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Extension (logic)
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 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 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 phrase "Wikipedia reader" includes each person w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linguistics
Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds and equivalent gestures in sign languages), phonology (the abstract sound system of a particular language, and analogous systems of sign languages), and pragmatics (how the context of use contributes to meaning). Subdisciplines such as biolinguistics (the study of the biological variables and evolution of language) and psycholinguistics (the study of psychological factors in human language) bridge many of these divisions. Linguistics encompasses Outline of linguistics, many branches and subfields that span both theoretical and practical applications. Theoretical linguistics is concerned with understanding the universal grammar, universal and Philosophy of language#Nature of language, fundamental nature of language and developing a general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathematics), modules, vector spaces, lattice (order), lattices, and algebra over a field, algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variable (mathematics), variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in mathematical education, pedagogy. Algebraic structures, with their associated homomorphisms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Possible Worlds
Possible Worlds may refer to: * Possible worlds, concept in philosophy * ''Possible Worlds'' (play), 1990 play by John Mighton ** ''Possible Worlds'' (film), 2000 film by Robert Lepage, based on the play * Possible Worlds (studio) * ''Possible Worlds'', poetry book by Peter Porter * ''Possible Worlds'', book by J. B. S. Haldane * ''Possible Worlds'', 1995 album by Markus Stockhausen See also * * * Possible (other) * World (other) {{dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaphysics
Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of human understanding. Some philosophers, including Aristotle, designate metaphysics as first philosophy to suggest that it is more fundamental than other forms of philosophical inquiry. Metaphysics encompasses a wide range of general and abstract topics. It investigates the nature of existence, the features all entities have in common, and their division into categories of being. An influential division is between particulars and universals. Particulars are individual unique entities, like a specific apple. Universals are general features that different particulars have in common, like the color . Modal metaphysics examines what it means for something to be possible or necessary. Metaphysicians also explore the concepts of space, time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Row (database)
In a relational database, a row or " record" or " tuple", represents a single, implicitly structured data Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ... item in a table. A database table can be thought of as consisting of rows and columns. Cory Janssen, Techopedia, retrieved 27 June 2014 Each row in a table represents a set of related data, and every row in the table has the same structure. For example, in a table that represents companies, each row might represent a single company. Columns might represent things like company name, address, etc. In a table that represents ''the association'' of empl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Schema
A logical data model or logical schema is a data model of a specific problem domain expressed independently of a particular database management product or storage technology ( physical data model) but in terms of data structures such as relational tables and columns, object-oriented classes, or XML tags. This is as opposed to a conceptual data model, which describes the semantics of an organization without reference to technology. Overview Logical data models represent the abstract structure of a domain of information. They are often diagrammatic in nature and are most typically used in business processes that seek to capture things of importance to an organization and how they relate to one another. Once validated and approved, the logical data model can become the basis of a physical data model and form the design of a database. Logical data models should be based on the structures identified in a preceding conceptual data model, since this describes the semantics of the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Database
In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application associated with the database. Before digital storage and retrieval of data have become widespread, index cards were used for data storage in a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flash c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characterization (mathematics)
In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. To say that "Property ''P'' characterizes object ''X''" is to say that not only does ''X'' have property ''P'', but that ''X'' is the ''only'' thing that has property ''P'' (i.e., ''P'' is a defining property of ''X''). Similarly, a set of properties ''P'' is said to characterize ''X'', when these properties distinguish ''X'' from all other objects. Even though a characterization identifies an object in a unique way, several characterizations can exist for a single object. Common mathematical expressions for a characterization of ''X'' in terms of ''P'' include "''P'' is necessary and sufficient for ''X''", and "''X'' holds if and only if ''P''". It is also common to find statements such as "Property ''Q'' characterizes ''Y'' up to isomorphism". The first type of statement says in different words that the extension o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Object
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a Glossary of mathematical symbols, symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, Expression (mathematics), expressions, shapes, function (mathematics), functions, and set (mathematics), sets. Mathematical objects can be very complex; for example, theorems, proof (mathematics), proofs, and even theory (mathematical logic), formal theories are considered as mathematical objects in proof theory. In Philosophy of mathematics, the concept of "mathematical objects" touches on topics of existence, Identity (philosophy), identity, and the Nature (philosophy), nature of reality. In metaphysics, objects are often considered Entity, entities that possess Property (philosophy), properties and can stand in various Relation (philosophy), relations to one another. Philosophers debate whether m ... [...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] |
