Formal linguistics in the context of "Alphabet (formal languages)"

Louis Trolle Hjelmslev (Danish: [ˈjelˀmsle̝w]; 3 October 1899 – 30 May 1965) was a Danish linguist whose ideas formed the basis of the Copenhagen School of linguistics. Born into an academic family (his father was the mathematician Johannes Hjelmslev), Hjelmslev studied comparative linguistics in Copenhagen, Prague and Paris (with Antoine Meillet and Joseph Vendryes, among others). In 1931, he founded the Cercle Linguistique de Copenhague. Together with Hans Jørgen Uldall he developed a structuralist theory of language which he called glossematics, which further developed the semiotic theory of Ferdinand de Saussure. Glossematics as a theory of language is characterized by a high degree of formalism. It is interested in describing the formal and semantic characteristics of language in separation from sociology, psychology or neurobiology, and has a high degree of logical rigour. Hjelmslev regarded linguistics – or glossematics – as a formal science. He was a pioneer of formal linguistics. Hjelmslev's theory became widely influential in structural and functional grammar, and in semiotics.

Usage-based linguistics is a linguistics approach within a broader functional/cognitive framework, that emerged since the late 1980s, and that assumes a profound relation between linguistic structure and usage. It challenges the dominant focus, in 20th century linguistics (and in particular in formalism-generativism), on considering language as an isolated system removed from its use in human interaction and human cognition. Rather, usage-based models posit that linguistic information is expressed via context-sensitive mental processing and mental representations, which have the cognitive ability to succinctly account for the complexity of actual language use at all levels (phonetics and phonology, morphology and syntax, pragmatics and semantics). Broadly speaking, a usage-based model of language accounts for language acquisition and processing, synchronic and diachronic patterns, and both low-level and high-level structure in language, by looking at actual language use.

The term usage-based was coined by Ronald Langacker in 1987. Usage-based models of language have become a significant new trend in linguistics since the early 2000s. Influential proponents of usage-based linguistics include Michael Tomasello, Joan Bybee and Morten Christiansen.

Concatenation theory, also called string theory, character-string theory, or theoretical syntax, studies character strings over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory. A generative grammar can be seen as a recursive definition in string theory.

The most basic operation on strings is concatenation; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a free monoid.

In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT includes a level of abstract mental representations (discourse representation structures, DRS) within its formalism, which gives it an intrinsic ability to handle meaning across sentence boundaries. DRT was created by Hans Kamp in 1981. A very similar theory was developed independently by Irene Heim in 1982, under the name of File Change Semantics (FCS). Discourse representation theories have been used to implement semantic parsers and natural language understanding systems.