them quasi-logical. (Id., p. 193)

According to the traditional definition, a fallacy is an argument that looks like a valid argument but is not. There is a striking similarity between this, and the definition given in the Treatise: quasi-logical argumentation “claim[s] to be similar” to formal reasoning, but is not.

S. Fallacies; Logic; Collections (III).