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SPASS
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 servers. Support for arithmetic using Mathematica Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ... was also added. References Sources *. External links *{{Official website, www.spass-prover.org Free theorem provers Unix programming t ... [...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 motivating factor for the development of computer science. Logical foundations While the roots of formalized logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His '' Foundations of Arithmetic'', published in 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Calculus
The superposition calculus is a calculus for reasoning in equational 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). Like 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. Many (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>(official web page ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic With Equality
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all ''x'', if ''x'' is a human, then ''x'' is mortal", where "for all ''x"'' is a quantifier, ''x'' is a variable, and "... ''is a human''" and "... ''is mortal''" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic, such as set theory, a theory for groups,A. Tarski, ''Undecidable Theories'' (1953), p. 77. Studies in Logic and the Foundation of Mathematics, North-Holland or a formal theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Planck Institute For Computer Science
The Max Planck Institute for Informatics (German: ''Max-Planck-Institut für Informatik'', abbreviated ''MPI-INF'' or ''MPII'') is a research institute in computer science with a focus on algorithms and their applications in a broad sense. It hosts fundamental research (algorithms and complexity, programming logics) as well a research for various application domains (computer graphics, geometric computation, constraint solving, computational biology). Founded November 1988 by the Max Planck Society, Germany's largest publicly funded body for foundation research, MPII is located on the campus of Saarland University. Research departments The institute promotes six departments and three independent research groups on its website. The six departments are Algorithms and Complexity; Computer Vision and Machine Learning; Internet Architecture; Computer Graphics; Databases and Information Systems; and Visual Computing and Artificial Intelligence. The three research groups are Auto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FreeBSD License
BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. This is in contrast to copyleft licenses, which have share-alike requirements. The original BSD license was used for its namesake, the Berkeley Software Distribution (BSD), a Unix-like operating system. The original version has since been revised, and its descendants are referred to as modified BSD licenses. BSD is both a license and a class of license (generally referred to as BSD-like). The modified BSD license (in wide use today) is very similar to the license originally used for the BSD version of Unix. The BSD license is a simple license that merely requires that all code retain the BSD license notice if redistributed in source code format, or reproduce the notice if redistributed in binary format. The BSD license (unlike some other licenses e.g. GPL) does not require that source code be distributed at all. Terms In addition to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Database
A relational database (RDB) is a database based on the relational model of data, as proposed by E. F. Codd in 1970. A Relational Database Management System (RDBMS) is a type of database management system that stores data in a structured format using rows and columns. Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. History The concept of relational database was defined by E. F. Codd at IBM in 1970. Codd introduced the term ''relational'' in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and later papers, he defined what he meant by ''relation''. One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has gradually come to describe a broader class of database systems, which at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Web Service
A web service (WS) is either: * a service offered by an electronic device to another electronic device, communicating with each other via the Internet, or * a server running on a computer device, listening for requests at a particular port over a network, serving web documents (HTML, JSON, XML, images). In a web service, a web technology such as HTTP is used for transferring machine-readable file formats such as XML and JSON. In practice, a web service commonly provides an object-oriented web-based interface to a database server, utilized for example by another web server, or by a mobile app, that provides a user interface to the end-user. Many organizations that provide data in formatted HTML pages will also provide that data on their server as XML or JSON, often through a Web service to allow syndication. Another application offered to the end-user may be a mashup, where a Web server consumes several Web services at different machines and compiles the content into one user int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linked Data
In computing, 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 rather than using them to serve web pages only for human readers, it extends them to share information in a way that can be read automatically by computers. Part of the vision of linked data is for the Internet to become a global database. Tim Berners-Lee, director of the World Wide Web Consortium (W3C), coined the term in a 2006 design note about the Semantic Web project. Linked data may also be open data, in which case it is usually described as Linked Open Data. Principles In his 2006 "Linked Data" note, Tim Berners-Lee outlined four principles of linked data, paraphrased along the following lines: #Uniform Resource Identifiers (URIs) should be used to name and identify individual things. #HTTP URIs should be used to allow these things to be looked up, interpreted, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematica
Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in ''Mathematica''. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. There is a substantial literature on the development of computer algebra systems (CAS). __TOC_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conference On Automated Deduction
A conference is a meeting, often lasting a few days, which is organized on a particular subject, or to bring together people who have a common interest. Conferences can be used as a form of group decision-making, although discussion, not always decisions, is the primary purpose of conferences. The term derives from the word ''confer''. History The first known use of "conference" appears in 1527, meaning "a meeting of two or more persons for discussing matters of common concern". It came from the word ''confer'', which means "to compare views or take counsel". However the idea of a conference far predates the word. Arguably, as long as there have been people, there have been meetings and discussions between people. Evidence of ancient forms of conference can be seen in archaeological ruins of common areas where people would gather to discuss shared interests such as "hunting plans, wartime activities, negotiations for peace or the organisation of tribal celebrations". Sinc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Theorem Provers
Free may refer to: Concept * Freedom, the ability to act or change without constraint or restriction * Emancipate, attaining civil and political rights or equality * Free (''gratis''), free of charge * Gratis versus libre, the difference between the two common meanings of the adjective "free". Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free software, software usable and distributable with few restrictions and no payment *, an emoji in the Enclosed Alphanumeric Supplement block. Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media personality * Free, a pseudonym for the activist and writer Abbie Hoffman * Free (active 2003–), American musician in the band FreeSol Arts and media Film and television * ''Free'' (film), a 2001 American dramedy * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unix Programming Tools
Unix (, ; trademarked as UNIX) is a family of Computer multitasking, multitasking, multi-user software, multi-user computer operating systems that derive from the original AT&T Corporation, AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, and others. Initially intended for use inside the Bell System, AT&T licensed Unix to outside parties in the late 1970s, leading to a variety of both academic and commercial Unix variants from vendors including University of California, Berkeley (Berkeley Software Distribution, BSD), Microsoft (Xenix), Sun Microsystems (SunOS/Solaris (operating system), Solaris), Hewlett-Packard, HP/Hewlett Packard Enterprise, HPE (HP-UX), and IBM (IBM AIX, AIX). The early versions of Unix—which are retrospectively referred to as "Research Unix"—ran on computers such as the PDP-11 and VAX; Unix was commonly used on minicomputers and Mainframe computer, mainframes from the 1970s onwards. It disti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
