Dynamics of Trust - Trust Theory: A Socio-Cognitive and Computational Model - page 171

Has Z the same relevant qualities? How much; how many? Does Z belong to the same
class/set of Y , based on the relevant features?
Does τ share the same relevant requirements as τ ? Does τ belong to the same kin/class/set
of services/goods as τ ?

6.6.3 Formal Analysis
In more systematic and formal terms we have tasks ( τ ) and agents ( Ag ): with τ ∈ T ≡ { τ 1 , ... ,

τ n } can be considered composed

of both a set of actions and the modalities of their running, this we call properties :

, and Ag ∈ AG ≡ { Ag 1 , ... ,Ag m } . We can say that each task τ

τ ≡{ p 1 ,..., p n } (6.14)

we consider this composition from the point of view of an agent ( Ag X ):

Bel Ag X ( τ ≡{ p 1 ,..., p n } ) (6.15)

In general each of these properties could be evaluated with a value ranging between a
minimum and maximum (i.e.: 0,1 ): representing the complete failure or the full satisfaction
of that action. So in general: 0 .

Of course, not all the properties of a task have the same relevance: some of them could be
considered indispensable for the realization of the task, others could be considered useful in
achieving greater success.
If we insert an apex c to all the properties that the agent ( Ag X ) considers indispensable ( core
properties ) for that task, we can write:

≤ p i ≤ 1 with i ∈ { 1, .. , n

}

p 1 ,..., p k }∪{

τ ≡{

p 1 ,..., p m } Bel Ag X ( ) (6.16)

C

p c 1 , , p c k }

NC

We call τ ≡ { ... and τ ≡ { p 1 , ... , p m } ,so

C NC

τ = τ ∪ τ (6.17)

The set of the core properties is particularly relevant for grouping tasks into classes and for
extending the reasoning behind generalization or specification.
Analogously, we can define the set of the features f AgY for an agent ( Ag Y ):

f AgY ≡{ f Y 1 ,..., f Yn } (6.18)

we consider this composition from the point of view of an agent ( Ag X ):

Bel Ag X ( f AgY ≡{ f Y 1 ,..., f Yn } ) (6.19)

Also in this case, each of these features could be evaluated with a value ranging between a
minimum and a maximum (i.e.: 0,1 ): representing the complete absence or the full presence of
that feature in the agent Ag Y , from the point of view of Ag X . So in general: 0 ≤ f i ≤ 1 with i ∈

{ Y 1 ,..., .

Given the previous definitions, we can say that Ag X could trust Ag Y on the task

Y n }

τ if Ag X has

the following beliefs: (6.19), (6.16) and

C

Bel Ag X ( ∀ p i ∈ τ , ∃{ f i }∈{ f Y 1 ,..., f Yn }|{ f i } =∅∩ p i i s satisfied from { f i } ) (6.20)