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Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
"... Smart premise selection is essential when using automated reasoning as a tool for largetheory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learningbased premise ..."
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Smart premise selection is essential when using automated reasoning as a tool for largetheory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learningbased premise selection in two ways. First, a newly available minimal dependency analysis of existing highlevel formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATPbased reverification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 largetheory mathematical problems is constructed, extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE stateoftheart system for automated reasoning in large theories.
Automated reasoning service for HOL Light
 of Lecture Notes in Computer Science
, 2013
"... Abstract. HOL(y)Hammer is an AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system, in particular for the users of the large Flyspeck library. The service uses several automated reasoning systems combined with several premise selection methods trained on pr ..."
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Abstract. HOL(y)Hammer is an AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system, in particular for the users of the large Flyspeck library. The service uses several automated reasoning systems combined with several premise selection methods trained on previous Flyspeck proofs, to attack a new conjecture that uses the concepts defined in the Flyspeck library. The public online incarnation of the service runs on a 48CPU server, currently employing in parallel for each task 25 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise are discussed, and an initial account of using the system is given. 1
A web interface for matita
 In Proceedings of Intelligent Computer Mathematics (CICM 2012
"... This article describes a prototype implementation of a web interface for the Matita proof assistant [2]. The motivations behind our work are similar to those of several recent, related efforts [7, 9, 1, 8] (see also [6]). In particular: 1. creation of a web collaborative working environment for inte ..."
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This article describes a prototype implementation of a web interface for the Matita proof assistant [2]. The motivations behind our work are similar to those of several recent, related efforts [7, 9, 1, 8] (see also [6]). In particular: 1. creation of a web collaborative working environment for interactive theorem proving, aimed at fostering knowledgeintensive cooperation, content creation and management; 2. exploitation of the markup in order to enrich the document with several kinds of annotations or active elements; annotations may have both a presentational/hypertextual nature, aimed to improve the quality of the proof script as a human readable document, or a more semantic nature, aimed to help the system in its processing (or reprocessing) of the script; 3. platform independence with respect to operating systems, and wider accessibility also for users using devices with limited resources; 4. overcoming the installation issues typical of interactive provers, also in view of attracting a wider audience, especially in the mathematical community.
HOL(y)Hammer: Online ATP service for HOL Light
 CoRR
"... Abstract. HOL(y)Hammer is an online AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures tha ..."
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Abstract. HOL(y)Hammer is an online AI/ATP service for formal (computerunderstandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48CPU server, currently employing in parallel for each task 7 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise and their solutions are discussed, and an initial account of using the system is given. 1.
Formalizing Physics: Automation, Presentation and Foundation Issues
"... Abstract. In this paper, we report our first experiments in using learningassisted automated reasoning for the formal analysis of physical systems. In particular, we investigate the performance of automated proofs as compared to interactive ones done in HOL for the verification of ray and electroma ..."
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Abstract. In this paper, we report our first experiments in using learningassisted automated reasoning for the formal analysis of physical systems. In particular, we investigate the performance of automated proofs as compared to interactive ones done in HOL for the verification of ray and electromagnetic optics. Apart from automation, we also provide brief initial exploration of more general issues in formalization of physics, such as its presentation and foundations.
Noname manuscript No. (will be inserted by the editor) LearningAssisted Automated Reasoning with Flyspeck
"... the date of receipt and acceptance should be inserted later Abstract The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machinelearning premise selection methods trained on the Flyspeck proofs, producing an AI syste ..."
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the date of receipt and acceptance should be inserted later Abstract The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machinelearning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a pushbutton mode (without any highlevel advice and user interaction) in 30 seconds of real time on a fourteenCPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped firstorder, polymorphic typed firstorder, and typed higherorder, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.
Collaborative Aspects
"... Abstract In this paper we give an overview of wikis and webbased systems for collaboration involving humans and also AI systems over large fully semantic (formal) corpora of mathematical knowledge. ..."
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Abstract In this paper we give an overview of wikis and webbased systems for collaboration involving humans and also AI systems over large fully semantic (formal) corpora of mathematical knowledge.
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