1. A Logical Viewpoint on Architectures
Frank de Boer, Marcello Bonsangue,
Joost Jacob, Andries Stam,
Leon van der Torre

2. Overview Research questions ArchiMate example Symbolic models
Interpretations
Semantic models
Summary and outlook

3. Research questions
How to provide a general mathematical foundation for (the use of formal methods in) enterprise architectures?
How to incorporate business process models in enterprise architectures to analyze and simulate their behavior?
How to provide architectural tool support for enterprise architectures with business process models?

4. establishes methods for 1..*
IEEE 1471 (partly)
has an
System
Architecture
has 1..*
Stakeholder
described by 1
identifies 1..*
Architectural
description
is addressed to 1..*
participates in
selects 1..*
organized by 1..*
Viewpoint
conforms to
View
aggregates 1..*
participates in 1..*
Model
establishes methods for 1..*
consists of 1..*

5. establishes methods for 1..*
IEEE 1471 extension
has an
System
Architecture 1
abstraction
has 1..*
Stakeholder
described by 1
identifies 1..*
Architectural
description
is addressed to 1..* *
Semantic
model
participates in
selects 1..*
organized by 1..*
Viewpoint
conforms to
View
interprets 1..*
participates in 1..*
Symbolic model
establishes methods for 1..*
consists of 1..* *
Signature
has 1

6. Running example (ArchiMate language)

7. Signature - definition
A signature consists of:
partially ordered set of primitive sorts (sort hierarchy);
partially ordered set of relations.
Extensions:
Product type (T1 x T2)
Function type (T1 → T2); can also be used for attributes
Functions F(T1): T2; possibly multi-valued

8. Signature - example Sorts: role object product Employee Product
Order_Registry
Product_Registry
Relations:
Owns
association

9. Signature - example IS-A relations: Employee is-a role
Product is-a product
Order_Registry is-a object
Product_Registry is-a object
Owns is-a association
Owns relation:
Employee Owns Product

10. Signature - example Functions: Register_order_placement Accept_product
domain:
Employee
Order_Registry
codomain:
Accept_product
domain
codomain
Etc.

11. Interpretations - definition
An interpretation of a signature assigns to each primitive sort S a set of individuals I(S)
For product types T1 x T2, the interpretation is the cartesian product I(T1) x I(T2)
For function types T1 → T2, the interpretation is the set of all functions for which holds that the image of I(T1) is contained in I(T2)

12. Interpretations - example
Product p1 p2
Employee
e1 order=p1 product=p1
e2 order=p1 product=p2
e3 order=p2 product=p1
e4 order=p2 product=p2

13. Semantic model - definitions
A Semantic model of a system involves its concrete components and their concrete relationships
It introduces names n:T that range over individuals of type T
The semantic model assigns to each symbolic function F(T1): T2 an interpretation of T1 → T2
A Semantic model may change in time (it describes the state of a system)

14. Semantic model - example
emp = e4 order=p2 product=p2
order-reg = {p1}

15. Semantic model - dynamics
In terms of transformations of semantic models
Two ways:
Functions as primitive actions
n := F(m)
introduction of Process Algebra
Functions as data transformers
Multi-valued functions with input- and output-channels
introduction of Data Flow Networks

16. Tool support Symbolic models represented as an XML or AML document.
Static semantics can be represented in the same way.
For dynamic semantics, we propose to use an XML transformation language: the Rule Markup Language (RML)
Set of XML constructs added to an existing vocabulary;
For creating rules that can be executed by RML tools;
General purpose, easy to use.

17. RML – example Consider the following XML fragment:
<employee order=p2 product=p2/>
<orderregistry>
<orders>
<order name=p1/>
</orders>
</orderregistry>
In AML (ASCII Markup Language)
employee
order = p2
product = p2
orderregistry
orders order name = p1

18. RML – example div class=rule name="Register_order_placement" employee
div class=antecedent
rml-Employee
order = rml-OrderName
product = rml-ProductName
orderregistry
orders
rml-list name = oldOrders
div class=consequence
rml-use name = oldOrders
order name = rml-OrderName
employee
order = p2
product = p2
orderregistry
orders order name = p1
order name = p2

19. Summary and outlook
Integration of business processes and enterprise architectures
Distinction between signature, symbolic model and semantic model
Formal basis for the description and analysis of architectures
Various formal techniques (process algebras, DF networks) can be integrated
Tool support for formal analysis with AML and RML
Various extensions are possible
logical languages (description logics, temporal logics)
design actions (transformations of symbolic models)

20. More information ArchiMate - http://archimate.telin.nl
RML -