Material conditionalThe material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics.
Free variables and bound variablesIn mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. The terms are opposites. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively.
Machine translationMachine translation is use of either rule-based or probabilistic (i.e. statistical and, most recently, neural network-based) machine learning approaches to translation of text or speech from one language to another, including the contextual, idiomatic and pragmatic nuances of both languages. History of machine translation The origins of machine translation can be traced back to the work of Al-Kindi, a ninth-century Arabic cryptographer who developed techniques for systemic language translation, including cryptanalysis, frequency analysis, and probability and statistics, which are used in modern machine translation.
Translation memoryA translation memory (TM) is a database that stores "segments", which can be sentences, paragraphs or sentence-like units (headings, titles or elements in a list) that have previously been translated, in order to aid human translators. The translation memory stores the source text and its corresponding translation in language pairs called “translation units”. Individual words are handled by terminology bases and are not within the domain of TM.
Exclusive orExclusive or or exclusive disjunction or exclusive alternation, also known as non-equivalence which is the negation of equivalence, is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator and by the infix operators XOR (ˌɛks_ˈɔ:r, ˌɛks_ˈɔ:, 'ksɔ:r or 'ksɔ:), EOR, EXOR, , , , ⩛, , and . It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator excludes that case.
NegationIn logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", standing for " is not true", written , or . It is interpreted intuitively as being true when is false, and false when is true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity (and vice versa).
Augustus De MorganAugustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. Augustus De Morgan was born in Madurai, in the Carnatic region of India in 1806. His father was Lieut.-Colonel John De Morgan (1772–1816), who held various appointments in the service of the East India Company, and his mother, Elizabeth (née Dodson, 1776–1856), was daughter of John Dodson and granddaughter of James Dodson, who computed a table of anti-logarithms (inverse logarithms).
Google TranslateGoogle Translate is a multilingual neural machine translation service developed by Google to translate text, documents and websites from one language into another. It offers a website interface, a mobile app for Android and iOS, as well as an API that helps developers build browser extensions and software applications. As of 2022, Google Translate supports languages at various levels; it claimed over 500 million total users , with more than 100 billion words translated daily, after the company stated in May 2013 that it served over 200 million people daily.
Income statementAn income statement or profit and loss account (also referred to as a profit and loss statement (P&L), statement of profit or loss, revenue statement, statement of financial performance, earnings statement, statement of earnings, operating statement, or statement of operations) is one of the financial statements of a company and shows the company's revenues and expenses during a particular period. It indicates how the revenues (also known as the “top line”) are transformed into the net income or net profit (the result after all revenues and expenses have been accounted for).
Financial statementFinancial statements (or financial reports) are formal records of the financial activities and position of a business, person, or other entity. Relevant financial information is presented in a structured manner and in a form which is easy to understand. They typically include four basic financial statements accompanied by a management discussion and analysis: A balance sheet or statement of financial position, reports on a company's assets, liabilities, and owners equity at a given point in time.
Domain-specific languageA domain-specific language (DSL) is a computer language specialized to a particular application domain. This is in contrast to a general-purpose language (GPL), which is broadly applicable across domains. There are a wide variety of DSLs, ranging from widely used languages for common domains, such as HTML for web pages, down to languages used by only one or a few pieces of software, such as MUSH soft code.
Equivalence classIn mathematics, when the elements of some set have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set into equivalence classes. These equivalence classes are constructed so that elements and belong to the same equivalence class if, and only if, they are equivalent. Formally, given a set and an equivalence relation on the of an element in denoted by is the set of elements which are equivalent to It may be proven, from the defining properties of equivalence relations, that the equivalence classes form a partition of This partition—the set of equivalence classes—is sometimes called the quotient set or the quotient space of by and is denoted by .
