An individual is an entity that is constantly changing (having different emotions, moods,
etc.). So, when we speak of an individual, we always refer to it relative to a time t. The moment that the individual starts existing is defined by t = 0. The abstract entity that represents the individual at a time t we will call It from now on. In the simple case, an individual
has a personality and an emotional state (we do not yet take mood into consideration). The
model based on this assumption is called PE. In our framework, the personality is constant
and initialized with a set of values on t = 0. The emotional state is dynamic and it is initialized to 0 at t = 0 (we will go in more detail about this later on). Thus we define It
as
a tuple (p, et), where p represents the personality and et represents the emotional state at
time t. In our example, Julie will portray emotions (that change over time) based on what
happens, but how she obtains these emotions and the behaviour that results from it, depends
on a static part of her being, the personality.
From psychology research, there are many personality models that consist of a set of dimensions, where every dimension is a specific property of the personality. Take for example
the OCEAN model [3], which has five dimensions (see Table 2) or the PEN model [2] that
has three dimensions.
Generalizing from these theories, we assume that a personality has n dimensions, where
each dimension is represented by a value in the interval [0, 1]. A value of 0 corresponds
to an absence of the dimension in the personality; a value of 1 corresponds to a maximum
presence of the dimension in the personality. The personality p of an individual can then be
represented by the following vector:
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p =








α1
.
αn








, ∀i ∈ [1, n] : αi ∈ [0, 1] (1)
As an example, we can specify an OCEAN personality (thus n = 5) that is very open, very
extravert but not very conscientious, quite agreeable and not very neurotic:
p =
















0.8
0.1
0.7
0.5
0.05
















(2)
Emotional state has a similar structure as personality. The emotional state is a set of
emotions with a certain intensity. The size of this set depends on the theory that is used.
For example, in the OCC model, 22 emotions are defined, while Ekman [17] defines 6 that
are used as a basis for facial expression classification. The emotional state is something
that can change over time (for example due to a decay factor). Therefore, when we speak
about an emotional state, we speak of it relative to a time t. We define the emotional state
e
t
as an m-dimensional vector, where all m emotion intensities are represented by a value
in the interval [0, 1]. A value of 0 corresponds to an absence of the emotion; a value of 1
corresponds to a maximum intensity of the emotion. This vector is given as follows:
8
e
t =







































β
1
.
βm










, ∀i ∈ [1, m] : β
i ∈ [0, 1] if t > 0
0 if t = 0
(3)
Furthermore, we define an emotional state history ωt
that contains all emotional states
until e
t
, thus:
ωt = he
0
, e
1
, . . . , e
t
i (4)
An extended version of the PE model can be given by including mood (we will call this
the PME model). As such, we now define the individual I
t
as a triple (p, m
t
, e
t
), where mt
represents the mood at a time t. Mood has never been as deeply researched and accepted as
the notions of personality and emotional state and therefore its definition can be a bit tricky
(which is why we omitted it from the basic framework). Mood is less static than personality
and less fluent than emotional state [10]. It is an intermediate form that exists between the
two and that describes a rather static state of being that lasts longer than the average emotion
(see also Figure 2). This state of being can be one-dimensional (being in a good or a bad
mood) or perhaps multi-dimensional (feeling in love, feeling depressed).
Whether or not it is justified from a psychological perspective to have a multi-dimensional
mood is not in the scope of this paper. However, we will provide for a possibility of having
9
multiple mood dimensions, since it is more general, so one can choose how many dimensions mood actually has. We define a mood dimension as a value that is either negative or
positive and that lies in the interval [−1, 1]. Supposing that there are k mood dimensions,
the mood can be described by a vector:
mt =







































γ
1
.
γ
k










, ∀i ∈ [1, k ] : γ
i ∈ [−1, 1] if t > 0
0 if t = 0
(5)
Just like for the emotional state, there is also a history of mood, σ
t
, that contains the
moods m0
until mt
:
σ
t = hm0, m
1, . . . , m
t
i (6)