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Formal Methods Terminology
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements ( forms, in Ancient Greek). They may refer to: Dress code and events * Formal wear, attire for formal events * Semi-formal attire, attire for semi-formal events * Informal attire, more controlled attire than casual but less than formal * Formal (university), official university dinner, ball or other event * School formal, official school dinner, ball or other event Logic and mathematics *Formal logic, or symbolic logic ** Informal logic, the complement, whose definition and scope is contentious *Formal fallacy, reasoning of invalid structure ** Informal fallacy, the complement *Informal mathematics, also called naïve mathematics * Formal cause, Aristotle's intrinsic, determining cause *Formal power series, a generalization of power series without requiring convergence, used in combinatorics * Formal calculation, a calculation which is systematic, but without ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of ''naive set theory''. After the discovery of Paradoxes of set theory, paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Derivative
In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. Formal differentiation is used in algebra to test for multiple roots of a polynomial. Definition Fix a ring R (not necessarily commutative) and let A = R /math> be the ring of polynomials over R. (If R is not commutative, this is the free algebra over a single indeterminate variable.) Then the formal derivative is an operation on elements of A, where if :f(x)\,=\,a_n x^n + \cdots + a_1 x + a_0, then its formal derivative is :f'(x)\,=\,Df(x) = n a_n x^ + \cdots + i a_i x^ + \cdots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ketal
In organic chemistry, an acetal is a functional group with the connectivity . Here, the R groups can be organic fragments (a carbon atom, with arbitrary other atoms attached to that) or hydrogen, while the R' groups must be organic fragments not hydrogen. The two R' groups can be equivalent to each other (a "symmetric acetal") or not (a "mixed acetal"). Acetals are formed from and convertible to aldehydes or ketones and have the same oxidation state at the central carbon, but have substantially different chemical stability and reactivity as compared to the analogous carbonyl compounds. The central carbon atom has four bonds to it, and is therefore saturated and has tetrahedral geometry. The term ketal is sometimes used to identify structures associated with ketones (both R groups organic fragments rather than hydrogen) rather than aldehydes and, historically, the term acetal was used specifically for the aldehyde-related cases (having at least one hydrogen in place of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is the number of moles of solute per liter of solution. Specifically, It is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/ dm3 (1000 mol/ m3) in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as + Definition Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic And Formal Equivalence
Dynamic equivalence and formal equivalence, in translation and semantics, are the principle approaches to translation, prioritizing respectively the meaning or the literal structure of the source text. The distinction was originally drawn by Eugene Nida in regard to Bible translation. Approaches to translation The "Formal-equivalence" approach emphasizes fidelity to the lexical details and grammatical structure of the source language, whereas "dynamic equivalence" tends to employ a rendering that is more natural to the target language. According to Eugene Nida, ''dynamic equivalence'', the term as he originally coined, is the "quality of a translation in which the message of the original text has been so transported into the receptor language that the ''response'' of the ''receptor'' is essentially like that of the original receptors." The desire is that the reader of both languages would understand the meanings of the text in a similar fashion. In later years, Ni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is generally effective, but there may be no method by which we can reliably find proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof. The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T–V Distinction
The T–V distinction is the contextual use of different pronouns that exists in some languages and serves to convey formality or familiarity. Its name comes from the Latin pronouns '' tu'' and '' vos''. The distinction takes a number of forms and indicates varying levels of politeness, familiarity, courtesy, age or even insult toward the addressee. The field that studies and describes this phenomenon is sociolinguistics. Many languages lack this type of distinction, instead relying on other morphological or discourse features to convey formality. English historically contained the distinction, using the pronouns ''thou'' and ''you'', but the familiar ''thou'' largely disappeared from the era of Early Modern English onward, with the exception of a few dialects. Additionally, British commoners historically spoke to nobility and royalty using the third person rather than the second person, a practice that has fallen out of favour. English speakers today often employ semantic a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colloquialism
Colloquialism (also called ''colloquial language'', ''colloquial speech'', ''everyday language'', or ''general parlance'') is the linguistic style used for casual and informal communication. It is the most common form of speech in conversation among persons in friendship, familial, intimate, and other informal contexts. Colloquialism is characterized by the usage of figurative language, contractions, filler words, interjections, and other informalities such as slang. In contrast to formal and professional communications, colloquial speech does not adhere to grammar and syntax rules and thus may be considered inappropriate and impolite in situations and settings where etiquette is expected or required. It has a rapidly changing lexicon and can also be distinguished by its usage of formulations with incomplete logical and syntactic ordering. Definition Colloquialism is distinct from formal speech or formal writing.colloquial. (n.d.) Dictionary.com Unabridged (v 1.1). Ret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammar
A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabet. A grammar does not describe the semantics, meaning of the strings — only their form. In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, Formal semantics (logic), formal semantics, mathematical logic, and other areas. A formal grammar is a Set_(mathematics), set of rules for rewriting strings, along with a "start symbol" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called ''well-formed words''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar. In computer science, formal languages are used, among others, as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages, in which the words of the language represent concepts that are associated with meanings or semantics. In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Concepts A formal system has the following: * Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). * Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal language. A formal system is said to be recursive (i.e. effective) or recursively enumerable if the set of axioms and the set of inference rules are decidable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
