Right Ideals of a Ring and Sublanguages of Science
This work addresses the mathematical modeling of linguistic structures, particularly for theoretical linguistics and computational applications, but appears incremental as it builds on existing theories.
The paper argues that sublanguages of science have a specific algebraic relationship to the larger language they are part of, specifically as right ideals in a ring, based on Zellig Harris's theory.
Among Zellig Harris's numerous contributions to linguistics his theory of the sublanguages of science probably ranks among the most underrated. However, not only has this theory led to some exhaustive and meaningful applications in the study of the grammar of immunology language and its changes over time, but it also illustrates the nature of mathematical relations between chunks or subsets of a grammar and the language as a whole. This becomes most clear when dealing with the connection between metalanguage and language, as well as when reflecting on operators. This paper tries to justify the claim that the sublanguages of science stand in a particular algebraic relation to the rest of the language they are embedded in, namely, that of right ideals in a ring.