Meta Meta Meta Data Draft 0.3

Previous drafts are 0.1, 0.1b and 0.2.

A theory of metadata

Say we have a collection of learning resources. Let call it S with elements s₁, s₂, s₃, ... s_n.

S = { s₁, s₂, s₃, ... s_n} --- (1)

Now, apply a "meta" operation, μ_j on each of the element in S which will produce a set M with elements m_1j, m_2j, m_3j, ... m_nj where m_1j is the metadata of s₁. These elements (m_1j, m_2j, m_3j, ... m_nj) are the metadata of the learning resources.

M = { m_1j, m_2j, m_3j, ... m_nj } where m_ij=μ_j(s_j) μ s_j ∈ S --- (2)

Note that elements of m_ij are data as well. These resources may themselves be learning resources and hence we can apply "meta" operation on these as well to produce another set of metadata. This is infinitely recursive.

What is interesting, and perhaps confusing, is that there exist more than one meta operation. In fact, there are infinite numbers of meta operations.

∃ j for μ_j where j ∈ {0,1,..,n,..} --- (3)

Explanation: Up to here, each element of any metadata schema (e.g. LOM or DC) is a meta operation because the result of the operation of each of the element is a specific characteristic of the underlying resource. For example, DC-creator extracts the "creator property" of the learning resource.

An agreed set of meta operations is a metadata schema, ∏.

∏ = { μ₁, μ₂,.., μ_n}

Applying all or some of the operations in ∏ on a learning resource produce a metadata record for the learning resource.

Since metadata record may be learning resources, applying all or some of the operations in ∏ is allowed. This is infinitely recursive. [Note: this concept goes beyond just a single reification, e.g. when the metadata operation is the DC creator. A second application of DC creator on the metadata is the creator of the metadata (not the original learning resource). Hence we can also describe the creator of the creator of the metadata of the learning resource.]

A subset of elements S_i in a set of learning resources may have an easily identified common characteristic or property. We further define an operation, Λ, as an operation on a set S_i which will extract the common characteristics/properties among all elements in the set S_i to produce ζ.

Λ( S_i)=ζ --- (4)

Explanation:A subset of learning resources, e.g. thesis, will have common characteristics such as "degree awarded", "Institute granting the award" or even some characteristics of the content structure. By applying an Λ operation on a set of learning resources, some learning resources will fail the Λ operation (i.e. ζ = null) while some will produce a valid value (e.g. thesis). Here we are only interested in the cases where ζ ≠ ∅ by looking at more general characteristic that applies to all learning resources or a subset of the learning resources.

Each meta operation will also produce a set of metadata carrying the implicit characteristics of the meta operation. We can

Λ( M_i)=ζ --- (5)

If all possible value of ζ is finite, we say that the meta operation μ is listable and can be constrained by a finite set of value. This set of value can be defined by a set of controlled vocabulary. In other situation, ζ may have been well defined in other community, we can leverage on the work of these communities and create better inter-operability.

Explanation: The remark on this note "In education, some resources are inter-related (e.g., academic papers may be related by citations; a PhD thesis may be related by some commonly accepted formats). In other situations, there may be dependency among resources (e.g., a lesson plan may include dependent resources such as reading material, testing items, examples)" is an application of equation 5 above.