Lexical Semantics
Lexical semantics ascribes a large part of the meaning of a sentence to the individual ``words''.
Definition: lexeme — an entity defined by its orthographic, phonological, and meaning representation
Definition: lexicon — collection of lexemes
Relationhips among lexemes and their senses
Some relevant terms
With rise in voice recognition processing, homophony and homonymy become an identical problem.
This definition requires altering/expanding the basic definition of lexeme, especially to distinguish its usage from that of homonymy. Homonymy is the distinction between two different lexemes. Polysemy is the situation of having a single lexeme mapped to multiple related meanings.
Therefore, the definition of a lexeme as a surface form — sense pairing is modified to become a pairing between a surface form and a set of related senses.
The determination of inclusion in the set of related meanings
is based on either of two criteria:
Coincidence is cited [JM] as a means of distinguishing between homonymy and polysemy. Homonyms seem to arise from coincidence; whereas other methods are needed to explain instances of polysemy.
Examples (offered by [JM] from WSJ corpus):
16.8 They rarely served meat ...
16.9 He served as U.S. ambassador to ...
16.10 He might have served his time ...
These can be reasonably argued as comprising three distinct senses. The question now appears to be whether they belong to three distinct sense classes — hence, constitute three lexemes.
The difficulty in the concept of same meaning, might be explained by the notion of substitutability.
Definition: substitutability — the ability of multiple lexemes to serve as replacements in a sentence without changing either the meaning or the acceptability of it.
Note that substitutability implies some environment or context under which the metrics (of meaning and acceptability) are to be applied [otherwise true synonyms are rare or nonexistent.] This is generally true in mathematical substitutions in other domains.
An aspect which affects substitutability is register — the "social" factors surrounding the use of synonyms. E.g., multisyllabic lexemes with Latin or Greek origins may be preferred when used in academic or technical contexts. [JM]