For the theory of strings in physics, see String theory.
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.[1] 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 1956 Alonzo Church wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".[2] Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by Hans Hermes and one by Alfred Tarski.[3] Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.[4] As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of Peirce's type-token distinction.
Referencesedit
^John Corcoran and Matt Lavine, "Discovering string theory". Bulletin of Symbolic Logic. 19 (2013) 253–4.
^Alonzo Church, Introduction to Mathematical Logic, Princeton UP, Princeton, 1956
^John Corcoran, William Frank and Michael Maloney, "String theory", Journal of Symbolic Logic, vol. 39 (1974) pp. 625– 637
^Pages 173–4 of Alfred Tarski, The concept of truth in formalized languages, reprinted in Logic, Semantics, Metamathematics, Hackett, Indianapolis, 1983, pp. 152–278
December 18, 2023
concatenation, theory, theory, strings, physics, string, theory, also, called, string, theory, character, string, theory, theoretical, syntax, studies, character, strings, over, finite, alphabets, characters, signs, symbols, marks, string, theory, foundational. For the theory of strings in physics see String theory 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 1 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 1956 Alonzo Church wrote Like any branch of mathematics theoretical syntax may and ultimately must be studied by the axiomatic method 2 Church was evidently unaware that string theory already had two axiomatizations from the 1930s one by Hans Hermes and one by Alfred Tarski 3 Coincidentally the first English presentation of Tarski s 1933 axiomatic foundations of string theory appeared in 1956 the same year that Church called for such axiomatizations 4 As Tarski himself noted using other terminology serious difficulties arise if strings are construed as tokens rather than types in the sense of Peirce s type token distinction References edit John Corcoran and Matt Lavine Discovering string theory Bulletin of Symbolic Logic 19 2013 253 4 Alonzo Church Introduction to Mathematical Logic Princeton UP Princeton 1956 John Corcoran William Frank and Michael Maloney String theory Journal of Symbolic Logic vol 39 1974 pp 625 637 Pages 173 4 of Alfred Tarski The concept of truth in formalized languages reprinted in Logic Semantics Metamathematics Hackett Indianapolis 1983 pp 152 278 Retrieved from https en wikipedia org w index php title Concatenation theory amp oldid 1133980746, wikipedia, wiki, book, books, library,
