The Experts below are selected from a list of 5682 Experts worldwide ranked by ideXlab platform
Li Dafa - One of the best experts on this subject based on the ideXlab platform.
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unification algorithms for eliminating and introducing quantifiers in natural deduction Automated Theorem Proving
Journal of Automated Reasoning, 1997Co-Authors: Li DafaAbstract:A natural deduction system was adapted from Gentzen system. It enables valid wffs to be deduced in a very ‘natural’ way. One need not transform a formula into other normal forms. Robinson’s unification algorithm is used to handle clausal formulas. Algorithms for eliminating and introducing quantifiers without Skolemization are presented, and unification Theorems for them are proved. A natural deduction Automated Theorem prover based on the algorithms was implemented. The rules for quantifiers are controlled by the algorithms. The Andrews challenge and the halting problem were proved by the system.
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a natural deduction Automated Theorem Proving system
Conference on Automated Deduction, 1992Co-Authors: Li DafaAbstract:Recently many people are researching the natural deduction system adapted from Gentzen system, it need not transform formulas into other normal form. Robinson's unification algorithm only uses the substitution rule, therefore it can't be used to handle formulas with quantifiers. we concluded an algorithm which can treat any wffs with quantifiers. that is, given two wffs, the algorithm tries to apply the rules for quantifiers to them to test if they become equal. The automatic natural deduction Proving system based on our algorithm has been implemented, the Andrews Challeges, Bledsoe Challenges and Pelletier Challenges were proved by our system.
Geoff Sutcliffe - One of the best experts on this subject based on the ideXlab platform.
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Semantic Derivation Verification
2020Co-Authors: Geoff Sutcliffe, Diego BelfioreAbstract:Abstract Automated Theorem Proving (ATP) systems are complex pieces of software, and thus may have bugs that make them unsound. In order to guard against such unsoundness, the derivations output by an ATP system may be semantically verified by a trusted system that checks the required semantic properties of each inference step. Such verification may need to be augmented by structural verification that checks that inferences have been used correctly in the context of the overall derivation. This paper describes techniques for semantic verification of derivations, and reports on their implementation in the DVDV verifier
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the cade 23 Automated Theorem Proving system competition casc 23
Ai Communications, 2012Co-Authors: Geoff SutcliffeAbstract:The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-23 was the sixteenth competition in the CASC series. Thirty-six ATP systems and system variants competed in the various competition and demonstration divisions. An outline of the competition design, and a commentated summary of the results, are presented.
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the 4th ijcar Automated Theorem Proving system competition casc j4
Ai Communications, 2009Co-Authors: Geoff SutcliffeAbstract:The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, first order Automated Theorem Proving (ATP) systems. CASC-J4 was the thirteenth competition in the CASC series. Twenty-six ATP systems and system variants competed in the various competition and demonstration divisions. An outline of the competition design, and a commentated summary of the results, are presented.
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Discrete Event Calculus Deduction using First-Order Automated Theorem Proving
2008Co-Authors: Geoff SutcliffeAbstract:Abstract. The event calculus is a powerful and highly usable formalism for reasoning about action and change. The discrete event calculus limits time to integers. This paper shows how discrete event calculus problems can be encoded in first-order logic, and solved using a first-order logic Automated Theorem Proving system. The following techniques are discussed: reification is used to convert event and fluent atoms into first-order terms, uniqueness-of-names axioms are generated to ensure uniqueness of event and fluent terms, predicate completion is used to convert second-order circumscriptions into first-order formulae, and a limited first-order axiomatization of integer arithmetic is developed. The performance of first-order Automated Theorem Proving is compared to that of satisfiability solving.
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reasoning in the event calculus using first order Automated Theorem Proving
The Florida AI Research Society, 2005Co-Authors: Erik T Mueller, Geoff SutcliffeAbstract:The event calculus (EC) (Shanahan 1999) is a powerful and highly usable formalism for reasoning about action and change, which is rapidly finding application in such areas as natural language processing and robotics. Kowalski and Sergot (1986) introduced the original event calculus, which was expressed as a logic program, and Shanahan and Miller introduced axiomatizations of the event calculus in firstorder logic (Shanahan 1997; Miller & Shanahan 2002). The discrete event calculus (DEC) was developed by Mueller (2004) in order to facilitate solution of event calculus reasoning problems using satisfiability (SAT) solvers. Since the introduction of the EC and DEC axiomatizations, several event calculus reasoning systems have been implemented. However, to our knowledge, nobody has ever attempted to solve event calculus reasoning problems using first-order logic Automated Theorem Proving (ATP) systems.
Konstantin Verchinine - One of the best experts on this subject based on the ideXlab platform.
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evidence algorithm and system for Automated deduction a retrospective view
Proceedings of the 10th ASIC and 9th MKM international conference and 17th Calculemus conference on Intelligent computer mathematics, 2010Co-Authors: Alexander V. Lyaletski, Konstantin VerchinineAbstract:A research project aimed at the development of an Automated Theorem Proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V. Glushkov, baptized it "Evidence Algorithm", EA1. The work on the project lasted, off and on, more than 40 years. In the framework of the project, the Russian and English versions of the System for Automated Deduction, SAD, were constructed. They may be already seen as powerful TheoremProving assistants. The paper gives a retrospective view to the whole history of the development of the EA and SAD. Theoretical and practical results obtained on the long way are systematized. No comparison with similar projects is made.
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evidence algorithm and system for Automated deduction a retrospective view
arXiv: Artificial Intelligence, 2010Co-Authors: Alexander V. Lyaletski, Konstantin VerchinineAbstract:A research project aimed at the development of an Automated Theorem Proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V.Glushkov, baptized it "Evidence Algorithm", EA. The work on the project lasted, off and on, more than 40 years. In the framework of the project, the Russian and English versions of the System for Automated Deduction, SAD, were constructed. They may be already seen as powerful Theorem-Proving assistants.
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evidence algorithm and system for Automated deduction a retrospective view in honor of 40 years of the ea announcement
2010Co-Authors: Alexander V. Lyaletski, Konstantin VerchinineAbstract:A research project aimed at the development of an Automated Theorem Proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V.Glushkov, baptized it "Evidence Algorithm", EA 1 . The work on the project lasted, off and on, more than 40 years. In the framework of the project, the Russian and English versions of the System for Automated De- duction, SAD, were constructed. They may be already seen as powerful Theorem- Proving assistants. The paper gives a retrospective view to the whole history of the development of the EA and SAD. Theoretical and practical results obtained on the long way are systematized. No comparison with similar projects is made.
Volker Sorge - One of the best experts on this subject based on the ideXlab platform.
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classification results in quasigroup and loop theory via a combination of Automated reasoning tools
Commentationes Mathematicae Universitatis Carolinae, 2008Co-Authors: Volker Sorge, Simon Colton, Roy Mccasland, Andreas MeierAbstract:We present some novel partial classification results in quasigroup and loop theory. For quasigroups up to size XXX and loops up to size YYY, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of Automated techniques – including machine learning and computer algebra – which we present here. Moreover, each result has been automatically verified, again using a variety of techniques – including Automated Theorem Proving, computer algebra and satisfiability solving – and we describe our bootstrapping approach to the generation and verification of these classification results.
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can a higher order and a first order Theorem prover cooperate
International Conference on Logic Programming, 2005Co-Authors: Christoph Benzmuller, Volker Sorge, Mateja Jamnik, Manfred KerberAbstract:State-of-the-art first-order Automated Theorem Proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably Proving Theorems that would be considered relatively simple by humans. For example, when reasoning about sets, relations, or functions, first-order systems still exhibit serious weaknesses. While it has been shown in the past that higher-order reasoning systems can solve problems of this kind automatically, the complexity inherent in their calculi and their inefficiency in dealing with large numbers of clauses prevent these systems from solving a whole range of problems.
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workshop the role of Automated deduction in mathematics
Conference on Automated Deduction, 2000Co-Authors: Simon Colton, Volker Sorge, Ursula MartinAbstract:The purpose of this workshop is to discuss the role of Automated deduction in all areas of mathematics. This will include looking at the interaction between Automated deduction programs and other computational systems which have been developed over recent years to automate different areas of mathematical activity. Such systems include computer algebra packages, tutoring programs, mathematical discovery systems and systems developed to help present and archive mathematical theories. The workshop will also include discussions of the use of Automated Theorem Proving in the wider mathematical community. Presentations which detail the employment of Automated deduction techniques in any area of mathematical research have been encouraged.
Josef Urban - One of the best experts on this subject based on the ideXlab platform.
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automating formalization by statistical and semantic parsing of mathematics
Interactive Theorem Proving, 2017Co-Authors: Cezary Kaliszyk, Josef Urban, Jiři VyskocilAbstract:We discuss the progress in our project which aims to automate formalization by combining natural language processing with deep semantic understanding of mathematical expressions. We introduce the overall motivation and ideas behind this project, and then propose a context-based parsing approach that combines efficient statistical learning of deep parse trees with their semantic pruning by type checking and large-theory Automated Theorem Proving. We show that our learning method allows efficient use of large amount of contextual information, which in turn significantly boosts the precision of the statistical parsing and also makes it more efficient. This leads to a large improvement of our first results in parsing Theorems from the Flyspeck corpus.
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learning assisted Theorem Proving with millions of lemmas
arXiv: Artificial Intelligence, 2014Co-Authors: Cezary Kaliszyk, Josef UrbanAbstract:Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for Proving further Theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen Automated Theorem Proving of new conjectures over large formal mathematical libraries such as Flyspeck.
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Theorem Proving in large formal mathematics as an emerging ai field
arXiv: Artificial Intelligence, 2012Co-Authors: Josef Urban, Jiři VyskocilAbstract:In the recent years, we have linked a large corpus of formal mathematics with Automated Theorem Proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the earlier large-scale Automated developments done by Quaife with McCune's Otter system, and to the discussions of the QED project about formalizing a significant part of mathematics. Then we summarize our adventure so far, argue that the QED dreams were right in anticipating the creation of a very interesting semantic AI field, and discuss its further research directions.
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evaluation of Automated Theorem Proving on the mizar mathematical library
International Congress on Mathematical Software, 2010Co-Authors: Josef Urban, Krystof Hoder, Andrei VoronkovAbstract:This paper investigates the strength of first-order automatic Theorem provers (ATPs) in Proving Theorems and lemmas from the Mizar proof assistant's formal mathematical library. Several Mizar use-cases are described and evaluated, as well as various ATP systems and strategies. The new version of the leading Vampire ATP system is included in the evaluation, experiments with Mizar-specific strategy-selection are performed with E the prover, and the SInE axiom selection is evaluated on large Mizar problems with both E and Vampire. A rough mathematical division of the Mizar library is introduced, and the ATP performance is evaluated on it.
