A Formal Model of Learning Object Metadata
Kris Cardinaels, Erik Duval, and Henk Olivie´
Katholieke Universiteit Leuven, Belgium
Kris.Cardinaels@cs.kuleuven.be, Erik.Duval@cs.kuleuven.be,
Henk.Olivie@cs.kuleuven.be
Abstract. In this paper, we introduce a new, formal model of learning
object metadata. The model enables more formal, rigorous reasoning over
metadata. An important feature of the model is that it allows for ’fuzzy’
metadata, that have an associated confidence value. Another important
aspect is that we explicitly address context dependent metadata.
1 The Formal Model of Metadata
In this paper we develop a formal or mathematical model for learning object
metadata. Such a model helps to build a formal, rigorous reasoning about meta-
data in the case of share and reuse. One of the situations in which such a formal
model is useful, is, for example, the discussion of automatic indexing of learning
objects.
One of the important aspects we introduce in this formal model is the rep-
resentation of context-awareness in metadata. A context represents a specific
situation in which a learning object can be used. These contexts allow us to
define more advanced metadata values which enable a better, i.e. more efficient
and more effective, retrievability of learning objects. We refer to the automatic
metadata generation framework that we implemented (see also [1]) for more
information about the use of contexts for metadata generation.
We build our model in different steps, starting with the most simple case in
which we only consider the learning objects themselves. Then we extend the
model by taking into account contexts in which learning objects are (re)used.
In the next step we look at learning objects with a complex structure, such as
aggregates.
We conclude the discussion of this model by pointing to an automatic indexing
framework we developed that implements this model.
1.1 Learning Objects and Metadata
Learning Objects. The first definitions of our model consider learning objects
and metadata. At the beginning we take learning objects in isolation from their
contexts in which they are used or reused. As a second simplification we consider
learning objects as atomic objects without a specific structure and not part of a
larger structure.
W. Nejdl and K. Tochtermann (Eds.): EC-TEL 2006, LNCS 4227, pp. 74–87, 2006.
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© Springer-Verlag Berlin Heidelberg 2006

A Formal Model of Learning Object Metadata 75
The definition of a learning object is given by the IEEE LOM standard [2]:
a learning object is any entity - digital or non-digital - that may be used for
learning, education or training.
In our formal model we do not explicitly define learning objects but define a
set of learning objects that we use throughout this model.
L = {l|l is a learning object} (1)
The above definition does not include details about learning objects, which
indeed corresponds to the given description of learning objects. For the moment,
a learning object is an abstract item of which we don’t have to know the details.
Metadata. Metadata are data about data. In our research we consider learning
object metadata – information about learning objects. In general, two approaches
to metadata are used; the first is the record approach (the approach taken by
the LOM standard), the second considers metadata items individually (adopted
by Dublin Core). To obtain a very general model we follow the second approach;
we will, however, also indicate that the record-based model can be derived from
the item-based approach.
We refer to metadata facets when we talk about properties. The term facet
is appropriate because we, in some way, are dealing with multi-faceted classi-
fications as introduced by Prieto-Dı´az in [3]. A facet is defined as a function
providing a value for that facet for a given learning object.
fi : L → CODfi (2)
The facet fi is a function that maps a learning object to a value from CODfi,
the codomain of fi. The codomain of a function is the set of possible values
resulting from applying the function. We assume that the set of possible values
always includes the value null for facets that are not applicable to a certain
learning object. We use the value null comparable to the use in relational data-
base systems, in which this value may indicate that the value of the facet is
unknown, unavailable or unapplicable [4, p.131]. The index i is used to facilitate
the distinction between different facets in the further definitions. Throughout
this text we refer to the value fi(l) as fil.
Analogously to learning objects, this definition of facets does not specify any-
thing about the possible values in the codomain. This approach opens the pos-
sibility to include all sorts of metadata items, even with a complex structure.
In definition 2 we implicitly made the assumption that every metadata facet
can only have one value for a learning object. In many situations this, however,
is not the case. Therefore, we immediately redefine a facet to include multiple
values also.
fi : L → (CODfi )n (3)