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\paperID{P3-19}
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\title{Proposal for a Quantity-based Data Model in the Virtual Observatory}
\titlemark{Proposal for a Quantity-based Data Model in the VO}
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\author{ Brian Thomas and Edward Shaya\altaffilmark{1}}
\affil{ Code 630.1,
Goddard Space Flight Center/NASA,
Greenbelt, MD 20771}
\altaffiltext{1}{Astronomy Department, University of Maryland}

\contact{ Brian Thomas}
\email{ brian.thomas@gsfc.nasa.gov}

\paindex{Thomas, B.}
\aindex{Shaya, E.}     % Remove this line if there is only one author

\authormark{Thomas \& Shaya}	%% Added FO 22.04.04

\keywords{ computing: distributed, data: model, Virtual Observatory}

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%			       Abstract
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\begin{abstract}          % Leave intact
We propose the beginnings of a data model for the Virtual Observatory (VO) built up from simple ``quantity'' objects. In this paper we present how an object-oriented, domain (or namespace)-scoped simple quantity may be used to describe astronomical data.  Our model is designed around the requirements that it be searchable and serve as a transport mechanism for all types of VO data and meta-data. In this paper we describe this model in terms of an OWL ontology and UML diagrams. An XML schema is available online.
\end{abstract}

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\section{Introduction: an object- and domain-oriented approach}
The VO community is currently attempting to
formulate a data model which might be shared across all data
repositories and used to facilitate the query, exchange and fusion of
astronomical data. This fundamental requirement must also be coupled
with the need for this data model to be able to replicate the
structure and content of the data at any participating VO data
repository. One possible avenue is to utilize an object-oriented
methodology to reuse important concepts and perhaps allow for a
mechanism whereby a computer may decompose advanced child concepts
into more digestible parent concept parts. As Plante (2002) has argued
this kind of approach, if done within a single domain, will result in
an increasing problem both for initial development and long-term
maintenance of the VO data model meta-data. If we however sever the
connection of the data model to the astronomical meta-data we will
allow for much greater progress on the problem of developing the data
model and its maintenance.

What is needed by the VO community is a new
data model which contains the ability to be extended in an
object-oriented fashion, has domains which may allow for separate
communities within the VO to apply their expertise without stepping on
other areas of work, and has the ability to be used as an exchange
format across the Internet.

Recently Plante (2003) has argued for a quantity-based data model, where
a quantity is used to model all of the data interactions. We have
taken this idea to develop our proposal 
paper based on our own work with 
\htmladdnormallinkfoot{XDF}{http://xml.gsfc.nasa.gov/XDF}
and guided by the work of
many others (refs above plus: McDowell 2002ab; Williams 2002;
\htmladdnormallinkfoot{UCD}{http://vizier.u-strasbg.fr/doc/UCD.htx}) 
and larger astronomy communities 
(\htmladdnormallinkfoot{FITS}{http://fits.gsfc.nasa.gov})
In this
paper we propose the beginnings of such a data model and describe how
adopting an object-, domain-, and quantity-oriented approach may serve to
promote a sharable, searchable standard amongst the various data
repositories of the VO.

\section{Theoretical basis : definition of quantities }


We start by introducing the "Quantity" as the object that associates a
value with a concept.  The concept may be any meaningful term or idea
which the VO community wishes to use (for example "X-ray star",
"visual flux", "CCD camera type", "index", etc.) and the value
indicates the amount or degree of the concept.  The value can be
stated as a number, a word ("full", "partial", "high", etc.), or a
symbol.

To serve as a general framework for manipulating concepts and their
values we create a entity or object which may serve as the package for
all of these tuples. This entity, the "quantity" is inherited (passes
on all of its properties) to all concepts (figure \ref{P3-19:fig-1}) and we
thus tie the meaning to the class of the object.

\begin{figure}
\epsscale{0.20}
\plotone{P3-19_f1.eps}
\caption{UML diagram of relationship between a concept, quantity and its value} \label{P3-19:fig-1}
\end{figure}

The value is itself a one-dimensional array, which may have one or
more "datum", e.g. the value V may be defined:
\begin{equation}
V = { d_{1}, d_{2}, d_{3},  .. d_{n} }
\end{equation}
where n is the number of datum in V and each d$_{i}$ are the individual
datum that may be either scalars, vectors or other quantities
(tuples). In the last case the child quantity serves as data but we
may also use child quantities to specify meta-data. To do so we insert
the child quantity directly within the parent quantity with the
designated relationship "metaData" (figure \ref{P3-19:fig-2}).

As the datum in V must describe scientific information (at least most
of the time) each datum must have associated with it some description
of its accuracy (errors) and scientific units.  Machine
understandability requires that each datum should also be described by
some type of a data format. In our model, we consider that all datum
in V for a given Q are "homogeneous"meaning that every datum of a
given Q has the same units and data format. Accuracy of scientific
data can, and often does, vary on a datum by datum basis. Thus, we
infer the existence of an array of accuracy values which is of the
same size as the array of V to which it refers.

Further description of the basis of our model, including how the model
may hold vectors and arbitrary tuples (tables) may be found in 
Thomas \&\ Shaya (2003).

\begin{figure}
\epsscale{0.20}
\plotone{P3-19_f2.eps}
\caption{Quantities use other quantities to capture meta-data} \label{P3-19:fig-2}
\end{figure}

\section{Practical application - development of domain-based ontologies}

In practical application our data model must be realizable in
software, thus we have described our model using the 
\htmladdnormallinkfoot{OWL}{http://www.w3.org/TR/owl-features}
ontology language (figure \ref{P3-19:fig-3}). We choose 
OWL because it may be used to
derive both the XML schema and UML diagrams (see Thomas \&\ Shaya 2003)
which will serve as the basis for
generating both code and XML instance documents.  Additionally, OWL,
and ontologies in general, can be used to formally define the
relationships between classes as well as their
instances. Of course, placed on this footing we may now talk of
quantities as classes in the object-oriented sense, which may be
"extended" to create concepts that will be queried for and traded
between participants in the VO. As a starting point, some important
concepts that the community might choose to extend the quantities into
in the VO domain include the space-time schema of Rots (2003) and the
UCD descriptors.

The development of ontologies that show the relationship between all
of the concepts in the VO will be an important task and we believe
that the quantity-based data model can form the basis for all the
other VO ontologies. We need not, nor is it desirable, create a single
all-encompassing ontology. It is better to have a spare, shared group
ontology, working in tandem with richer, but localized
ontologies. Mapping between localized ontologies can serve to bridge
differences in defined concepts. Under this formulation then, each
ontology should belong to its own namespace or domain.

\begin{figure}
\epsscale{0.80}
\plotone{P3-19_f3.eps}
\caption{OWL diagram of quantity} \label{P3-19:fig-3}
\end{figure}

\section {Discussion}

With this model, we have managed to
meet all of our set requirements and design goals. The model is
sparse, with few classes, yet powerful enough to encompass many types
of data that will exist in the VO. By casting the model in terms of an
ontology, we may use it to support sophisticated concept-based
searches.  Furthermore, we have managed to cast this model in terms of
an XML representation, which is important for transport of information
across the Internet as well as used in designing catalogs for
searching holdings at data repositories. Additional issues are 
discussed in Thomas \&\ Shaya (2003).

\section { Summary }

We have produced a rudimentary data model based on theoretical
considerations and mapped them into an ontological space.  In
addition, we have given thought to how this data model may be utilized
in terms of software, and how the community would approach designing
concepts for search and interchange.  Software resources related to
this work, including an XML schema, an XML example that wraps a FITS
file and simple Java code may be found at the following URL: {\tt
http://nvo.gsfc.nasa.gov/QuantityDataModel}

{\it Acknowledgment:} Support for this work was provided in part by NSF through  Cooperative Agreement AST0122449 to the Johns Hopkins University.
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\begin{references}
\reference McDowell, J., et al. 2002a, ``Data Models for the VO: overview'',\\
        http://bill.cacr.caltech.edu/cfdocs/usvo-pubs/files/vodm003.ps
\reference McDowell, J., et al. 2002b, ``Data Models for the VO: Metadata objects for the VO'', 
	http://bill.cacr.caltech.edu/cfdocs/usvo-pubs/files/vodm003.ps
\reference Plante, R. 2002, ``A Scalable Metadata Framework for the Virtual Observatory'',
	http://bill.cacr.caltech.edu/cfdocs/usvo-pubs/files/fw-draft2.pdf
\reference Plante, R. 2003, NVO Cambridge workshop presentation.
\reference Rots, A. 2003, ``Space-Time Coordinate Specification for VO Metadata''
\reference Thomas, B. and Shaya, E. 2003, astro-ph/0312604
\reference Williams, R., et al. 2002, ``VOTable: A Proposed XML Format for Astronomical Tables''
\end{references}
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