arXiv subjects

Josef Urban

Publications and source records attributed to Josef Urban.

78 records · Page 5Linked to original sources

arXiv2012

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory 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 learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification 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 large-theory 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 state-of-the-art system for automated reasoning in large theories.

cs.LG↗

arXiv2012

Dependencies in Formal Mathematics: Applications and Extraction for Coq and Mizar

Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and the Mizar Mathematical Library. Several applications of the detailed dependency analysis are described and proposed. Motivated by the different applications, we discuss the various kinds of dependencies that we are interested in,and the suitability of various dependency extraction methods.

cs.DL↗

arXiv2011

Licensing the Mizar Mathematical Library

The Mizar Mathematical Library (MML) is a large corpus of formalised mathematical knowledge. It has been constructed over the course of many years by a large number of authors and maintainers. Yet the legal status of these efforts of the Mizar community has never been clarified. In 2010, after many years of loose deliberations, the community decided to investigate the issue of licensing the content of the MML, thereby clarifying and crystallizing the status of the texts, the text's authors, and the library's long-term maintainers. The community has settled on a copyright and license policy that suits the peculiar features of Mizar and its community. In this paper we discuss the copyright and license solutions. We offer our experience in the hopes that the communities of other libraries of formalised mathematical knowledge might take up the legal and scientific problems that we addressed for Mizar.

cs.DL↗

arXiv2011

Large Formal Wikis: Issues and Solutions

We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in \cite{DBLP:conf/aisc/UrbanARG10}. A smart re-verification scheme for the large formal libraries in the wiki is suggested for Mizar/MML and Coq/CoRN, based on recently developed precise tracking of mathematical dependencies. We propose to use features of state-of-the-art filesystems to allow real-time cloning and sandboxing of the entire libraries, allowing also to extend the wiki to a true multi-user collaborative area. A number of related issues are discussed.

cs.DL↗

arXiv2010

Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.

cs.AI↗

arXiv2010

A Wiki for Mizar: Motivation, Considerations, and Initial Prototype

Formal mathematics has so far not taken full advantage of ideas from collaborative tools such as wikis and distributed version control systems (DVCS). We argue that the field could profit from such tools, serving both newcomers and experts alike. We describe a preliminary system for such collaborative development based on the Git DVCS. We focus, initially, on the Mizar system and its library of formalized mathematics.

cs.DL↗