Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry; Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
In artificial intelligence, 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 reasoning through bodies of knowledge, represented mainly as if–then rules rather than through conventional procedural code. The first expert systems were created in the 1970s and then proliferated in the 1980s. Expert systems were among the first truly successful forms of artificial intelligence (AI) software. An expert system is divided into two subsystems: the inference engine and the knowledge base. The knowledge base represents facts and rules. The inference engine applies the rules to the known facts to deduce new facts. Inference engines can also include explanation and debugging abilities.
Kerberos is a computer-network authentication protocol that works on the basis of tickets to allow nodes communicating over a non-secure network to prove their identity to one another in a secure manner. Its designers aimed it primarily at a client–server model, and it provides mutual authentication—both the user and the server verify each other's identity. Kerberos protocol messages are protected against eavesdropping and replay attacks.
Truth is the property of being in accord with fact or reality. In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.
Hearsay is testimony from a witness under oath who is reciting an out-of-court statement that is being offered to prove the truth of the matter asserted.
In computer programming, specifically when using the imperative programming paradigm, an assertion is a predicate connected to a point in the program, that always should evaluate to true at that point in code execution. Assertions can help a programmer read the code, help a compiler compile it, or help the program detect its own defects.
In logic, a three-valued logic 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 which provide only for true and false.
William Kingdon Clifford was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, geometry, and computing. Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression mind-stuff.
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
Clifford Walter Dupont, GCLM, ID was a British-born Rhodesian politician who served in the internationally unrecognised positions of officer administrating the government and president. Born in London and qualifying as a solicitor, Dupont served during the Second World War as an officer of the British Royal Artillery in North Africa before first visiting Southern Rhodesia in 1947. He returned a year later, started a ranch and emigrated full-time during the early 1950s, by which time the country had become a territory of the Federation of Rhodesia and Nyasaland.
A temporal database stores data relating to time instances. It offers temporal data types and stores information relating to past, present and future time. Temporal databases could be uni-temporal, bi-temporal or tri-temporal.
In temporal databases, valid time (VT) is the time period during which a database fact is valid in the modeled reality. As of December 2011, ISO/IEC 9075, Database Language SQL:2011 Part 2: SQL/Foundation included clauses in table definitions to define "application-time period tables". Valid time was coined by Richard T. Snodgrass and his doctoral student.
In mathematical logic, a tautology is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball.
A real-time database is a database system which uses real-time processing to handle workloads whose state is constantly changing. This differs from traditional databases containing persistent data, mostly unaffected by time. For example, a stock market changes very rapidly and is dynamic. The graphs of the different markets appear to be very unstable and yet a database has to keep track of current values for all of the markets of the New York Stock Exchange. Real-time processing means that a transaction is processed fast enough for the result to come back and be acted on right away. Real-time databases are useful for accounting, banking, law, medical records, multi-media, process control, reservation systems, and scientific data analysis.
The Herrmann Brain Dominance Instrument (HBDI) is a system to measure and describe thinking preferences in people, developed by William "Ned" Herrmann while leading management education at General Electric's Crotonville facility. It is a type of cognitive style measurement and model, and is often compared to psychological assessments such as the Myers-Briggs Type Indicator, Learning Orientation Questionnaire, DISC assessment, and others.
Feist Publications, Inc., v. Rural Telephone Service Co., 499 U.S. 340 (1991), was a landmark decision by the Supreme Court of the United States establishing that information alone without a minimum of original creativity cannot be protected by copyright. In the case appealed, Feist had copied information from Rural's telephone listings to include in its own, after Rural had refused to license the information. Rural sued for copyright infringement. The Court ruled that information contained in Rural's phone directory was not copyrightable and that therefore no infringement existed.
In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
Richard Thomas Snodgrass is an American computer scientist and writer and is professor emeritus at the University of Arizona. He is best known for his work on temporal databases, query language design, query optimization and evaluation, storage structures, database design, and ergalics.
