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Logical Machine
A logical machine is a tool containing a set of parts that uses energy to perform formal logic operations. Early logical machines were mechanical devices that performed basic operations in Boolean logic. Contemporary logical machines are computer-based electronic programs that perform proof assistance with theorems in mathematical logic. In the 21st century, these proof assistant programs have given birth to a new field of study called mathematical knowledge management. Origins The earliest logical machines were mechanical constructs built in the late 19th century. William Stanley Jevons invented the first logical machine in 1869, the logic piano. In 1883, Allan Marquand invented a new logical machine that performed the same operations as Jevons' logic piano but with improvements in design simplification, portability, and input-output controls. See also *Allan Marquand *William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English econo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tool
A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for preparation of food, hunting, manufacture of weapons, and working of materials to produce clothing and useful artifacts. The development of metalworking made additional types of tools possible. Harnessing energy sources, such as animal power, wind, or steam, allowed increasingly complex tools to produce an even larger range of items, with the Industrial Revolution marking an inflection point in the use of tools. The introduction of widespread automation in the 19th and 20th centuries allowed tools to operate with minimal human supervision, further increasing the productivity of ... [...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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses Logical connective, logical operators such as Logical conjunction, conjunction (''and'') denoted as ∧, Logical disjunction, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''The Laws of Thought, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Assistant
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. System comparison * ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. * Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification. * HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems the logical core is a library of their programming language. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Knowledge Management
Mathematical knowledge management (MKM) is the study of how society can effectively make use of the vast and growing literature on mathematics. It studies approaches such as databases of mathematical knowledge, automated processing of formulae and the use of semantic information, and artificial intelligence. Mathematics is particularly suited to a systematic study of automated knowledge processing due to the high degree of interconnectedness between different areas of mathematics. See also *OMDoc *QED manifesto *Areas of mathematics *MathML External links * www.nist.gov/mathematical-knowledge-management NIST's MKM pageThe MKM Interest Group(archived) a programme at the Isaac Newton Institute
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William Stanley Jevons
William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in economics. It made the case that economics, as a science concerned with quantities, is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons's contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. Jevons broke off his studies of the natural sciences in London in 1854 to work as an assayer in Sydney, where he acquired an interest in political economy. Returning to the UK in 1859, h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Allan Marquand
Allan Marquand (; December 10, 1853 – September 24, 1924) was an art historian at Princeton University and a curator of the Princeton University Art Museum. Early life Marquand was born on December 10, 1853 in New York City. He was a son of Elizabeth Love (née Allen) Marquand (1826–1895) and Henry Gurdon Marquand, a prominent philanthropist and art collector who served as the second president of the Metropolitan Museum of Art. After graduating from Princeton in 1874, Allan obtained his Ph.D. in Philosophy at the Johns Hopkins University in 1880. His thesis, supervised by Charles Sanders Peirce, was on the logic of Philodemus. Career After obtaining his Ph.D., he returned to Princeton in 1881 to teach Latin and logic. During the 1881–1882 academic year, Marquand built a mechanical logical machine that is still extant; he was inspired by related efforts of William S. Jevons in the UK. In 1887, following a suggestion of Peirce's, he outlined a machine to do logic usi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logics For Computability
Logics for computability are formulations of logic which capture some aspect of computability as a basic notion. This usually involves a mix of special logical connectives as well as semantics which explains how the logic is to be interpreted in a computational way. Probably the first formal treatment of logic for computability is the '' realizability interpretation'' by Stephen Kleene in 1945, who gave an interpretation of intuitionistic number theory in terms of Turing machine computations. His motivation was to make precise the '' Heyting-Brouwer-Kolmogorov (BHK) interpretation'' of intuitionism, according to which proofs of mathematical statements are to be viewed as constructive procedures. With the rise of many other kinds of logic, such as modal logic and linear logic, and novel semantic models, such as game semantics, logics for computability have been formulated in several contexts. Here we mention two. Modal logic for computability Kleene's original realizability interpre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce Bibliography
This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), see the (Chronological Overview) on the (Writings) page for Charles Sanders Peirce. Abbreviations Click on abbreviation in order to jump down this page to the relevant edition information. Click on the abbreviation appearing with that edition information in order to return here. Main editions (posthumous) Other Primary literature Bibliographies and microfilms Other bibliographies of primary literature * Burks, Arthur W. (1958). "Bibliography of the Works of Charles Sanders Peirce." CP 8:260–321. * Cohen, Morris R. (1916). "Charles S. Peirce and a Tentative Bibliography of His Published Writings." ''The Journal of Philosophy, Psychology, and Scientific Methods'' 13(26):726–37. *Fisch, Max H. (1964). "A First Supplement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
