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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: "A ... [...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 In artificial intelligence (AI), an expert system is a computer system emulating the decision-making ability of a human expert. Expert systems are designed to solve complex problems by Automated reasoning system, reasoning through bodies of knowl ... were developed to tackle the problem of extracting scientific hypotheses from data, with or without interacting with a human scientist. These syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Douglas Lenat
Douglas Bruce Lenat (September 13, 1950 – August 31, 2023) was an American computer scientist and researcher in artificial intelligence who was the founder and CEO of Cycorp, Inc. in Austin, Texas. Lenat 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 the 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 A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Lisp Programming Language
Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized Polish notation#Explanation, prefix notation. Originally specified in the late 1950s, it is the second-oldest high-level programming language still in common use, after Fortran. Lisp has changed since its early days, and many Programming language dialect, dialects have existed over its history. Today, the best-known general-purpose Lisp dialects are Common Lisp, Scheme (programming language), Scheme, Racket (programming language), 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, includ ... [...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) * And ... [...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 list of unsolved problems in mathematics, unsolved problems in number theory and all of mathematics. It states that every even and odd numbers, 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 but remains unproven despite considerable effort. History Origins On 7 June 1742, the Prussian 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 Prime number#Primality of one, considering 1 to be a prime number, so that a sum of units would 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 th ... [...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 is prime or 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; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Eurisko
Eurisko ( Gr., ''I discover'') is a discovery system written by Douglas Lenat in 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 development of Cyc. Lenat envisioned ultimately coupling the Cyc knowledge base 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 frame language based representation he called RLL ( Representation Language Language), heuristic cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Heuristic
A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. 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. Context Gigerenzer & Gaissmaier (2011) state that sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer-assisted Proof
Automation describes a wide range of technologies that reduce human intervention in processes, mainly by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines. Automation has been achieved by various means including mechanical, hydraulic, pneumatic, electrical, electronic devices, and computers, usually in combination. Complicated systems, such as modern factories, airplanes, and ships typically use combinations of all of these techniques. The benefit of automation includes labor savings, reducing waste, savings in electricity costs, savings in material costs, and improvements to quality, accuracy, and precision. Automation includes the use of various equipment and control systems such as machinery, processes in factories, boilers, and heat-treating ovens, switching on telephone networks, steering, stabilization of ships, aircraft and other applications and vehicles with reduced human ... [...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 motivating factor for the development of computer science. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ... [...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 langua ... [...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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |