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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) ..."
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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 ..."
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Cited by 9 (2 self)
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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
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 ..."
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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.
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 ..."
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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 ..."
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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.
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 ..."
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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
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 ..."
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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.
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"... sadhana manuscript No. (will be inserted by the editor) A compact kernel for the calculus of inductive constructions ..."
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sadhana manuscript No. (will be inserted by the editor) A compact kernel for the calculus of inductive constructions
Annotations, Collaborative Tagging, and Searching Mathematics in ELearning
"... Abstract—This paper presents a new framework for adding semantics into elearning system. The proposed approach relies on two principles. The first principle is the automatic addition of semantic information when creating the mathematical contents. The second principle is the collaborative tagging a ..."
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Abstract—This paper presents a new framework for adding semantics into elearning system. The proposed approach relies on two principles. The first principle is the automatic addition of semantic information when creating the mathematical contents. The second principle is the collaborative tagging and annotation of the elearning contents and the use of an ontology to categorize the elearning contents. The proposed system encodes the mathematical contents using presentation MathML with RDFa annotations. The system allows students to highlight and annotate specific parts of the elearning contents. The objective is to add meaning into the elearning contents, to add relationships between contents, and to create a framework to facilitate searching the contents. This semantic information can be used to answer semantic queries (e.g., SPARQL) to retrieve information request of a user. This work is implemented as an embedded code into Moodle elearning system. Keywords Semantic Web; MathML; Adaptive elearning; Folksonomies; Collaborative tagging.