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Automated Mathematician
The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts;. for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. Controversy Lenat claimed that the system was composed of hundreds of data structures called "concepts," together with hundreds of "heuristic rules" and a simple flow of control: "AM ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Discovery System (AI Research)
A discovery system is an artificial intelligence system that attempts to discover new scientific concepts or laws. The aim of discovery systems is to automate scientific data analysis and the scientific discovery process. Ideally, an artificial intelligence system should be able to search systematically through the space of all possible hypotheses and yield the hypothesis - or set of equally likely hypotheses - that best describes the complex patterns in data. During the era known as the second AI summer (approximately 1978-1987), various systems akin to the era's dominant expert systems were developed to tackle the problem of extracting scientific hypotheses from data, with or without interacting with a human scientist. These systems included Autoclass, Automated Mathematician, Eurisko, which aimed at general-purpose hypothesis discovery, and more specific systems such as Dalton, which uncovers molecular properties from data. The dream of building systems that discover scientifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Douglas Lenat
Douglas Bruce Lenat (born 1950) is the CEO of Cycorp, Inc. of Austin, Texas, and has been a prominent researcher in artificial intelligence; he was awarded the biannual IJCAI Computers and Thought Award in 1976 for creating the machine learning program, AM. He has worked on (symbolic, not statistical) machine learning (with his AM and Eurisko programs), knowledge representation, "cognitive economy", blackboard systems, and what he dubbed in 1984 "ontological engineering" (with his Cyc program at MCC and, since 1994, at Cycorp). He has also worked in military simulations, and numerous projects for US government, military, intelligence, and scientific organizations. In 1980, he published a critique of conventional random-mutation Darwinism. He authored a series of articles in the Journal of Artificial Intelligence exploring the nature of heuristic rules. Lenat was one of the original Fellows of the AAAI, and is the only individual to have served on the Scientific Advisory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Lisp Programming Language
Lisp (historically LISP) is a family of programming languages with a long history and a distinctive, fully parenthesized prefix notation. Originally specified in 1960, Lisp is the second-oldest high-level programming language still in common use, after Fortran. Lisp has changed since its early days, and many dialects have existed over its history. Today, the best-known general-purpose Lisp dialects are Common Lisp, Scheme, Racket and Clojure. Lisp was originally created as a practical mathematical notation for computer programs, influenced by (though not originally derived from) the notation of Alonzo Church's lambda calculus. It quickly became a favored programming language for artificial intelligence (AI) research. As one of the earliest programming languages, Lisp pioneered many ideas in computer science, including tree data structures, automatic storage management, dynamic typing, conditionals, higher-order functions, recursion, the self-hosting compiler, and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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IJCAI Computers And Thought Award
The IJCAI Computers and Thought Award is presented every two years by the International Joint Conference on Artificial Intelligence (IJCAI), recognizing outstanding young scientists in artificial intelligence. It was originally funded with royalties received from the book ''Computers and Thought'' (edited by Edward Feigenbaum and Julian Feldman), and is currently funded by IJCAI. It is considered to be "the premier award for artificial intelligence researchers under the age of 35". Laureates *Terry Winograd (1971) *Patrick Winston (1973) *Chuck Rieger (1975) *Douglas Lenat (1977) * David Marr (1979) *Gerald Sussman (1981) * Tom Mitchell (1983) * Hector Levesque (1985) *Johan de Kleer (1987) *Henry Kautz (1989) *Rodney Brooks (1991) * Martha E. Pollack (1991) * Hiroaki Kitano (1993) * Sarit Kraus (1995) * Stuart Russell (1995) * Leslie Kaelbling (1997) * Nicholas Jennings (1999) * Daphne Koller (2001) *Tuomas Sandholm (2003) * Peter Stone (2007) *Carlos Guestrin (2009) * Andrew Ng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Goldbach's Conjecture
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort. History On 7 June 1742, the German mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture: Goldbach was following the now-abandoned convention of considering 1 to be a prime number, so that a sum of units would indeed be a sum of primes. He then proposed a second conjecture in the margin of his letter, which implies the first: Euler replied in a letter dated 30 June 1742 and reminded Goldbach of an earlier conversation they had had (), in which Goldbach had remarked that the first of those two conjectures would follow from the statement This is in fact equivalent to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fundamental Theorem Of Arithmetic
In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. For example, : 1200 = 2^4 \cdot 3^1 \cdot 5^2 = (2 \cdot 2 \cdot 2 \cdot 2) \cdot 3 \cdot (5 \cdot 5) = 5 \cdot 2 \cdot 5 \cdot 2 \cdot 3 \cdot 2 \cdot 2 = \ldots The theorem says two things about this example: first, that 1200 be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product. The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, 12 = 2 \cdot 6 = 3 \cdot 4). This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique; for exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Eurisko
Eurisko (greek language, Gr., ''I discover'') is a Discovery system (AI research), discovery system written by Douglas Lenat in Representation Language Language, RLL-1, a representation language itself written in the Lisp programming language. A sequel to Automated Mathematician, it consists of heuristics, i.e. rules of thumb, including heuristics describing how to use and change its own heuristics. Lenat was frustrated by Automated Mathematician's constraint to a single domain and so developed Eurisko; his frustration with the effort of encoding domain knowledge for Eurisko led to Lenat's subsequent (and, , continuing) development of Cyc. Lenat envisions ultimately coupling the Cyc knowledgebase with the Eurisko discovery engine. History Development commenced at Carnegie Mellon in 1976 and continued at Stanford University in 1978 when Lenat returned to teach. "For the first five years, nothing good came out of it", Lenat said. But when the implementation was changed to a fram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples that employ heuristics include using trial and error, a rule of thumb or an educated guess. Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues. When an individual applies a heuristic in practice, it generally performs as expected. However it can alternati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer-assisted Proof
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program. Attempts have also been made in the area of artificial intelligence research to create smaller, explicit, new proofs of mathematical theorems from the bottom up using automated reasoning techniques such as heuristic search. Such automated theorem provers have proved a number of new results and found new proofs for known theorems. Additionally, interactive proof assistants allow mathematicians to develop human-readable proofs which are nonetheless formally verified for correctness. Since these proofs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Automated Theorem Proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. Logical foundations While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's '' Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His ''Foundations of Arithmetic'', published 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential '' Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Symbolic Mathematics
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes ''exact'' computation with expressions containing variables that have no given value and are manipulated as symbols. Software applications that perform symbolic calculations are called ''computer algebra systems'', with the term ''system'' alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Experimental Mathematics
Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit." As expressed by Paul Halmos: "Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does." History Mathematicians have always practiced experimental mathematics. Existing records ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |