Lemma

A lemma is a canonical form of a word used as the headword in dictionaries and as the unit of analysis in linguistic tasks such as lemmatization. In many languages, inflected forms reflect tense, mood, number, or case and are derived from the lemma. For example, the verb run has the lemma run, while forms like runs, ran, and running are inflected forms mapped to that lemma. In computational linguistics, lemmatization reduces words to their lemmas, often with the aid of a morphological analyzer; this is distinct from stemming, which may produce non-dictionary base forms.

In mathematics and logic, a lemma is a proven proposition used as a stepping-stone toward a larger theorem. Lemmas are typically of secondary interest themselves, but they enable more substantial results. Classic examples include Euclid's lemma, which states that if a prime divides a product and does not divide one factor, it divides the other; and Zorn's lemma, a principle equivalent to the axiom of choice used to establish numerous theorems.

The term derives from the Greek lemmá, meaning "assumption" or "premise." In dictionaries, the lemma is the form under which all inflected variants are organized. In natural language processing and corpus linguistics, lemmatization supports consistent indexing and search by collapsing inflected variants to their lemmas.