Defining Virtual Organizations Following a Formal Approach - Agents and Artificial Intelligence - page 370

Environment Dimension. The Environment Dimension describes the artifacts, i.e.
entities that populate the environment of a MAS. This dimension uses the concept
of artifact [16], an element introduced by the Agents & Artifacts (A&A) conceptual
framework. These elements are employed by agents in order to reach their goals, since
artifacts have no associated goals. Additionally, the A&A framework presents the con-
cept of workspace, used to define the topology of the environment of a MAS.

Definition 4 . The Environment Dimension of a Virtual Organization is defined as ED =

WS , AR , EnvFunc where:

- W S is the set of workspaces that build the environment of a MAS, where ws ∈ WS

is defined as ws = Loc and Loc is referred to the location of the workspace inside

the environment.
- AR is the set of artifacts, where an artifact ar ∈ AR is defined as ar = PR , OP , LO , St ,

where:
• PR are the observable properties of an artifact that agents can check without

executing any operation on it.

• OP is the set of operations that agents can execute when interacting with the

artifact.

• LO refers to the link operations, which allows the composition and distribution

of artifacts.

St is the internal state of an artifact.
- EnvFunc =

•

Located , Composition is the set of functions that act on the environ-

mental elements, where:
•

2 WS describes the set of workspaces where an artifact is lo-

→

Located : AR

cated.

2 WS allows defining intersection and nesting relations
between workspaces that build the environment.

• Composition : WS →

Properties of the Relations. The Composition relation is reflexive and symmetrical,
since a workspace can intersect with itself. Additionally, it is necessary for an artifact
to be contained, at least, in a workspace. Formally:

∀ ∈ ∃ ∈ → ⊆

Located ( ar ) ar Ar : ws WS ws (10)

Normative Dimension. The Normative Dimension describes normative restrictions on
the behavior of the entities of the system, including sanctions and rewards, based on the
work by Criado et al. [17].

Definition 5 . The Normative Dimension of a Virtual Organization is defined as ND =

N ,> n where:

- N is the set of norms of the system.
- > n is an order relationship between norms, defining the priority between them. This
relation establishes a total relation order between the norms governing the system,
avoiding the priority confusion when a norm is executed.

Formally, a norm is defined as: