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(for example, in Fig. 2.10 the domain concept C 3 is delivered to the learner
before the domain concept C 5 ); “part-of” that declares that a concept belongs to
another concept (for example, in Fig. 2.10 the domain concept C 2 in includes the
domain concepts C 10 , C 11 and C 12 ); the dependence relation that declares that the
knowledge level of a domain concept is affected by the learner's knowledge level
on another related concept (For example, in Fig. 2.10 the knowledge level of the
domain concepts C 14 , C 8 and C 9 is affected by the learner's knowledge level on
the concept C 15 ).
The dependence relations allow the tutoring system to identify how the knowl-
edge level of a concept is affected by the learner's knowledge level on other
related concepts. A dependence relation is characterized by the symbol ' + ' or the
symbol ' ' and a number (strength of impact). The symbol depicts the order in
which the two related concepts are delivered to the learner. If the symbol ' + ' is
labeled on the arc that connects Ci i with C j with direction from Ci i to C j (C i C j ),
then it denotes that Ci i is taught before Ci j . Otherwise, if the symbol that is labeled
on the particular directed arc is the symbol ' ', then it denoted that that C j is
taught before Ci. i . The numbers that are labeled on the directed arcs depict the
degree at which the knowledge level of a domain concept is affected regarding
the knowledge level of its related domain concepts. In other words, they depict
the “strength of impact” of a domain concept on a related concept. The particu-
lar numbers are only positive. This is happened due to the fact that the increase
of the knowledge level of a domain concept leads to the increase of the knowl-
edge level of a depended domain concept, and the decrease of the knowledge level
of a domain concept leads to the decrease of the knowledge level of a depended
domain concept. Therefore, the numbers of the directed arcs that depict the
knowledge dependencies belong to the interval (0, 1]. For example, in Fig. 2.10 ,
the value ' + 0.8' that is labeled on the directed arc, which connects C 10 with
C 13 (C 10 C 13 ), denotes that the concept C 10 is delivered to the learner before
the concept C 13 and the “strength of impact” of C 10 on C 13 is 0.8. Similarly, the
value ' 0.72' that is labeled on the directed arc, which connects C 15 with C 14
(C 15 C 14 ), denotes that the concept C 15 is delivered to the learner after the
concept C 14 and the “strength of impact” of C 15 to C 14 is 0.72.
The arcs in the FR-CN, which represent the domain concepts' dependencies
of the knowledge domain, are bidirectional. Furthermore, the value of the arc
C i C j is not essentially equal to the value of the arc Ci j C i . This is hap-
pened due to the fact that changes on the knowledge level of Ci i may affect the
knowledge level of Ci. j in a different degree than changes on the knowledge level
of C j affect the knowledge level of Ci. i . It has to be clear that the value 1 on the
directed arc that connects two dependent domain concepts does not mean that
the two dependent concepts are the same. It implies that if a learner knows a
domain concept of a section, s/he may know a related concept of another sec-
tion at the same degree. The percentage of increase or decrease of the knowledge
level of a domain concept that occurs due to changes on the knowledge level of
another concept related with this domain concept is defined by experts of the
knowledge domain.
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