9.6. The AN Formalism

Formally, an AN is defined on the basis of a set of object types OT, a set of event types ET and a set of activity types AT as a directed graph ⟨ N, D ⟩ with two types of nodes N = EN ⋃ AN, event nodes and activity nodes, and two types of directed edges D = ED ⋃ AD, event scheduling edges and resource-dependent activity scheduling edges, with ED ⊆ N ⨉ EN and AD ⊆ N ⨉ AN, such that

1. each event node n ∈ EN is associated with

   1. an event type E ∈ ET with event participation roles P_E,
   2. an event variable e representing an event of type E,
   3. a (possibly empty) set of auxiliary (shortcut) object variables o defined with the help of event participation roles p ∈ P_E by setting o := e.p,
   4. a (possibly empty) set of definitions of on-event object state transition functions { f_p | p ∈ P_E };

2. each activity node n ∈ AN is associated with

   1. an activity type A ∈ AT with activity participation roles P_A,
   2. an activity variable a representing an activity of type A,
   3. a (possibly empty) set of auxiliary (shortcut) object variables o defined with the help of activity participation roles p ∈ P_A by setting o := a.p,
   4. a (possibly empty) set of definitions of on-activity-start object state transition functions { sf_p | p ∈ P_E };
   5. a (possibly empty) set of definitions of on-activity-end object state transition functions { ef_p | p ∈ P_E };
3. each event scheduling edge ⟨ n₁, n₂ ⟩ ∈ ED may be associated with
   1. a numeric delay expression δ possibly expressed with the help of the variables associated with n₁,
   2. a condition (or Boolean expression) C expressed with the help of the variables associated with n₁.