|
Formal Concept Analysis
In information science, formal concept analysis (FCA) is a principled way of deriving a ''concept hierarchy'' or formal ontology from a collection of objects and their properties. Each concept in the hierarchy represents the objects sharing some set of properties; and each sub-concept in the hierarchy represents a subset of the objects (as well as a superset of the properties) in the concepts above it. The term was introduced by Rudolf Wille in 1981, and builds on the mathematical theory of lattices and ordered sets that was developed by Garrett Birkhoff and others in the 1930s. Formal concept analysis finds practical application in fields including data mining, text mining, machine learning, knowledge management, semantic web, software development, chemistry and biology. Overview and history The original motivation of formal concept analysis was the search for real-world meaning of mathematical order theory. One such possibility of very general nature is that data tables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and distribution of life. Central to biology are five fundamental themes: the cell (biology), cell as the basic unit of life, genes and heredity as the basis of inheritance, evolution as the driver of biological diversity, energy transformation for sustaining life processes, and the maintenance of internal stability (homeostasis). Biology examines life across multiple biological organisation, levels of organization, from molecules and cells to organisms, populations, and ecosystems. Subdisciplines include molecular biology, physiology, ecology, evolutionary biology, developmental biology, and systematics, among others. Each of these fields applies a range of methods to investigate biological phenomena, including scientific method, observation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal 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] |
Port-Royal Logic
''Port-Royal Logic'', or ''Logique de Port-Royal'', is the common name of ''La logique, ou l'art de penser'', an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered on Port-Royal. Blaise Pascal likely contributed considerable portions of the text. Its linguistic companion piece is the '' Port-Royal Grammar'' (1660) by Arnauld and Lancelot. The book helped popularize the concept that a definition with more qualifications or features (the intension) denotes a class with fewer members (the extension), and vice versa. It was based on Aristotle's ideas about ''genus'' and ''species''. The same concept would later become a fundamental element in the works of Gottfried Wilhelm Leibniz. Use as a textbook on Cartesian metaphysics and epistemology Written in French, it became quite popular and was in use up to the twentieth century, introducing the reader to logic, and exhibiting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles S
Charles is a masculine given name predominantly found in English language, English and French language, French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic, Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was ''Churl, Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinisation of names, Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as ''Carolus (other), Carolus''. Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as wikt:churl, churl (< Old English ''ċeorl''), which developed its deprecating sense in the Middle English period. Some Germanic languages, for example Dutch language, Dutch and German ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technische Universität Darmstadt
The Technische Universität Darmstadt (official English name Technical University of Darmstadt, sometimes also referred to as Darmstadt University of Technology), commonly known as TU Darmstadt, is a research university in the city of Darmstadt, Germany. It was founded in 1877 and received the right to award doctorates in 1899. In 1882, it was the first university in the world to set up a chair in electrical engineering. In 1883, the university founded the first Department of Electrical Engineering and Information Technology of TU Darmstadt, faculty of electrical engineering and introduced the world's first degree course in electrical engineering.History of the department of Electrical Engineering: (German) In 2004, it became the first German university to be declared as an autonomous university. TU Darmstadt has assumed a pioneering role in Germany. Computer science, electrical engineering, artificial intelligence, mechatronics, business informatics, political science and man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Burmeister
Peter Burmeister (16 July 1941 – 20 January 2019) was a German mathematician. He was a professor of mathematics at Darmstadt University of Technology. He was born in Berlin, Germany. Burmeister died on 20 January 2019 in Reinheim, Germany at the age of 77. Academic Career Peter Burmeister studied mathematics at the Free University of Berlin with an exchange year at the University of Münster. In 1966, he received his PhD from the Rheinische Friedrich-Wilhelms-University Bonn, supervised by Jürgen Schmidt, with a dissertation titled ''Über die Mächtigkeiten und Unabhängigkeitsgrade der Basen freier Algebren'' (On the Cardinalities and Independence Degrees of the Bases of Free Algebras). In 1971, he habilitated at the University of Bonn under Wolfram Schwabhäuser with the work ''Primitive Classes of Partial Algebras''. The same year, he was appointed Professor of Mathematics at the Technical University of Darmstadt. He retired in 2004. Work Peter Burmeister's research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Set
In mathematics, especially order theory, a partial order on a Set (mathematics), set is an arrangement such that, for certain pairs of elements, one precedes the other. The word ''partial'' is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is Reflexive relation, reflexive, antisymmetric relation, antisymmetric, and Transitive relation, transitive. A partially ordered set (poset for short) is an ordered pair P=(X,\leq) consisting of a set X (called the ''ground set'' of P) and a partial order \leq on X. When the meaning is clear from context and there is no ambiguity about the partial order, the set X itself is sometimes called a poset. Partial order relations The term ''partial order'' usually refers to the reflexive partial order relatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intension
In any of several fields of study that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language—an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word ''plant'' include properties such as "being composed of cellulose (not always true)", "alive", and "organism", among others. A '' comprehension'' is the collection of all such intensions. Overview The meaning of a word can be thought of as the bond between the ''idea the word means'' and the ''physical form of the word''. Swiss linguist Ferdinand de Saussure (1857–1913) contrasts three concepts: # the ''signifier'' – the "sound image" or the string of letters on a page that one recognizes as the form of a sign # the ''signified'' – the meaning, the concept or idea that a sign expresses or evokes # the ''referen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension (logic), comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question. In philosophical semantics or the philosophy of language, the 'extension' of a concept or expression is the set of things it extends to, or applies to, if it is the sort of concept or expression that a single object by itself can satisfy. Concepts and expressions of this sort are monad (Greek philosophy), monadic or "one-place" concepts and expressions. So the extension of the word "dog" is the set of all (past, present and future) dogs in the world: the set includes Fido, Rover, Lassie, Rex, and so on. The extension of the ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and reference. Sense is given by the ideas and concepts associated with an expression while reference is the object to which an expression points. Semantics contrasts with syntax, which studies the rules that dictate how to create grammatically correct sentences, and pragmatics, which investigates how people use language in communication. Lexical semantics is the branch of semantics that studies word meaning. It examines whether words have one or several meanings and in what lexical relations they stand to one another. Phrasal semantics studies the meaning of sentences by exploring the phenomenon of compositionality or how new meanings can be created by arranging words. Formal semantics (natural language), Formal semantics relies o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
