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William McCune
William Walker McCune (December 17, 1953 – May 2, 2011) was an American computer scientist and logician working in the fields of automated reasoning, algebra, logic, and formal methods. He was best known for the development of the Otter, Prover9, and Mace4 automated reasoning systems, and the automated proof of the Robbins conjecture In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by \lor, and a single unary operation usually denoted by \neg. These operations satisfy the following axioms: For all elements ''a'', ''b'', ... using the EQP theorem prover. In 2000, McCune received the Herbrand Award for Distinguished Contributions to Automated Reasoning. In 2013, ''Automated Reasoning and Mathematics - Essays in Memory of William W. McCune'' was published in his honour. References External links Prover9 softwareWilliam McCune home pageUpdated version of Prover9 software 2011 deaths 1953 births American comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Technology
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, engineering, mathematical, technological and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology and software engineering. The term "computing" is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers. History The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. Computing is intimately tied to the representation of numbers, though mathematical concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of New Mexico
The University of New Mexico (UNM; es, Universidad de Nuevo México) is a public research university in Albuquerque, New Mexico. Founded in 1889, it is the state's flagship academic institution and the largest by enrollment, with over 25,400 students in 2021. UNM comprises twelve colleges and schools, including the only law school in New Mexico. It offers 94 baccalaureate, 71 masters, and 37 doctoral degrees. The main campus spans in central Albuquerque, with branch campuses in Gallup, Los Alamos, Rio Rancho, Taos, and Los Lunas. UNM is classified among "R1: Doctoral Universities – Very high research activity", and spent over $243 million on research and development in 2021, ranking 103rd in the nation. UNM's NCAA Division I program ( FBS for football) offers 16 varsity sports; known as the Lobos, the teams compete in the Mountain West Conference and have won national championships in skiing and cross country running. The official school colors are cherry and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otter (theorem Prover)
Otter is an automated theorem prover developed by William McCune at Argonne National Laboratory in Illinois. Otter was the first widely distributed, high-performance theorem prover for first-order logic, and it pioneered a number of important implementation techniques. ''Otter'' is an acronym for ''Organized Techniques for Theorem-proving and Effective Research''. Description Otter is based on resolution and paramodulation, constrained by term orderings similar to those in the superposition calculus. The prover also supports positive and negative hyperresolution and a set-of-support strategy. Proof search is based on saturation using a version of the given-clause algorithm, and is controlled by several heuristics. There also are meta-heuristics determining search parameters automatically. Otter also pioneered the use of efficient term indexing techniques to speed up the search for inference partners in large clause sets. Otter has been very stable for a number of years but is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mace4
Mace stands for "Models And Counter-Examples", and is a model finder. Most automated theorem provers try to perform a proof by refutation on the clause normal form of the proof problem, by showing that the combination of axioms and negated conjecture can never be simultaneously true, i.e. does not have a model. A model finder such as Mace, on the other hand, tries to find an explicit model of a set of clauses. If it succeeds, this corresponds to a counter-example for the conjecture, i.e. it disproves the (claimed) theorem. Mace is GNU GPL licensed. See also * Otter (theorem prover) * Prover9 Prover9 is an automated theorem prover for first-order and equational logic developed by William McCune. Description Prover9 is the successor of the Otter theorem prover also developed by William McCune. Prover9 is noted for producing relatively ... References External links System download Free theorem provers Free software {{logic-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prover9
Prover9 is an automated theorem prover for first-order and equational logic developed by William McCune. Description Prover9 is the successor of the Otter theorem prover also developed by William McCune. Prover9 is noted for producing relatively readable proofs and having a powerful hints strategy. Prover9 is intentionally paired with Mace4, which searches for finite models and counterexamples. Both can be run simultaneously from the same input, with Prover9 attempting to find a proof, while Mace4 attempts to find a (disproving) counter-example. Prover9, Mace4, and many other tools are built on an underlying library named LADR ("Library for Automated Deduction Research") to simplify implementation. Resulting proofs can be double-checked by Ivy, a proof-checking tool that has been separately verified using ACL2. In July 2006 the LADR/Prover9/Mace4 input language made a major change (which also differentiates it from Otter). The key distinction between "clauses" and "formulas" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robbins Conjecture
In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by \lor, and a single unary operation usually denoted by \neg. These operations satisfy the following axioms: For all elements ''a'', ''b'', and ''c'': # Associativity: a \lor \left(b \lor c \right) = \left(a \lor b \right) \lor c # Commutativity: a \lor b = b \lor a # ''Robbins equation'': \neg \left( \neg \left(a \lor b \right) \lor \neg \left(a \lor \neg b \right) \right) = a For many years, it was conjectured, but unproven, that all Robbins algebras are Boolean algebras. This was proved in 1996, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra". History In 1933, Edward Huntington proposed a new set of axioms for Boolean algebras, consisting of (1) and (2) above, plus: *''Huntington's equation'': \neg(\neg a \lor b) \lor \neg(\neg a \lor \neg b) = a. From these axioms, Huntington derived the usual axioms of Boolean algebra. Very soon thereafte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Scientist
A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (although there is overlap). Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering, information theory, database theory, computational complexity theory, numerical analysis, programming language theory, computer graphics, and computer vision), their foundation is the theoretical study of computing from which these other fields derive. A primary goal of computer scientists is to develop or validate models, often mathematical, to describe the properties of computational systems (processors, programs, computers interacting with people, computers interacting with other computers, etc.) with an overall objective of discovering des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logician
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 und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Reasoning
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science and philosophy. The most developed subareas of automated reasoning are automated theorem proving (and the less automated but more pragmatic subfield of interactive theorem proving) and automated proof checking (viewed as guaranteed correct reasoning under fixed assumptions). Extensive work has also been done in reasoning by analogy using induction and abduction. Other important topics include reasoning under uncertainty and non-monotonic reasoning. An important part of the uncertainty field is that of argumentation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Methods
In computer science, formal methods are mathematically rigorous techniques for the specification, development, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design. Formal methods employ a variety of theoretical computer science fundamentals, including logic calculi, formal languages, automata theory, control theory, program semantics, type systems, and type theory. Background Semi-Formal Methods are formalisms and languages that are not considered fully “formal”. It defers the task of completing the semantics to a later stage, which is then done either by human interpretation or by interpretation through software like code or test case generators. Taxonomy Formal methods can be used at a number of levels: Level 0: Formal specification may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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