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Model Elimination
Model elimination is the name attached to a pair of proof procedures invented by Donald W. Loveland, the first of which was published in 1968 in the ''Journal of the ACM''. Their primary purpose is to carry out automated theorem proving, though they can readily be extended to logic programming, including the more general disjunctive logic programming. Model elimination is closely related to resolution while also bearing characteristics of a tableaux method. It is a progenitor of the SLD resolution procedure used in the Prolog Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving, and computational linguistics. Prolog has its roots in first-order logic, a formal logic. Unlike many other programming language ... logic programming language. While somewhat eclipsed by attention to, and progress in, resolution theorem provers, model elimination has continued to attract the attention of researchers and software develope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Procedure
{{Short description, Systematic method for producing proofs In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements. Types of proof calculi used There are several types of proof calculi. The most popular are natural deduction, sequent calculi (i.e., Gentzen-type systems), Hilbert systems, and semantic tableaux or trees. A given proof procedure will target a specific proof calculus, but can often be reformulated so as to produce proofs in other proof styles. Completeness A proof procedure for a logic is ''complete'' if it produces a proof for each provable statement. The theorems of logical systems are typically recursively enumerable, which implies the existence of a complete but usually extremely inefficient proof procedure; however, a proof procedure is only of interest if it is reasonably efficient. Faced with an unprovable statement, a complete proof procedure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald W
Donald is a Scottish masculine given name. It is derived from the Gaelic name ''Dòmhnall''.. This comes from the Proto-Celtic *''Dumno-ualos'' ("world-ruler" or "world-wielder"). The final -''d'' in ''Donald'' is partly derived from a misinterpretation of the Gaelic pronunciation by English speakers. A short form of Donald is Don, and pet forms of Donald include Donnie and Donny. The feminine given name Donella is derived from Donald. ''Donald'' has cognates in other Celtic languages: Modern Irish ''Dónal'' (anglicised as ''Donal'' and ''Donall'');. Scottish Gaelic ''Dòmhnall'', ''Domhnull'' and ''Dòmhnull''; Welsh '' Dyfnwal'' and Cumbric ''Dumnagual''. Although the feminine given name '' Donna'' is sometimes used as a feminine form of ''Donald'', the names are not etymologically related. Variations Kings and noblemen Domnall or Domhnall is the name of many ancient and medieval Gaelic kings and noblemen: * Dyfnwal Moelmud (Dunvallo Molmutius), legendary kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' (''JACM'') is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are i ...'' References External links * {{DEFAULTSORT:Journal Of The Acm Academic journals established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals ... [...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 motivating factor for the development of computer science. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Programming
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain. Major logic programming language families include Prolog, Answer Set Programming (ASP) and Datalog. In all of these languages, rules are written in the form of ''clauses'': :A :- B1, ..., Bn. and are read as declarative sentences in logical form: :A if B1 and ... and Bn. A is called the ''head'' of the rule, B1, ..., Bn is called the ''body'', and the Bi are called '' literals'' or conditions. When n = 0, the rule is called a ''fact'' and is written in the simplified form: :A. Queries (or goals) have the same syntax as the bodies of rules and are commonly written in the form: :?- B1, ..., Bn. In the simplest case of Horn clauses (or "definite" clauses), all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjunctive Logic Programming
Answer set programming (ASP) is a form of declarative programming oriented towards difficult (primarily NP-hard) search problems. It is based on the stable model (answer set) semantics of logic programming. In ASP, search problems are reduced to computing stable models, and ''answer set solvers''—programs for generating stable models—are used to perform search. The computational process employed in the design of many answer set solvers is an enhancement of the DPLL algorithm and, in principle, it always terminates (unlike Prolog query evaluation, which may lead to an infinite loop). In a more general sense, ASP includes all applications of answer sets to knowledge representation and reasoning and the use of Prolog-style query evaluation for solving problems arising in these applications. History An early example of answer set programming was the planning method proposed in 1997 by Dimopoulos, Nebel and Köhler. Their approach is based on the relationship between plans an ... [...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] |
Method Of Analytic Tableaux
In proof theory, the semantic tableau (; plural: tableaux), also called an analytic tableau, truth tree, or simply tree, is a decision procedure for sentential logic, sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. Computation constructs this tree and uses it to prove or refute the whole formula. The tableau method can also determine the satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure for modal logics. A method of truth trees contains a fixed set of rules for producing trees from a given logical formula, or set of logical formulas. Those trees will have more formulas at each branch, and in some cases, a branch can come to contain both a formula and its negation, which is to say, a contradiction. In that case, the branch is said to close. If ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SLD Resolution
SLD resolution (''Selective Linear Definite'' clause resolution) is the basic rule of inference, inference rule used in logic programming. It is a refinement of Resolution (logic), resolution, which is both Soundness, sound and refutation Completeness (logic), complete for Horn clauses. The SLD inference rule Given a goal clause, represented as the negation of a problem to be solved: \neg L_1 \lor \cdots \lor \neg L_i \lor \cdots \lor \neg L_n with selected literal \neg L_i , and an input definite clause: L \lor \neg K_1 \lor \cdots \lor \neg K_m whose positive literal (atom) L\, unification (computing), unifies with the atom L_i \, of the selected literal \neg L_i \, , SLD resolution derives another goal clause, in which the selected literal is replaced by the negative literals of the input clause and the unifying substitution \theta \, is applied: (\neg L_1 \lor \cdots \lor \neg K_1 \lor \cdots \lor \neg K_m\ \lor \cdots \lor \neg L_n)\theta In the simple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prolog
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving, and computational linguistics. Prolog has its roots in first-order logic, a formal logic. Unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and Horn clause, rules, which define Finitary relation, relations. A computation is initiated by running a ''query'' over the program. Prolog was one of the first logic programming languages and remains the most popular such language today, with several free and commercial implementations available. The language has been used for automated theorem proving, theorem proving, expert systems, term rewriting, type systems, and automated planning, as well as its original intended field of use, natural language processing. See also Watson (computer). Prolog is a Turing-complete, general-purpose programming language, which is well-suited for inte ... [...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 motivating factor for the development of computer science. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Calculi
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
