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Mace4
Models And Counter-Examples (Mace) 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 proving, automated theorem prover for first-order logic, first-order and equational logic developed by William McCune. Description Prover9 is the successor of the Otter (theorem prover), Otter theorem prover also dev ... References External links System download Free theorem provers Software using the GNU General Public License {{logic-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prover9
Prover9 is an automated theorem proving, automated theorem prover for first-order logic, first-order and equational logic developed by William McCune. Description Prover9 is the successor of the Otter (theorem prover), 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 automated proof checking, proof-checking tool that has been separately verified using ACL2. In July 2006 the LADR/Prover9/Mace4 input language made a major change (which ... [...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] |
Otter (theorem Prover)
OTTER (Organized Techniques for Theorem-proving and Effective Research) 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their Structure (mathematical logic), models (those Structure (mathematical logic), structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be definable set, defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clause Normal Form
In Boolean algebra, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. In automated theorem proving, the notion "''clausal normal form''" is often used in a narrower sense, meaning a particular representation of a CNF formula as a set of sets of literals. Definition A logical formula is considered to be in CNF if it is a conjunction of one or more disjunctions of one or more literals. As in disjunctive normal form (DNF), the only propositional operators in CNF are or (\vee), and (\and), and not (\neg). The ''not'' operator can only be used as part of a literal, which means that it can only precede a propositional variable. The following is a context-free grammar for CNF: : ''CNF'' \, \to \, ''Disjunct'' \, \mid \, ''Disjunct'' \, \land \, ''CNF'' : ''Disjunct'' \, \to \, ''Literal'' \, \mid\, ''Literal'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an ''axiom'' may be a " logical axiom" or a " non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example ''a'' + 0 = ''a'' in integer arithmetic. N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU GPL
The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first copyleft license available for general use. It was originally written by Richard Stallman, the founder of the Free Software Foundation (FSF), for the GNU Project. The license grants the recipients of a computer program the rights of the Free Software Definition. The licenses in the GPL series are all copyleft licenses, which means that any derivative work must be distributed under the same or equivalent license terms. The GPL is more restrictive than the GNU Lesser General Public License, and even more distinct from the more widely used permissive software licenses such as BSD, MIT, and Apache. Historically, the GPL license family has been one of the most popular software licenses in the free and open-source software (FOSS) domain. Promi ... [...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] |
