An Exploration in the Space of Mathematical Knowledge

Kohlhase, Andrea; Kohlhase, Michael

doi:10.1007/11618027_2

Cited by 6 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These can range from community tools like peer reviewed periodicals (aka. academic journals) to technical means like intra-and cross-realm search engines (as realms are built upon theory graphs, specialization of the ♭search engine [KI12] will be a good starting point.) It will be very important to provide a set of interactions for the interface of a realm that users can understand.…”

Section: Interface Mattersmentioning

confidence: 99%

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Carette

Farmer

Kohlhase

2014

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract.Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.

show abstract

Section: Interface Mattersmentioning

confidence: 99%

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Carette

Farmer

Kohlhase

2014

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…This not only allows a user assistance system H to offer semantic services and semantic interactions, but also to redefine appropriateness of help in terms of content and not form only. In [9] we elaborated on this feature of semantic data. In particular, we observed that each knowledge object includes implicit formalizations (content) and explicit realizations (form) and that this set of variants can be structured by notions of equality we called substance equivalences, which represent meaning-conserving relations.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Modeling task experience in user assistance systems

Kohlhase

2009

Proceedings of the 27th ACM International Conference on Design of Communication

Self Cite

View full text Add to dashboard Cite

One of the major issues for user assistance systems consists of "providing help at an appropriate level". In this paper we analyze the problem of modeling task experience -a prerequisite for provisioning adequate help. In contrast to level-based approaches we propose an ontology-based model, which allows fine-grained modeling of task experience using the concepts of the task domain as granules. The model is semantic in the sense that it allows to take advantage of the relations between concepts to provide novel semantic services and interactions. We present the SACHS (Semantic Annotations for a Controlling Help System, a semantic help system for a spreadsheet-based financial controlling system) software as an exemplary application of the proposed task experience model.

show abstract

“…as valid substance equivalences. In [KK05] we present the Mathematical Knowledge Space (MKS), which we can now interpret under a CoP perspective. Wenger explicates that any "community of practice produces abstractions, symbols, stories, terms, and concepts that reify something of that practice in a congealed form" [Wen99,59].…”

Section: Mathematical Practicementioning

confidence: 99%

“…They reacted with this situated learning approach against the dominant AI scheme of human intelligence as a complex computer program.2 In[KK05] we chose to introduce the concept via the learning object itself, mutating from raw data to information to a knowledge object within a community of practice (based on[BD00] and[PRR97]). …”

mentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Knowledge Management

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Mathematical knowledge management (MKM) is an emerging interdisciplinary field of research in the intersection of mathematics, computer science, library science, and scientific publishing. Its main objective is to develop new and better ways of managing mathematical knowledge using sophisticated software tools. Two other important aims are to obtain a better understanding of the nature of mathematical knowledge and to investigate new modes of consuming and producing mathematical knowledge. The MKM conferences bring together mathematicians, software developers, users of mathematics, librarians, publishers, and educators who are interested in advancing the management of mathematical knowledge.MKM 2006 received 22 submissions. Of these, 20 were reviewed by three Program Committee members or external reviewers and two were reviewed by two.

show abstract

An Exploration in the Space of Mathematical Knowledge

Cited by 6 publications

References 15 publications

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Modeling task experience in user assistance systems

Mathematical Knowledge Management

Contact Info

Product

Resources

About