Fuzzy logic Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. Compared to traditional binary sets (where variables may take on true or false values) fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false.[1] Furthermore, when linguistic variables are used, these degrees may be managed by specific functions. Irrationality can be described in terms of what is known as the fuzzjective.[citation needed] The term "fuzzy logic" was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Overview[edit] Classical logic only permits propositions having a value of truth or falsity. Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first. Applying truth values[edit] Fuzzy logic temperature Linguistic variables[edit]
Entropy (information theory) 2 bits of entropy. A single toss of a fair coin has an entropy of one bit. A series of two fair coin tosses has an entropy of two bits. This definition of "entropy" was introduced by Claude E. Entropy is a measure of unpredictability of information content. Now consider the example of a coin toss. English text has fairly low entropy. If a compression scheme is lossless—that is, you can always recover the entire original message by decompressing—then a compressed message has the same quantity of information as the original, but communicated in fewer characters. Shannon's theorem also implies that no lossless compression scheme can compress all messages. Named after Boltzmann's H-theorem, Shannon defined the entropy H (Greek letter Eta) of a discrete random variable X with possible values {x1, ..., xn} and probability mass function P(X) as: Here E is the expected value operator, and I is the information content of X.[8][9] I(X) is itself a random variable. . The average uncertainty , with
Linear function In mathematics, the term linear function refers to two different, although related, notions:[1] As a polynomial function[edit] In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero). For a function of any finite number independent variables, the general formula is and the graph is a hyperplane of dimension k. A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. In this context, the other meaning (a linear map) may be referred to as a homogeneous linear function or a linear form. As a linear map[edit] In linear algebra, a linear function is a map f between two vector spaces that preserves vector addition and scalar multiplication: Some authors use "linear function" only for linear maps that take values in the scalar field;[4] these are also called linear functionals. See also[edit]
Three-valued logic In logic, a three-valued logic (also trivalent, ternary, trinary logic, or trilean,[citation needed] sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false. Conceptual form and basic ideas were initially created by Jan Łukasiewicz and C. I. Lewis. Representation of values[edit] As with bivalent logic, truth values in ternary logic may be represented numerically using various representations of the ternary numeral system. Inside a ternary computer, ternary values are represented by ternary signals. This article mainly illustrates a system of ternary propositional logic using the truth values {false, unknown, and true}, and extends conventional Boolean connectives to a trivalent context. Logics[edit] Kleene logic[edit] See also[edit]
Ada Lovelace Augusta Ada King, Countess of Lovelace (10 December 1815 – 27 November 1852), born Augusta Ada Byron and now commonly known as Ada Lovelace, was an English mathematician and writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the Analytical Engine. Her notes on the engine include what is recognised as the first algorithm intended to be carried out by a machine. Because of this, she is often described as the world's first computer programmer.[1][2][3] Ada described her approach as "poetical science" and herself as an "Analyst (& Metaphysician)". As a young adult, her mathematical talents led her to an ongoing working relationship and friendship with fellow British mathematician Charles Babbage, and in particular Babbage's work on the Analytical Engine. Biography[edit] Childhood[edit] Ada, aged four On 16 January 1816, Annabella, at George's behest, left for her parents' home at Kirkby Mallory taking one-month-old Ada with her. Adult years[edit]
Polynomial The graph of a polynomial function of degree 3 Etymology[edit] According to the Oxford English Dictionary, polynomial succeeded the term binomial, and was made simply by replacing the Latin root bi- with the Greek poly-, which comes from the Greek word for many. The word polynomial was first used in the 17th century.[1] Notation and terminology[edit] It is a common convention to use upper case letters for the indeterminates and the corresponding lower case letters for the variables (arguments) of the associated function. It may be confusing that a polynomial P in the indeterminate X may appear in the formulas either as P or as P(X). Normally, the name of the polynomial is P, not P(X). In particular, if a = X, then the definition of P(a) implies This equality allows writing "let P(X) be a polynomial" as a shorthand for "let P be a polynomial in the indeterminate X". Definition[edit] A polynomial in a single indeterminate can be written in the form where For example: is a term. then is from
Principle of explosion The principle of explosion, (Latin: ex falso quodlibet, "from a falsehood, anything follows", or ex contradictione sequitur quodlibet, "from a contradiction, anything follows") or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction.[1] That is, once a contradiction has been asserted, any proposition (or its negation) can be inferred from it. As a demonstration of the principle, consider two contradictory statements - “All lemons are yellow” and "Not all lemons are yellow", and suppose (for the sake of argument) that both are simultaneously true. If that is the case, anything can be proven, e.g. "Santa Claus exists", by using the following argument: Symbolic representation[edit] The principle of explosion can be expressed in the following way (where " " symbolizes the relation of logical consequence): or This can be read as, "If one claims something is both true ( .
Top 50 Free Open Source Classes on Computer Science : Comtechtor Computer science is an interesting field to go into. There are a number of opportunities in computer science that you can take advantage of. With computers increasingly becoming a regular part of life, those who can work with computers have good opportunities. You can find a good salary with a program in computer science, and as long as you are careful to keep up your skills. Introduction to Computer Science Learn the basics of computer science, and get a foundation in how computer science works. Introduction to Computer Science: Learn about the history of computing, as well as the development of computer languages. Comprehensive Computer Science Collections If you are interested in courses that are a little more comprehensive in nature, you can get a good feel for computer science from the following collections: Programming and Languages Get a handle on computer programming, and learn about different computer languages used in programming. Computer Software Computer Processes and Data
How to Murder Time » Podcasters without portfolio Ignoratio elenchi Ignoratio elenchi, also known as irrelevant conclusion,[1] is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question. Ignoratio elenchi falls into the broad class of relevance fallacies.[2] It is one of the fallacies identified by Aristotle in his Organon. In a broader sense he asserted that all fallacies are a form of ignoratio elenchi.[3][4] Ignoratio Elenchi, according to Aristotle, is a fallacy which arises from “ignorance of the nature of refutation.” The phrase ignoratio elenchi is Latin meaning "an ignoring of a refutation". An example might be a situation where A and B are debating whether the law permits A to do something. See also[edit] References[edit] External links[edit]