Linguistics

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all x, if x is a human, then x is mortal", where "for all x" is a quantifier, x is a variable, and "... is a human" and "... is mortal" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, first-order logic is an extension of propositional logic.

A theory about a topic, such as set theory, a theory for groups, or a formal theory of arithmetic, is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axioms believed to hold about them. "Theory" is sometimes understood in a more formal sense as just a set of sentences in first-order logic.

Gottfried Wilhelm Leibniz (or Leibnitz; 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labour. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science.

Leibniz contributed to the field of library science, developing a cataloguing system (at the Herzog August Library in Wolfenbüttel, Germany) that came to serve as a model for many of Europe's largest libraries. His contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.

A vocabulary (also known as a lexicon) is a set of words, typically the set in a language or the set known to an individual. The word vocabulary originated from the Latin vocabulum, meaning "a word, name". It forms an essential component of language and communication, helping convey thoughts, ideas, emotions, and information. Vocabulary can be oral, written, or signed and can be categorized into two main types: active vocabulary (words one uses regularly) and passive vocabulary (words one recognizes but does not use often). An individual's vocabulary continually evolves through various methods, including direct instruction, independent reading, and natural language exposure, but it can also shrink due to forgetting, trauma, or disease. Furthermore, vocabulary is a significant focus of study across various disciplines, like linguistics, education, psychology, and artificial intelligence. Vocabulary is not limited to single words; it also encompasses multi-word units known as collocations, idioms, and other types of phraseology. Acquiring an adequate vocabulary is one of the largest challenges in learning a second language.

In linguistics, a neologism (/niˈɒlədʒɪzəm/, /ˌniːoʊˈloʊ-/; also known as a coinage) is any newly formed word, term, or phrase that has gained popular or institutional recognition and is becoming accepted into mainstream language.

Neologisms are one facet of lexical innovation, i.e., the linguistic process of new terms and meanings entering a language's lexicon. The most precise studies into language change and word formation, in fact, identify the process of a "neological continuum": a nonce word is any single-use term that may or may not grow in popularity; a protologism is such a term used exclusively within a small group; a prelogism is such a term that is gaining usage but is still not mainstream; and a neologism has become accepted or recognized by social institutions.

In the study of language, description or descriptive linguistics is the work of objectively analyzing and describing how language is actually used (or how it was used in the past) by a speech community.

All academic research in linguistics is descriptive; like all other scientific disciplines, it aims to describe reality, without the bias of preconceived ideas about how it ought to be. Modern descriptive linguistics is based on a structural approach to language, as exemplified in the work of Leonard Bloomfield and others. This type of linguistics utilizes different methods in order to describe a language such as basic data collection, and different types of elicitation methods.

In linguistics, grammatical number is a feature of nouns, pronouns, adjectives and verb agreement that expresses count distinctions (such as "one", "two" or "three or more"). English and many other languages present number categories of singular or plural. Some languages also have a dual, trial and paucal number or other arrangements.

The word "number" is also used in linguistics to describe the distinction between certain grammatical aspects that indicate the number of times an event occurs, such as the semelfactive aspect, the iterative aspect, etc. For that use of the term, see "Grammatical aspect".

In linguistics, codification is the social process of a language's natural variation being reduced and features becoming more fixed or subject to prescriptive rules. Codification is a precursor to standardization: the development of a standard variety of a language.

Codifying a language can vary from case to case and depends on the stage of standardization that might have already occurred naturally. It typically means to develop a writing system, set up normative rules for grammar, orthography, pronunciation, and usage of vocabulary as well as publish grammar books, dictionaries and similar guidelines. In cases where several variants exist for a specific aspect, e.g. different ways of spelling a word, decisions on which variant is going to be the standard one have to be made.

In linguistics and social sciences, markedness is the state of standing out as nontypical or divergent as opposed to regular or common. In a marked–unmarked relation, one term of an opposition is the broader, dominant one. The dominant default or minimum-effort form is known as unmarked; the other, secondary one is marked. In other words, markedness involves the characterization of a "normal" linguistic unit against one or more of its possible "irregular" forms.

In linguistics, markedness can apply to, among others, phonological, grammatical, and semantic oppositions, defining them in terms of marked and unmarked oppositions, such as honest (unmarked) vs. dishonest (marked). Marking may be purely semantic, or may be realized as extra morphology. The term derives from the marking of a grammatical role with a suffix or another element, and has been extended to situations where there is no morphological distinction.

General American English, known in linguistics simply as General American (abbreviated GA or GenAm), is the umbrella accent of American English used by a majority of Americans, encompassing a continuum rather than a single unified accent. It is often perceived by Americans themselves as lacking any distinctly regional, ethnic, or socioeconomic characteristics, though Americans with high education, or from the (North) Midland, Western New England, and Western regions of the country are the most likely to be perceived as using General American speech. The precise definition and usefulness of the term continue to be debated, and the scholars who use it today admittedly do so as a convenient basis for comparison rather than for exactness. Some scholars prefer other names, such as Standard American English, though this can be a wider term encompassing more than just accent.

Standard Canadian English accents may be considered to fall under General American, especially in opposition to the United Kingdom's Received Pronunciation. Noted phonetician John C. Wells, for instance, claimed in 1982 that typical Canadian English accents align with General American in nearly every situation where British and American accents differ.

In linguistics, productivity is the degree to which speakers of a language use a particular grammatical process, especially in word formation. It compares grammatical processes that are in frequent use to less frequently used ones that tend towards lexicalization. Generally the test of productivity concerns identifying which grammatical forms would be used in the coining of new words: these will tend to only be converted to other forms using productive processes.