Nonsyllogistic Inference

an inference whose premises and conclusion are judgments about certain specific relations (a nonsyllogistic inference in the narrow sense of the word), or, in general, any inference that is correct within the framework of some logical calculus but cannot be formalized syllogistically (a nonsyllogistic inference in the broad sense).

The replacement of the syllogistic with more powerful and flexible logical theories and the possibility of “modernizing” the syllogistic by applying such theories demonstrate the relative nature of the classification of inferences as syllogistic or nonsyllogistic. For this reason, the concept of nonsyllogistic inference has lost its relevance in modern formal logic.