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Superposition Calculus
The superposition calculus is a calculus for reasoning in equational first-order logic. It was developed in the early 1990s and combines concepts from first-order resolution with ordering-based equality handling as developed in the context of (unfailing) Knuth–Bendix completion. It can be seen as a generalization of either resolution (to equational logic) or unfailing completion (to full clausal logic). As most first-order calculi, superposition tries to show the ''unsatisfiability'' of a set of first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation-complete—given unlimited resources and a ''fair'' derivation strategy, from any unsatisfiable clause set a contradiction will eventually be derived. , most of the (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement the pure calculus. Implementations * E * SPASS * Vampire * Waldmeisterbr>(off ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined abstraction, system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive Symbol (formal), symbols (which collectively form an Alphabet (computer science), alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SPASS Theorem Prover
SPASS is an automated theorem prover for first-order logic with equality developed at the Max Planck Institute for Computer Science and using the superposition calculus. The name originally stood for ''Synergetic Prover Augmenting Superposition with Sorts''. The theorem proving system is released under the FreeBSD license. An extension of SPASS called SPASS-XDB added support for on-the-fly retrieval of positive unit axioms from external sources. SPASS-XDB can thus incorporate facts coming from relational databases, web services, or linked data In computing, linked data (often capitalized as Linked Data) is structured data which is interlinked with other data so it becomes more useful through semantic queries. It builds upon standard Web technologies such as HTTP, RDF and URIs, but ... servers. Support for arithmetic using Mathematica was also added. References Sources *. External links *{{Official website, www.spass-prover.org Free theorem provers Unix programming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Press
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962. History The MIT Press traces its origins back to 1926 when MIT published under its own name a lecture series entitled ''Problems of Atomic Dynamics'' given by the visiting German physicist and later Nobel Prize winner, Max Born. Six years later, MIT's publishing operations were first formally instituted by the creation of an imprint called Technology Press in 1932. This imprint was founded by James R. Killian, Jr., at the time editor of MIT's alumni magazine and later to become MIT president. Technology Press published eight titles independently, then in 1937 entered into an arrangement with John Wiley & Sons in which Wiley took over marketing and editorial responsibilities. In 1962 the association with Wiley came to an end after a further 125 titles had been published. The press acquired its modern name af ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit marg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Handbook Of Automated Reasoning
The ''Handbook of Automated Reasoning'' (, 2128 pages) is a collection of survey articles on the field of automated reasoning. Published in June 2001 by MIT Press, it is edited by John Alan Robinson and Andrei Voronkov. Volume 1 describes methods for classical logic, first-order logic with equality and other theories, and induction. Volume 2 covers higher-order, non-classical and other kinds of logic. Index Volume 1 ;History ;Classical Logic ;Equality and Other Theories ;Induction Volume 2 ;Higher-Order Logic and Logical Frameworks ;Nonclassical Logics ;Decidable Classes and Model Building ;Implementation {{Ordered list , start=26 , I.V. Ramakrishnan, R.Sekar, Andrei Voronkov. Term Indexing, pp. 1853–1964. , Christoph Weidenbach Christoph is a male given name and surname. It is a German variant of Christopher. Notable people with the given name Christoph * Christoph Bach (1613–1661), German musician * Christoph Büchel (born 1966), Swiss artist * Ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harald Ganzinger
Harald Ganzinger (31 October 1950, Werneck – 3 June 2004, Saarbrücken) was a German computer scientist who together with Leo Bachmair developed the superposition calculus, which is (as of 2007) used in most of the state-of-the-art automated theorem provers for first-order logic. He received his Ph.D. from the Technical University of Munich in 1978. Before 1991 he was a Professor of Computer Science at University of Dortmund. Then he joined the Max Planck Institute for Computer Science in Saarbrücken shortly after it was founded in 1991. Until 2004 he was the Director of the Programming Logics department of the Max Planck Institute for Computer Science and honorary professor at Saarland University. His research group created the SPASS automated theorem prover. He received the Herbrand Award in 2004 (posthumous) for his important contributions to automated theorem proving. References *Rewrite-Based Equational Theorem Proving with Selection and Simplification', Leo Bachm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waldmeister Theorem Prover
''Waldmeister'' (''Woodruff'') is an operetta written by Johann Strauss II to a libretto by . It was first performed on 4 December 1895 at the Theater an der Wien. Although not as popular as some of Strauss' other operettas, such as ''Der Zigeunerbaron'' and ''Die Fledermaus'', it was given eighty-eight performances, and was much admired by Johannes Brahms, a friend of the composer. Roles Synopsis Overture \relative b' Act 1 ''The inside of a mill in the forest'' The apprentice foresters are on a hunting trip to the mill in the forest with the singer Pauline and her friends when they are surprised by the rain and get completely drenched. They are given dry clothes by the miller boys and maids of foreman Martin for a good price. Professor Müller, who is applying for a job at the forest academy and botanizing in the forest, is also driven into the mill by the rain. He meets the cute Jeanne, Pauline's travel companion, whom he likes and who, like everything that interests ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vampire Theorem Prover
Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester. Up to Version 3, it was developed by Andrei Voronkov together with Kryštof Hoder and previously with Alexandre Riazanov. Since Version 4, the development has involved a wider international team including Laura Kovacs, Giles Reger, and Martin Suda. Since 1999 it has won at least 53 trophies in the CADE ATP System Competition, the "world cup for theorem provers", including the most prestigious FOF division and the theory-reasoning TFA division. Background Vampire's kernel implements the calculi of ordered binary resolution and superposition for handling equality. The splitting rule and negative equality splitting can be simulated by the introduction of new predicate definitions and dynamic folding of such definitions. A DPLL-style algorithm splitting is also supported. A number of standard redundancy criteria and simplification ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E Equational Theorem Prover
E is a high-performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely equational paradigm. It has been integrated into other theorem provers and it has been among the best-placed systems in several theorem proving competitions. E is developed by Stephan Schulz, originally in the ''Automated Reasoning Group'' at TU Munich, now at Baden-Württemberg Cooperative State University Stuttgart. System The system is based on the equational superposition calculus. In contrast to most other current provers, the implementation actually uses a purely equational paradigm, and simulates non-equational inferences via appropriate equality inferences. Significant innovations include shared term rewriting (where many possible equational simplifications are carried out in a single operation), several efficient term indexing data structures for speeding up inferences, advanced inference literal selection strategies, and v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 and inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Theorem Prover
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 and inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unsatisfiable
In mathematical logic, a Well-formed formula, formula is ''satisfiable'' if it is true under some assignment of values to its Variable (mathematics), variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over the integers. The dual concept to satisfiability is Validity (logic), validity; a formula is ''valid'' if every assignment of values to its variables makes the formula true. For example, x+3=3+x is valid over the integers, but x+3=y is not. Formally, satisfiability is studied with respect to a fixed logic defining the Syntax (logic), syntax of allowed symbols, such as first-order logic, second-order logic or propositional calculus, propositional logic. Rather than being syntactic, however, satisfiability is a semantics, semantic property because it relates to the ''meaning'' of the symbols, for example, the meaning of + in a formula such as x+1=x. Formally, we define an interpretation (logic), i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
