A Review of Mathematical Knowledge Management

Carette, Jacques; Farmer, William M.

doi:10.1007/978-3-642-02614-0_21

Cited by 16 publications

(7 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Evaluation is discussed in Section 3.5. Mathematical Information Retrieval (MIR) is a relatively new research area, lying at the intersection of text-based information retrieval [62,125], content-based image retrieval [35,38,132] and Mathematical Knowledge Management (MKM [25]). Mathematical knowledge management is concerned with the representation, archiving, extraction, and use of mathematical information.…”

Section: Overview Of Mathematical Information Retrievalmentioning

confidence: 99%

Recognition and retrieval of mathematical expressions

Zanibbi

Blostein

2011

IJDAR

234

112

View full text Add to dashboard Cite

Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with wide-spread availability of Optical Character Recognition (OCR) and text-based search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.

show abstract

Section: Overview Of Mathematical Information Retrievalmentioning

confidence: 99%

Recognition and retrieval of mathematical expressions

Zanibbi

Blostein

2011

IJDAR

234

112

View full text Add to dashboard Cite

show abstract

“…Frameworks for logics and proofs The exact nature of what is accepted as formal proofs has been a long-standing debate, and it has spawned lots of work on logical frameworks [37] as well as mathematical knowledge management systems and frameworks [20]. Clearly, certain well understood and flexible logics should be accepted by any framework: these include, for example, first-order classical and intuitionistic logics.…”

Section: Formal Proofmentioning

confidence: 99%

A Distributed and Trusted Web of Formal Proofs

Miller

2019

Distributed Computing and Internet Technology

View full text Add to dashboard Cite

Most computer checked proofs are tied to the particular technology of a prover's software. While sharing results between proof assistants is a recognized and desirable goal, the current organization of theorem proving tools makes such sharing an exception instead of the rule. In this talk, I argue that we need to turn the current architecture of proof assistants and formal proofs inside-out. That is, instead of having a few mature theorem provers include within them their formally checked theorems and proofs, I propose that proof assistants should sit on the edge of a web of formal proofs and that proof assistant should be exporting their proofs so that they can exist independently of any theorem prover. While it is necessary to maintain the dependencies between definitions, theories, and theorems, no explicit library structure should be imposed on this web of formal proofs. Thus a theorem and its proofs should not necessarily be located at a particular URL or within a particular prover's library. While the world of symbolic logic and proof theory certainly allows for proofs to be seen as global and permanent objects, there is a lot of research and engineering work that is needed to make this possible. I describe some of the required research and development that must be done to achieve this goal.

show abstract

“…Perhaps the area of mathematical software with the greatest potential for machine learning applications is Mathematical Knowledge Management (MKM) [12] since many of the tasks are similar to Natural Language Processing (NLP) where machine learning has seen extensive use. For example, [35] describes the automatic identification of a suitable top level from the Mathematics Subject Classification (MSC) system for thousands of articles using an SVM; while [29] describes how NLP techniques were adapted to build a part of speech tagger used for key phrase extraction in the database zbMATH.…”

Section: Mathematical Knowledge Managementmentioning

confidence: 99%

Machine Learning for Mathematical Software

England

2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the authors own work and similar applications for other mathematical software. It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.

show abstract

A Review of Mathematical Knowledge Management

Cited by 16 publications

References 28 publications

Recognition and retrieval of mathematical expressions

Recognition and retrieval of mathematical expressions

A Distributed and Trusted Web of Formal Proofs

Machine Learning for Mathematical Software

Contact Info

Product

Resources

About