Natural language in the context of Waggle dance

A cradle of civilization is a location and a culture where civilization was developed independently of other civilizations in other locations. A civilization is any complex society characterized by the development of the state, social stratification, urbanization, and symbolic systems of communication beyond signed or spoken languages (namely, writing systems and graphic arts).

Scholars generally acknowledge six cradles of civilization: Mesopotamia, Ancient Egypt, Ancient India and Ancient China are believed to be the earliest in Afro-Eurasia, while the Caral–Supe civilization of coastal Peru and the Olmec civilization of Mexico are believed to be the earliest in the Americas. All of the cradles of civilization depended upon agriculture for sustenance (except possibly Caral–Supe which may have depended initially on marine resources). All depended upon farmers producing an agricultural surplus to support the centralized government, political leaders, religious leaders, and public works of the urban centers of the early civilizations.

A civilization (also spelled civilisation in British English) is any complex society characterized by the development of the state, social stratification, urbanization, and symbolic systems of communication beyond signed or spoken languages (namely, writing systems).

Civilizations are organized around densely populated settlements, divided into more or less rigid hierarchical social classes of division of labour, often with a ruling elite and subordinate urban and rural populations, which engage in intensive agriculture, mining, small-scale manufacture and trade. Civilization concentrates power, extending human control over the rest of nature, including over other human beings. Civilizations are characterized by elaborate agriculture, architecture, infrastructure, technological advancement, currency, taxation, regulation, and specialization of labour.

In natural language and physical science, a physical object or material object (or simply an object or body) is a contiguous collection of matter, within a defined boundary (or surface), that exists in space and time. Usually contrasted with abstract objects and mental objects.

Also in common usage, an object is not constrained to consist of the same collection of matter. Atoms or parts of an object may change over time. An object is usually meant to be defined by the simplest representation of the boundary consistent with the observations. However the laws of physics only apply directly to objects that consist of the same collection of matter.

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 work." Premises and conclusions express propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions are made up of simpler propositions linked by logical vocabulary like ${\displaystyle \land }$ (and) or ${\displaystyle \to }$ (if...then). Simple propositions also have parts, like "Sunday" or "work" in the example. The truth of a proposition usually depends on the meanings of all of its parts. However, this is not the case for logically true propositions. They are true only because of their logical structure independent of the specific meanings of the individual parts.

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.

Proofs employ logic expressed in mathematical symbols, along with natural language that usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures. The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.

A lingua franca (/ˌlɪŋɡwə ˈfræŋkə/; lit. 'Frankish tongue'; for plurals see § Usage notes), also known as a bridge language, common language, trade language, auxiliary language, link language or language of wider communication (LWC), is a language systematically used to make communication possible between groups of people who do not share a native language or dialect, particularly when it is a third language that is distinct from both of the speakers' native languages.

Linguae francae have developed around the world throughout human history, sometimes for commercial reasons (so-called "trade languages" facilitated trade), but also for cultural, religious, diplomatic and administrative convenience, and as a means of exchanging information between scientists and other scholars of different nationalities. The term is taken from the medieval Mediterranean Lingua Franca, a Romance-based pidgin language used especially by traders in the Mediterranean Basin from the 11th to the 19th centuries. A world language—a language spoken internationally and by many people—is a language that may function as a global lingua franca.

Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed forms, and may also be conveyed through writing. Human language is characterized by its cultural and historical diversity, with significant variations observed between cultures and across time. Human languages possess the properties of productivity and displacement, which enable the creation of an infinite number of sentences, and the ability to refer to objects, events, and ideas that are not immediately present in the discourse. The use of human language relies on social convention and is acquired through learning.

Estimates of the number of human languages in the world vary between 5,000 and 7,000. Precise estimates depend on an arbitrary distinction (dichotomy) established between languages and dialects. Natural languages are spoken, signed, or both; however, any language can be encoded into secondary media using auditory, visual, or tactile stimuli – for example, writing, whistling, signing, or braille. In other words, human language is modality-independent, but written or signed language is the way to inscribe or encode the natural human speech or gestures.

In philosophy and linguistics, the denotation of a word or expression is its strictly literal meaning. For instance, the English word "warm" denotes the property of having high temperature. Denotation is contrasted with other aspects of meaning, in particular connotation. For instance, the word "warm" may evoke calmness, coziness, or kindness (as in the warmth of someone's personality) but these associations are not part of the word's denotation. Similarly, an expression's denotation is separate from pragmatic inferences it may trigger. For instance, describing something as "warm" often implicates that it is not hot, but this is once again not part of the word's denotation.

Denotation plays a major role in several fields. Within semantics and philosophy of language, denotation is studied as an important aspect of meaning. In mathematics and computer science, assignments of denotations are assigned to expressions are a crucial step in defining interpreted formal languages. The main task of formal semantics is to reverse engineer the computational system which assigns denotations to expressions of natural languages.

Onomatopoeia (or rarely echoism) is a type of word, or the process of creating a word, that phonetically imitates, resembles, or suggests the sound that it describes. Common onomatopoeias in English include animal noises such as oink, meow, roar, and chirp, among other sounds such as beep or hiccup.

Onomatopoeia can differ by language: it conforms to some extent to the broader linguistic system. Hence, the sound of a clock may be expressed variously across languages: as tick tock in English, tic tac in Spanish and Italian (see photo), dī dā in Mandarin, kachi kachi in Japanese, or ṭik-ṭik in Hindi, Urdu, and Bengali.

Vernacular is the ordinary, informal, spoken form of a language or dialect, particularly when perceived as having lower social status or less prestige than standard language, which is more codified, institutionally promoted, literary, or formal. More narrowly, any particular variety of a natural language that does not hold a widespread high-status perception, and sometimes even carries social stigma, is also called a vernacular, vernacular dialect, nonstandard dialect, etc. and is typically its speakers' native variety. Regardless of any such stigma, all nonstandard dialects are full-fledged varieties of language with their own consistent grammatical structure, sound system, body of vocabulary, etc.

Informal fallacies are a type of incorrect argument in natural language. The source of the error is not necessarily due to the form of the argument, as is the case for formal fallacies, but is due to its content and context. Fallacies, despite being incorrect, usually appear to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit.

Traditionally, a great number of informal fallacies have been identified, including the fallacy of equivocation, the fallacy of amphiboly, the fallacies of composition and division, the false dilemma, the fallacy of begging the question, the ad hominem fallacy and the appeal to ignorance. There is no general agreement as to how the various fallacies are to be grouped into categories. One approach sometimes found in the literature is to distinguish between fallacies of ambiguity, which have their root in ambiguous or vague language, fallacies of presumption, which involve false or unjustified premises, and fallacies of relevance, in which the premises are not relevant to the conclusion despite appearances otherwise.

The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol ${\displaystyle \to }$ is interpreted as material implication, a formula ${\displaystyle P\to Q}$ is true unless ${\displaystyle P}$ is true and ${\displaystyle Q}$ is false.

Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language.

In linguistics, grammar is the set of rules for how a natural language is structured, as demonstrated by its speakers or writers. Grammar rules may concern the use of clauses, phrases, and words. The term may also refer to the study of such rules, a subject that includes phonology, morphology, and syntax, together with phonetics, semantics, and pragmatics. There are, broadly speaking, two different ways to study grammar: traditional grammar and theoretical grammar.

Fluency in a particular language variety involves a speaker internalizing these rules, many or most of which are acquired by observing other speakers, as opposed to intentional study or instruction. Much of this internalization occurs during early childhood; learning a language later in life usually involves more direct instruction. The term grammar can also describe the linguistic behaviour of groups of speakers and writers rather than individuals. Differences in scale are important to this meaning: for example, English grammar could describe those rules followed by every one of the language's speakers. At smaller scales, it may refer to rules shared by smaller groups of speakers.

Sign languages (also known as signed languages) are languages that use the visual-manual modality to convey meaning, instead of spoken words. Sign languages are expressed through manual articulation in combination with non-manual markers. Sign languages are full-fledged natural languages with their own grammar and lexicon. Sign languages are not universal and are usually not mutually intelligible, although there are similarities among different sign languages.

Wherever communities of people with hearing challenges or people who experience deafness exist, sign languages have developed as useful means of communication and form the core of local deaf cultures. Although signing is used primarily by the deaf and hard of hearing, it is also used by hearing individuals, such as those with deaf family members including children of deaf adults.

Natural language processing (NLP) is the processing of natural language information by a computer. The study of NLP, a subfield of computer science, is generally associated with artificial intelligence. NLP is related to information retrieval, knowledge representation, computational linguistics, and more broadly with linguistics.

Major processing tasks in an NLP system include: speech recognition, text classification, natural language understanding, and natural language generation.

Controlled natural languages (CNLs) are subsets of natural languages that are obtained by restricting the grammar and vocabulary in order to reduce or eliminate ambiguity and complexity. Traditionally, controlled languages fall into two major types: those that improve readability for human readers (e.g. non-native speakers),and those that enable reliable automatic semantic analysis of the language.

The first type of languages (often called "simplified" or "technical" languages), for example ASD Simplified Technical English, Caterpillar Technical English, IBM's Easy English, are used in the industry to increase the quality of technical documentation, and possibly simplify the semi-automatic translation of the documentation. These languages restrict the writer by general rules such as "Keep sentences short", "Avoid the use of pronouns", "Only use dictionary-approved words", and "Use only the active voice".

A constructed language is a language for communication between humans (i.e. not with or between computers) but unlike most languages that naturally emerge from human interaction, is intentionally devised by a person or group for a particular purpose. The term constructed language is often shortened to conlang and, as a relatively broad term, it encompasses subcategories including: fictional, artificial, engineered, planned and invented languages. Conlangs may include aspects reminiscent of natural language including phonology, grammar, orthography, and vocabulary. Interlinguistics includes the study of constructed languages.