Automated theorem proving 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.
The Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As an LCF-style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring — yet supporting — explicit proof objects.
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.
Paradox is a finite-domain model finder for pure first-order logic (FOL) with equality developed by Koen Lindström Claessen and Niklas Sörensson at the Chalmers University of Technology. It can a participate as part of an automated theorem proving system. The software is primarily written in the Haskell programming language. It is released under the terms of the GNU General Public License and is free.
J Strother Moore is an American computer scientist. He is a co-developer of the Boyer–Moore string-search algorithm, Boyer–Moore majority vote algorithm, and the Boyer–Moore automated theorem prover, Nqthm. He made pioneering contributions to structure sharing including the piece table data structure and early logic programming. An example of the workings of the Boyer–Moore string search algorithm is given in Moore's website. Moore received his Bachelor of Science (BS) in mathematics at Massachusetts Institute of Technology in 1970 and his Doctor of Philosophy (Ph.D.) in computational logic at the University of Edinburgh in Scotland in 1973.
The Conference on Automated Deduction (CADE) is the premier academic conference on automated deduction and related fields. The first CADE was organized in 1974 at the Argonne National Laboratory near Chicago. Most CADE meetings have been held in Europe and the United States. However, conferences have been held all over the world. Since 1996, CADE has been held yearly. In 2001, CADE was, for the first time, merged into the International Joint Conference on Automated Reasoning (IJCAR). This has been repeated biannually since 2004.
The Herbrand Award for Distinguished Contributions to Automated Reasoning is an award given by the Conference on Automated Deduction (CADE), Inc., to honour persons or groups for important contributions to the field of automated deduction. The award is named after the French scientist Jacques Herbrand and given at most once per CADE or International Joint Conference on Automated Reasoning (IJCAR). It comes with a prize of US$1,000. Anyone can be nominated, the award is awarded after a vote among CADE trustees and former recipients, usually with input from the CADE/IJCAR programme committee.
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.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings. The name is derived from the fact that these expressions are interpreted within ("modulo") a certain formal theory in first-order logic with equality. SMT solvers are tools that aim to solve the SMT problem for a practical subset of inputs. SMT solvers such as Z3 and cvc5 have been used as a building block for a wide range of applications across computer science, including in automated theorem proving, program analysis, program verification, and software testing.
The International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX) is an annual international academic conference that deals with all aspects of automated reasoning with analytic tableaux. Periodically, it joins with CADE and TPHOLs into the International Joint Conference on Automated Reasoning (IJCAR).
SNARK, , is a theorem prover for multi-sorted first-order logic intended for applications in artificial intelligence and software engineering, developed at SRI International.
The International Workshop on First-Order Theorem Proving (FTP) is a scientific meeting of researchers interested in automated theorem proving for first-order logic and related fields. FTP workshops are less formal than many conferences, but more formal than most workshops. While FTP proceedings are published informally, most FTP workshops have resulted in a special issue of a recognized peer-reviewed academic journal.
Geoff Sutcliffe is a US-based computer scientist working in the field of automated reasoning. He was born in the former British colony of Northern Rhodesia , grew up in South Africa, and earned his PhD in Australia. Sutcliffe currently works at the University of Miami, and is of both British and Australian nationality.
The CADE ATP System Competition (CASC) is an annual competition of fully automated theorem provers for classical logic
Ulrike M. Sattler is a professor of computer science in the information management group of the Department of Computer Science at the University of Manchester and a visiting professor at the University of Oslo.
Interactive Theorem Proving (ITP) is an annual international academic conference on the topic of automated theorem proving, proof assistants and related topics, ranging from theoretical foundations to implementation aspects and applications in program verification, security, and formalization of mathematics.
The Vienna Summer of Logic was a scientific event in the summer of 2014, combining 12 major conferences and several workshops from the fields of mathematical logic, logic in computer science, and logic in artificial intelligence. The meetings took place from July 9 to 24, 2014, and attracted more than 2000 scientists and researchers.
Christoph Walther is a German computer scientist, known for his contributions to automated theorem proving. He is Professor emeritus at Darmstadt University of Technology.
Andrei Anatolievič Voronkov is a Professor of Formal methods in the Department of Computer Science at the University of Manchester.
