WP6 Workshop: Knowledge representation in mathematical software and databases St Andrews (UK), 2016-01-25 to 2016-06-27

## Main goals

Semiannual OpenDreamKit project meeting joined with a WP6 ``Data/Knowledge/Software bases’’ kickoff workshop dedicated to the exploration of how mathematical knowledge could be better represented and exploited within systems and for communicating between systems.

## OpenDreamKit implication

St Andrews hosted this event which was organized by Paris Sud (project meeting) and Jacobs Uni (WP6 workshop).

## Event summary

Tuesday morning was dedicated to OpenDreamKit’s semiannual steering committee meeting, including progress reports from all sites. A couple additional OpenDreamKit participants joined physically or remotely for this meeting.

The rest of the week was dedicated to Work Package 6 activities. To bootstrap the discussions, we started with a presentation by Michael Kohlhase of his ideas for a Knowledge First strategy\footnote{This eventually became the Math-in-the-Middle'' paradigm~\cite{DehKohKon:iop16}}, followed by presentations of how knowledge is represented in various components of OpenDreamKit (FindStat: Viviane Pons, LMFDB: Paul-Olivier Dehaye, GAP: Markus Pfeiffer, SageMath: Nicolas M. Thiéry), in preparation for \longdelivref{dksbases}{design}. There was also a brief presentation of a proof-of-concept Knowledge-aware Sage-GAP interface developed the week before at the GAP/Sage Days. Current practices where discussed as well: commonalities indumping math data on the web’’ process (FindStat, LMFDB,…). Then came a tutorial presentation of MMT to explore how knowledge representation in MMT could serve as a generic knowledge backbone for integrating the various systems. After these warm up activities, we moved on to brainstorms and joint code sprints, developing proof-of-concepts formalizations of the knowledge in the various components and exploring applications: detecting bugs and inconsistencies in code and data, generating more complete documentation, supporting generic handle interfaces, …

A fine grained report of the activities is available here.

Results and impact

The Math-in-the-Middle approach was born at this workshop. This led to a joint paper at the CICM conference~\cite{DehKohKon:iop16} and kicked off and fueled much of the activity on WP6 since then, in particular around \longtaskref{dksbases}{data-design}, \delivref{dksbases}{design}, \delivref{dksbases}{dkstheories}, and \delivref{component-architecture}{semantic-interface-sage-gap}.

\begin{figure}[ht] \caption*{WP6 Workshop: Knowledge representation in mathematical software and databases} \includegraphics[scale=0.5]{pictures/2016-01-25-DKS-group-picture.jpg} \end{figure}

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