Lemma

Lemma is a minor theorem or result that is used to help prove a more complex or significant theorem. It’s essentially a stepping stone along the way to proving a larger, overarching theory. Lemmas are used to break down a complex proof into smaller, more consumable parts. While they might seem trivial or auxiliary on their own, they are often critical for the reasoning and proofs of more extensive results or theorems.

In natural language processing (NLP) lemma refers to something different. Here, a lemma is considered the base or dictionary form of a word. It serves as the way of grouping together the inflected forms of a word so they can be analyzed as a single item. For example, the words “run”, “running”, “ran”, and “runs” are all different forms of the same lexeme with “run” being the lemma. This process, called lemmatization, is used in linguistics to aid in accurate and efficient linguistic analysis of a text.

Despite being completely different concepts, whether in mathematics or natural language processing, a lemma serves as a form of simplification. In mathematics, it breaks down complex theories into simpler ones to aid understanding. In natural language processing, it simplifies text analysis by reducing words to their basic form.