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
Quantum Aspects of Life Quantum Aspects of Life is a 2008 science text, with a foreword by Sir Roger Penrose, which explores the open question of the role of quantum mechanics at molecular scales of relevance to biology. The book adopts a debate-like style and contains chapters written by various world-experts; giving rise to a mix of both sceptical and sympathetic viewpoints. The book addresses questions of quantum physics, biophysics, nanoscience, quantum chemistry, mathematical biology, complexity theory, and philosophy that are inspired by the 1944 seminal book What Is Life? by Erwin Schrödinger. Contents[edit] Foreword by Sir Roger Penrose Section 1: Emergence and Complexity Chapter 1: "A Quantum Origin of Life?" Section 2: Quantum Mechanisms in Biology Chapter 3: "Quantum Coherence and the Search for the First Replicator" by Jim Al-Khalili and Johnjoe McFaddenChapter 4: "Ultrafast Quantum Dynamics in Photosynthesis" by Alexandra Olaya-Castro, Francesca Fassioli Olsen, Chiu Fan Lee, and Neil F. 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]
The Emperor's New Mind The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics is a 1989 book by mathematical physicist Sir Roger Penrose. Penrose argues that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer. Penrose hypothesizes that quantum mechanics plays an essential role in the understanding of human consciousness. The collapse of the quantum wavefunction is seen as playing an important role in brain function. The majority of the book is spent reviewing, for the scientifically minded layreader, a plethora of interrelated subjects such as Newtonian physics, special and general relativity, the philosophy and limitations of mathematics, quantum physics, cosmology, and the nature of time. Penrose states that his ideas on the nature of consciousness are speculative, and his thesis is considered erroneous by experts in the fields of philosophy, computer science, and robotics.[1][2][3] See also[edit]
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
Orchestrated objective reduction Orchestrated objective reduction (Orch-OR) is a controversial 20-year-old theory of consciousness conceptualized by the theoretical physicist Sir Roger Penrose and anesthesiologist Stuart Hameroff, which claims that consciousness derives from deeper level, finer scale quantum activities inside the cells, most prevalent in the brain neurons. It combines approaches from the radically different angles of molecular biology, neuroscience, quantum physics, pharmacology, philosophy, quantum information theory, and aspects of quantum gravity.[1] The Penrose–Lucas argument[edit] The Penrose–Lucas argument states that, because humans are capable of knowing the truth of Gödel-unprovable statements, human thought is necessarily non-computable.[23] In 1931, mathematician and logician Kurt Gödel proved that any effectively generated theory capable of proving basic arithmetic cannot be both consistent and complete. Criticism of the Penrose–Lucas argument[edit] Objective reduction[edit] Motivation[edit]
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]