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Calculus Ratiocinator
The Calculus ratiocinator
Calculus ratiocinator
is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned characteristica universalis, a universal conceptual language.Contents1 Two views1.1 The analytic view 1.2 The synthetic view2 Notes 3 See also 4 References 5 External linksTwo views[edit] There are two contrasting points of view on what Leibniz meant by calculus ratiocinator
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General Systems Theory
Systems
Systems
theory is the interdisciplinary study of systems. A system is a cohesive conglomeration of interrelated and interdependent parts that is either natural or man-made. Every system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose or nature and expressed in its functioning. In terms of its effects, a system can be more than the sum of its parts if it expresses synergy or emergent behavior. Changing one part of the system usually affects other parts and the whole system, with predictable patterns of behavior. For systems that are self-learning and self-adapting, the positive growth and adaptation depend upon how well the system is adjusted with its environment. Some systems function mainly to support other systems by aiding in the maintenance of the other system to prevent failure
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Charles Sanders Peirce
CDPT: Commens Dictionary of Peirce's Terms CP x.y: Collected Papers, volume x, paragraph y EP x:y: The Essential Peirce, volume x, page y W x:y Writings of Charles S. Peirce, volume x, page yv t e Charles Sanders Peirce
Charles Sanders Peirce
(/pɜːrs/,[9] like "purse"; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism". He was educated as a chemist and employed as a scientist for 30 years. Today he is appreciated largely for his contributions to logic, mathematics, philosophy, scientific methodology, and semiotics, and for his founding of pragmatism. An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself, first and foremost, a logician. He made major contributions to logic, but logic for him encompassed much of that which is now called epistemology and philosophy of science
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Leibniz Wheel
A Leibniz wheel
Leibniz wheel
or stepped drum is a cylinder with a set of teeth of incremental lengths which, when coupled to a counting wheel, can be used in the calculating engine of a class of mechanical calculators. Invented by Leibniz in 1673, it was used for three centuries until the advent of the electronic calculator in the mid-1970s. Leibniz built a machine called the stepped reckoner based on that design in 1694.[1] It was made famous by
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Commonsense Knowledge (artificial Intelligence)
In artificial intelligence research, a commonsense knowledge base is a semantic network that focuses on capturing commonsense knowledge. Commonsense knowledge consists of facts about the everyday world, such as "Lemons are sour", that all humans are expected to know. Commonsense knowledge can underpin a commonsense reasoning process, to attempt inferences such as "You might bake a cake because you want to people to eat the cake". A natural language processing process can be attached to the commonsense knowledge base to allow the knowledge base to attempt to answer commonsense questions about the world.[1]Contents1 Commonsense reasoning 2 Applications 3 Data 4 Commonsense knowledge bases 5 See also 6 ReferencesCommonsense reasoning[edit] Main article: Commonsense reasoning Commonsense reasoning
Commonsense reasoning
simulates the human ability to make presumptions about the type and essence of ordinary situations they encounter every day
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Hartley Rogers
Hartley Rogers Jr. (1926–2015) was a mathematician who worked in recursion theory, and was a professor in the Mathematics Department of the Massachusetts Institute of Technology. The Rogers equivalence theorem is named after him. Born in 1926 in Buffalo, New York,[1] he studied under Alonzo Church at Princeton, and received his Ph.D. there in 1952. He served on the MIT faculty from 1956 until his death, July 17, 2015.[2] There he had been involved in many scholarly extracurricular activities, including running SPUR (Summer Program in Undergraduate Research) for MIT undergraduates, overseeing the mathematics section of RSI (Research Science Institute) for advanced high school students, and coaching the MIT Putnam exam team for nearly two decades starting in 1990, including the years 2003 and 2004 when MIT won for the first time since 1979
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Louis Couturat
Louis Couturat (French: [kutyʁa]; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist.Contents1 Life 2 Works 3 Notes 4 References 5 External linksLife[edit] Born in Ris-Orangis, Essonne, France. In 1887 he entered École Normale Supérieure to study philosophy and mathematics. In 1895 he lectured in philosophy at the University of Toulouse
University of Toulouse
and 1897 lectured in philosophy of mathematics at University of Caen Normandy, taking a stand in favor of transfinite numbers
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Stepped Reckoner
... it is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine. — Gottfried Leibniz[1]The step reckoner (or stepped reckoner) was a digital mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1672 and completed in 1694.[1] The name comes from the translation of the German term for its operating mechanism, Staffelwalze, meaning 'stepped drum'. It was the first calculator that could perform all four arithmetic operations.[2] Its intricate precision gearwork, however, was somewhat beyond the fabrication technology of the time; mechanical problems, in addition to a design flaw in the carry mechanism, prevented the machines from working reliably.[3][4] Two prototypes were built; today only one survives in the National Library of Lower Saxony
Lower Saxony
(Niedersächsische Landesbibliothek) in Hanover, Germany
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Norbert Wiener
Norbert Wiener
Norbert Wiener
(November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
(MIT)
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Electronic Engineering
Electronic engineering
Electronic engineering
(also called electronics and communications engineering) is an electrical engineering discipline which utilizes nonlinear and active electrical components (such as semiconductor devices, especially transistors, diodes and integrated circuits) to design electronic circuits, devices, VLSI
VLSI
devices and their systems. The discipline typically also designs passive electrical components, usually based on printed circuit boards. Electronics
Electronics
is a subfield within the wider electrical engineering academic subject but denotes a broad engineering field that covers subfields such as analog electronics, digital electronics, consumer electronics, embedded systems and power electronics
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Cybernetics
Cybernetics
Cybernetics
is a transdisciplinary[1] approach for exploring regulatory systems—their structures, constraints, and possibilities. Norbert Wiener
Norbert Wiener
defined cybernetics in 1948 as "the scientific study of control and communication in the animal and the machine."[2] In the 21st century, the term is often used in a rather loose way to imply "control of any system using technology." In other words, it is the scientific study of how humans, animals and machines control and communicate with each other. Cybernetics
Cybernetics
is applicable when a system being analyzed incorporates a closed signaling loop—originally referred to as a "circular causal" relationship—that is, where action by the system generates some change in its environment and that change is reflected in the system in some manner (feedback) that triggers a system change
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Proof Theory
Proof theory is a major branch[1] of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity
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Frege
Friedrich Ludwig Gottlob Frege
Gottlob Frege
(/ˈfreɪɡə/;[10] German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language and mathematics. Though largely ignored during his lifetime, Giuseppe Peano
Giuseppe Peano
(1858–1932) and Bertrand Russell (1872–1970) introduced his work to later generations of logicians and philosophers. His contributions include the development of modern logic in the Begriffsschrift
Begriffsschrift
and work in the foundations of mathematics. His book the Foundations of Arithmetic
Foundations of Arithmetic
is the seminal text of the logicist project, and is cited by Michael Dummett
Michael Dummett
as where to pinpoint the linguistic turn
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Computer Program
A computer program is a structured collection of instruction sequences[1][2] that perform a specific task when executed by a computer. A computer requires programs to function. A computer program is usually written by a computer programmer in a programming language. From the program in its human-readable form of source code, a compiler can derive machine code—a form consisting of instructions that the computer can directly execute. Alternatively, a computer program may be executed with the aid of an interpreter. The evolution of a process is directed by a pattern of rules called a program. People create programs to direct processes. A formal model of some part of a computer program that performs a general and well-defined task is called an algorithm. A collection of computer programs, libraries, and related data are referred to as software
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Mathematical Logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science.[1] The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic
Logic
in computer science for those. Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics
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Logic
Logic
Logic
(from the Ancient Greek: λογική, translit. logikḗ[1]), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth,[2] and is now generally held to consist of the systematic study of the form of valid inference. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. (In ordinary discourse, inferences may be signified by words like therefore, hence, ergo, and so on.) There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference, including fallacies, and the study of semantics, including paradoxes
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