Results 1 
8 of
8
CCoRN, the Constructive Coq Repository at Nijmegan
"... We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) ..."
Abstract

Cited by 18 (9 self)
 Add to MetaCart
We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) applications of such a library.
Efficient Retrieval of Mathematical Statements
 In Proceeding of the Third International Conference on Mathematical Knowledge Management, MKM 2004. Bialowieza, Poland. LNCS 3119
, 2004
"... Abstract. The paper describes an innovative technique for efficient retrieval of mathematical statements from large repositories, developing and substantially improving the metadatabased approach introduced in [13]. 1 ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Abstract. The paper describes an innovative technique for efficient retrieval of mathematical statements from large repositories, developing and substantially improving the metadatabased approach introduced in [13]. 1
A proofcentric approach to mathematical assistants
 Journal of Applied Logic: Special Issue on Mathematics Assistance Systems
, 2005
"... We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a f ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a flexible environment for the exploration, certification, and presentation of mathematical proof.
Methods of Relevance Ranking and Hitcontent Generation in Math Search
, 2007
"... To be effective and useful, math search systems must not only maximize precision and recall, but also present the query hits in a form that makes it easy for the user to identify quickly the truly relevant hits. To meet that requirement, the search system must sort the hits according to domainappro ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
To be effective and useful, math search systems must not only maximize precision and recall, but also present the query hits in a form that makes it easy for the user to identify quickly the truly relevant hits. To meet that requirement, the search system must sort the hits according to domainappropriate relevance criteria, and provide with each hit a queryrelevant summary of the hit target.
Improving Mathematics Retrieval
"... Abstract. Despite the popularity of storing mathematical objects on the web, searching for mathematical expressions is extremely limited. Conventional retrieval systems are inadequate for mathematical expressions, because they are not tuned for text with complex structures that include only a few di ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Abstract. Despite the popularity of storing mathematical objects on the web, searching for mathematical expressions is extremely limited. Conventional retrieval systems are inadequate for mathematical expressions, because they are not tuned for text with complex structures that include only a few distinct terms. Surprisingly current approaches to the problem of retrieving mathematical information do not include a formal definition of the similarity between two expressions, and thus fail to find many relevant documents. In this paper, we present steps to advance mathematics retrieval to incorporate best practices from modern information retrieval. We first review encodings of mathematical expressions currently found on the web, and present the results of our efforts to create an experimental testbed. We formally define the similarity between two mathematical expressions and present the problem of searching for similar mathematical expressions. 1
Roles of Math Search in Mathematics
 in Mathematical Knowledge Management, Proceedings of the 5th International Conference on Mathematical Knowledge Management, Lecture
"... Abstract. Mathaware finegrain search is expected to be widely available. A key question is what roles it can play in mathematics. It will be argued that, besides finding information, math search can help advance and manage mathematical knowledge. This paper will present the shortterm goals and st ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. Mathaware finegrain search is expected to be widely available. A key question is what roles it can play in mathematics. It will be argued that, besides finding information, math search can help advance and manage mathematical knowledge. This paper will present the shortterm goals and state of the art of mathaware finegrain search. Afterwards, it will focus on how math search can help advance and manage mathematical knowledge, and discuss what needs to be done to fulfill those roles, emphasizing two key components. The first is similarity search, and how it applies to (1) discovering and drawing upon connections between different fields, and (2) proof development. The second is math metadata, which math search will surely encourage and benefit from, and which will be pivotal to mathematical knowledge management. 1
A Review of Mathematical Knowledge Management ⋆
"... Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to de ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to define what MKM is, what it worries about, etc. In this paper, we review the literature of MKM and gather various metadata from these papers. After offering some definitions surrounding MKM, we analyse the metadata we have gathered from these papers, in an effort to cast more light on the field of MKM and its evolution.
An RDF Vocabulary for the Representation and Exploration of Expressions with an Illustration on Mathematical Search
, 2013
"... Abstract. Complex expressions, as used in mathematics and logics, account for a large part of human knowledge. It is therefore desirable to allow for their representation in RDF and for their exploration through semantic search. We propose an RDF vocabulary that fulfills three objectives. The first ..."
Abstract
 Add to MetaCart
Abstract. Complex expressions, as used in mathematics and logics, account for a large part of human knowledge. It is therefore desirable to allow for their representation in RDF and for their exploration through semantic search. We propose an RDF vocabulary that fulfills three objectives. The first objective is the accurate representation of expressions in standard RDF, so that expressive mathematical search is made possible. We here propose a syntactic extension of Turtle and SPARQL for the concise notation of such expressions. The second objective is the automated generation of expression labels that are close to usual mathematical notations (e.g., infix operators, symbols). The third objective is the compatibility with existing practice and legacy data in the Semantic Web community for the representation of expressions and structures (e.g., OWL/RDF, SPIN). We illustrate the use of this vocabulary on mathematical search using SEWELIS, a tool for the guided exploration and edition of RDF graphs, and discuss the benefits compared to stateoftheart in mathematical search. 1