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Concatenation 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. 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". Church was evidently unaware t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntax
In linguistics, syntax ( ) is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), agreement, the nature of crosslinguistic variation, and the relationship between form and meaning (semantics). Diverse approaches, such as generative grammar and functional grammar, offer unique perspectives on syntax, reflecting its complexity and centrality to understanding human language. Etymology The word ''syntax'' comes from the ancient Greek word , meaning an orderly or systematic arrangement, which consists of (''syn-'', "together" or "alike"), and (''táxis'', "arrangement"). In Hellenistic Greek, this also specifically developed a use referring to the grammatical order of words, with a slightly altered spelling: . The English term, which first appeared in 1548, is partly borrowed from Latin () and Greek, though the L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of character (computing), characters, either as a literal (computer programming), literal constant or as some kind of Variable (computer science), variable. The latter may allow its elements to be Immutable object, mutated and the length changed, or it may be fixed (after creation). A string is often implemented as an array data structure of bytes (or word (computer architecture), words) that stores a sequence of elements, typically characters, using some character encoding. More general, ''string'' may also denote a sequence (or List (abstract data type), list) of data other than just characters. Depending on the programming language and precise data type used, a variable (programming), variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Linguistics
Formal linguistics is a branch of mathematical linguistics which uses formal languages, formal grammars and first-order logical expressions for the analysis of natural languages. Formal linguistics forms much of the basis of computational linguistics. Since the 1980s, the term is often used to refer to Chomskyan linguistics. Approaches Semiotic Methods of formal linguistics were introduced by semiotics, semioticians such as Charles Sanders Peirce and Louis Hjelmslev. Building on the work of David Hilbert and Rudolf Carnap, Hjelmslev proposed the use of formal grammars to analyse, generate and explain language in his 1943 book ''Prolegomena to a Theory of Language''. In this view, language is regarded as arising from a mathematical relationship between meaning and form. The formal description of language was further developed by linguists including J. R. Firth and Simon Dik, giving rise to modern grammatical frameworks such as systemic functional linguistics and functional discourse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generative Grammar
Generative grammar is a research tradition in linguistics that aims to explain the cognitive basis of language by formulating and testing explicit models of humans' subconscious grammatical knowledge. Generative linguists, or generativists (), tend to share certain working assumptions such as the competence–performance distinction and the notion that some domain-specific aspects of grammar are partly innate in humans. These assumptions are rejected in non-generative approaches such as usage-based models of language. Generative linguistics includes work in core areas such as syntax, semantics, phonology, psycholinguistics, and language acquisition, with additional extensions to topics including biolinguistics and music cognition. Generative grammar began in the late 1950s with the work of Noam Chomsky, having roots in earlier approaches such as structural linguistics. The earliest version of Chomsky's model was called Transformational grammar, with subsequent itera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalizations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary infix operator, and in some it is written without an operator. This is implemented in different ways: * Overloading the plus sign + Example from C#: "Hello, " + "World" has the value "Hello, World". * Dedicated operator, such as . in PHP, & in Visual Basic, and , , in SQL. This has the advantage over reusing + that it allows implicit type conversion to string. * string literal concatenation, which means that adjacent strings are concatenated without any operator. Example from C: "Hello, " "World" has the value "Hello, World". In many scientific publications or standards the con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Monoid
In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element. The free monoid on a set ''A'' is usually denoted ''A''∗. The free semigroup on ''A'' is the sub semigroup of ''A''∗ containing all elements except the empty string. It is usually denoted ''A''+./ref> More generally, an abstract monoid (or semigroup) ''S'' is described as free if it is isomorphic to the free monoid (or semigroup) on some set. As the name implies, free monoids and semigroups are those objects which satisfy the usual universal property defining free objects, in the respective categories of monoids and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alonzo Church
Alonzo Church (June 14, 1903 – August 11, 1995) was an American computer scientist, mathematician, logician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the ''Entscheidungsproblem'' ("decision problem"), the Frege–Church ontology, and the Church–Rosser theorem. Alongside his doctoral student Alan Turing, Church is considered one of the founders of computer science. Life Alonzo Church was born on June 14, 1903, in Washington, D.C., where his father, Samuel Robbins Church, was a justice of the peace and the judge of the Municipal Court for the District of Columbia. He was the grandson of Alonzo Webster Church (1829–1909), United States Senate Librarian from 1881 to 1901, and great-grandson of Alonzo Church, a professor of Mathematics and Astronomy and 6th President of the University of Ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Hermes
Hans Hermes (; 12 February 1912 – 10 November 2003) was a German mathematician and logician, who made significant contributions to the foundations of mathematical logic. Life Hermes was born in Neunkirchen. From 1931, he studied mathematics, physics, chemistry, biology and philosophy at the University of Freiburg. In 1937, he passed the state examination in Münster and was attending there in 1938 when the physicist Adolf Kratzer was present. After that, he went on a scholarship to the University of Göttingen and then became an assistant at the University of Bonn. During World War II, he was a soldier on the Channel Island of Jersey until 1943 and then on to the Chemical Physics Institute of the Navy in Kiel. At the end of the war, he moved to Toplitzsee, where he was tasked with working on new encryption methods. In 1947, he became a lecturer at the University of Bonn where he took his habilitation, his thesis called ''Analytical manifolds in Riemannian areas''. In 1949 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Tarski
Alfred Tarski (; ; born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician and mathematician. A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, type theory, and analytic philosophy. Educated in Poland at the University of Warsaw, and a member of the Lwów–Warsaw school, Lwów–Warsaw school of logic and the Warsaw school of mathematics, he immigrated to the United States in 1939 where he became a naturalized citizen in 1945. Tarski taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death in 1983.#FefA, Feferman A. His biographers Anita Burdman Feferman and Solomon Feferman state that, "Along with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Corcoran (logician)
John Corcoran ( ; March 20, 1937 – January 8, 2021) was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on concepts such as the nature of inference, relations between conditions, argument-deduction-proof distinctions, the relationship between logic and epistemology, and the place of proof theory and model theory in logic. Nine of Corcoran's papers have been translated into Spanish, Portuguese, Persian, and Arabic; his 1989 "signature" essay was translated into three languages. Fourteen of his papers have been reprinted; one was reprinted twice. His work on Aristotle's logic of the '' Prior Analytics'' is regarded as being highly faithful both to the Greek text and to the historical context. It is the basis for many subsequent investigations. His mathematical results on definitional equivalence of formal character-string theories, sciences of strings of characters over finite alphabets, are foundationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
