# Lemma

(Redirected from Mathematical Corollary)

## References

• http://en.wiktionary.org/wiki/lemma
• 1. (mathematics) A proposition proved or accepted for immediate use in the proof of some other proposition.
• 2. (linguistics, usually) The canonical form of an inflected word; usually, for verbs: the infinitive or the present tense, first person singular; and for nouns: the nominative singular.
• 3. (linguistics, less frequently) A lexeme; all the inflected forms of a term.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Lemma_(linguistics)#Psycholinguistics
• Psycholinguistics: When we produce a word, we are essentially turning our thoughts into sounds (a process known as lexicalisation). In many psycholinguistic models this is considered to be at least a two-stage process. The lemma is thus intermediate between the semantic level (where meaning is specified) and the phonological level (where the sounds of the word are specified). It is an abstract form containing syntactic information (about how the word can be used in a sentence), but no information about the pronunciation of the word. In this context, the lexeme is the phonologically specified form that is selected after the lemma.
• This two-staged model is the most widely supported theory of speech production in psycholinguistics [2], although it has been recently challenged. [3] For example, there is some evidence to indicate that the grammatical gender of a noun is retrieved from the word's phonological form (the lexeme) rather than from the lemma. [4] This is easily explained by Caramazza's Independent Network model, which does not assume a distinct level between the semantic and the phonological stages (so there is no lemma representation); in this model, syntactic information about the word in this model is activated in the semantic or phonological level (so gender would be activated in the latter). [5]
• http://planetmath.org/encyclopedia/Lemma.html
• There is no technical distinction between a lemma, a proposition, and a theorem. A lemma is a proven statement, typically named a lemma to distinguish it as a truth used as a stepping stone to a larger result rather than an important statement in and of itself. Of course, some of the most powerful statements in mathematics are known as lemmas, including Zorn's Lemma, Bezout's Lemma, Gauss' Lemma, Fatou's lemma, etc., so one clearly can't get too much simply by reading into a proposition's name.
• Even less well-defined is the distinction between a proposition and a theorem. Many authors choose to name results only one or the other, or use both more or less interchangeably. A partially standard set of nomenclature is to use the term proposition to denote a significant result that is still shy of deserving a proper name. In contrast, a theorem under this format would represent a major result, and would often be named in relation to mathematicians who worked on or solved the problem in question.
• The Greek word “lemma” itself means “anything which is received, such as a gift, profit, or a bribe.” According to [1], the plural 'Lemmas' is commonly used. The correct Greek plural of lemma, however, is lemmata. The Greek “Theoria” means “view, or vision" and is clearly linguistically related to the word “theatre.” The apparent relation is that a theorem is a mathematical fact which you see to be true (and can now show others!).
• A somewhat more distinct concept (though still subject to author discretion) is that of a corollary, which is a result that can be considered an immediate consequence of a previous theorem (typically, the preceding theorem in the text).

### 1998

• (Roelofs et al, 1998) ⇒ Ardi Roelofs, Antje S. Meyer, and Willem J.M. Levelt. (1998). “Case for the Lemma/Lexeme Distinction in Models of Speaking: Comment on Caramazza and Miozzo (1997).” In: Cognition, 69.
• In lexical access, speakers draw on stored knowledge about words. This stored information comprises the meanings of words, their syntactic properties (such as the word class, subcategorization features for verbs, and grammatical gender for nouns), and information about their morphological structure and phonological form. The received view holds that lexical access consists of two major steps, corresponding to the formulation stages of syntactic encoding and morphophonological encoding, respectively. During the first step, often called lemma retrieval, a word’s syntactic properties and, on some views, its meaning are retrieved from memory. During the second step, information about the word’s morphophonological form, often called its lexeme, is recovered.