Adaptive Sequencing of Information for Lifelong Learners - E-Infrastructures and Technologies for Lifelong Learning - page 278

Figure 1. Sequencing graph example

environments in SG (one for each user), I is the set
of initialization actions, V is the set of variables, η
⊂

A condition c specifies a boolean expression.
Operators allowed for integer comparison are =,
<, ≤, >, ≥. Strings (including booleans) can only
be checked for equality. The allowed boolean
connectives are negation (NOT), conjunction
(AND) and disjunction (OR).
An edge e

V is the upwards interface, and elements of the
set Υ are downwards interfaces. SG is called the
parent node of each n in N, while they are called
its children nodes.
A node n N is either a state associated to a

learning activity (referenced by means of a URL)
or a sequencing graph. In the former case, it is
called an activity node; in the latter, it is called a
container node. At the parent node, there must be
one and only one downwards interface for each
container node.
A variable v

E is a tuple (ns, nd, c, A), where ns
is the source node and nd is the destination node,
c is the condition and A is the set of actions. An
edge defines a possible transition from its source
to its destination when its condition evaluates to
“true”. If the edge is followed, the corresponding
set of actions A is executed, modifying the envi-
ronment. For an edge in a sequencing graph, the
parent node of its source must be its destination or
the parent of its destination; in other words, there
are not any edges connecting nodes in different SG
or different levels of the hierarchy: all transitions
are defined between siblings or from the child to
the parent. An edge whose destination is the parent
node of its source is called an exit edge.
An initialization action i

∈ ∈

V is a name that identifies a
value in the environment of the student.
An environment π

∈

is a set of pairs variable-
value, where information about the student and its
relation to the graph can be stored. For the sake
of simplicity, attribute values are of two types:
strings and integers. Changes in the environment
can be performed by the learning activities or by
the actions at the edges. Each student has its own
environment. Actions fired by a student when
following an edge change only the environment
of that student.
An action a determines a change in the environ-
ment. It assigns a value to a variable, that can be
a constant or the result of a complex arithmetical
operation regarding others variables and constant-
data. Operations include addition, subtraction,
multiplication, division, max and min.

Π

∈ ∗

I is an action that is
executed when the user enters a container node. It
adds a new pair to the environment. There must be
an initialization action i for each variable v

∈

V.

∈

Φ is a possible node in
which to start the sequencing when going down
in the hierarchy of nodes. See Traversal Algo-
rithm, below.
The upwards interface η is the set of variables
that are exported to the upper level: when the
student follows an exit edge, these variables are

An entry node φ

∈