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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 bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 inferen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argonne National Laboratory
Argonne National Laboratory is a science and engineering research national laboratory operated by UChicago Argonne LLC for the United States Department of Energy. The facility is located in Lemont, Illinois, outside of Chicago, and is the largest national laboratory by size and scope in the Midwest. Argonne had its beginnings in the Metallurgical Laboratory of the University of Chicago, formed in part to carry out Enrico Fermi's work on nuclear reactors for the Manhattan Project during World War II. After the war, it was designated as the first national laboratory in the United States on July 1, 1946. In the post-war era the lab focused primarily on non-weapon related nuclear physics, designing and building the first power-producing nuclear reactors, helping design the reactors used by the United States' nuclear navy, and a wide variety of similar projects. In 1994, the lab's nuclear mission ended, and today it maintains a broad portfolio in basic science research, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—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, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. 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 is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resolution (logic)
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic, resolution can be used as the basis for a semi-algorithm for the unsatisfiability problem of first-order logic, providing a more practical method than one following from Gödel's completeness theorem. The resolution rule can be traced back to Davis and Putnam (1960); however, their algorithm required trying all ground instances of the given formula. This source of combinatorial explosion was eliminated in 1965 by John Alan Robinson's syntactical unification algorithm, which allowed one to instantiate the formula during the proof "on demand" just as far as needed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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>( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term Indexing
In computer science, a term index is a data structure to facilitate fast lookup of terms and clauses in a logic program, deductive database, or automated theorem prover. Overview Many operations in automatic theorem provers require search in huge collections of terms and clauses. Such operations typically fall into the following scheme. Given a collection S of terms (clauses) and a query term (clause) q, find in S some/all terms t related to q according to a certain retrieval condition. Most interesting retrieval conditions are formulated as existence of a substitution that relates in a special way the query and the retrieved objects t. Here is a list of retrieval conditions frequently used in provers: * term q is unifiable with term t, i.e., there exists a substitution \theta , such that q\theta = t\theta * term t is an instance of q, i.e., there exists a substitution \theta, such that q\theta = t * term t is a generalisation of q, i.e., there exists a substitution \theta, suc ... [...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 "formula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public Domain
The public domain (PD) consists of all the creative work to which no exclusive intellectual property rights apply. Those rights may have expired, been forfeited, expressly waived, or may be inapplicable. Because those rights have expired, anyone can legally use or reference those works without permission. As examples, the works of William Shakespeare, Ludwig van Beethoven, Leonardo da Vinci and Georges Méliès are in the public domain either by virtue of their having been created before copyright existed, or by their copyright term having expired. Some works are not covered by a country's copyright laws, and are therefore in the public domain; for example, in the United States, items excluded from copyright include the formulae of Newtonian physics, cooking recipes,Copyright Protection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chicago is consistently ranked among the best universities in the world and it is among the most selective in the United States. The university is composed of College of the University of Chicago, an undergraduate college and five graduate research divisions, which contain all of the university's graduate programs and interdisciplinary committees. Chicago has eight professional schools: the University of Chicago Law School, Law School, the Booth School of Business, the Pritzker School of Medicine, the Crown Family School of Social Work, Policy, and Practice, the Harris School of Public Policy, the University of Chicago Divinity School, Divinity School, the Graham School of Continuing Liberal and Professional Studies, and the Pritzker School of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
