1. Ontologies Reasoning Components Agents Simulations Ontologies Jacques Robin

2. Outline  Ontologies  What is an ontology?  Elements of an ontology  Services provided by an ontology  The pluridisciplinary origin of ontological engineering  Typology of ontologies  Sub-fields and general issues in ontological engineering  The Object Constraint Language (OCL)  What is OCL?  Motivating examples  OCL expression contexts  The link between the OCL and UML metamodels  The OCL metamodel  OCL Types  Inheritance and encapsulation in OCL  Local variale definitions  The OCL operator library  OCL vs. UML  OCL vs. Java

3. What is an Ontology?  Definition: explicit, formal (or semi-formal) specification of a shared conceptualization  Conceptualization:  Conceptualization: model of entities, relations, constraints and rules of a given domain or field  Formal:  Machine-processable;  Allowing automated reasoning;  With declarative semantics;  Shared:  By a knowledge community;  Allowing common understanding and effective communication of largely implicitly specified content,  completed by inference based on the shared explicit knowledge in the ontology  Related concepts:  Reusable knowledge base  Database schema

4. Elements of an Ontology: Concept Generalization Hierarchy  Entity Classes:  Each entity class defined by a set of slot-facet-value triple  Correspond to:  Classes of OO models  Entities of relational models  Terms of logical models  Property slots x relational slots  Filled by atomic values (primitive data types) x by other concepts  Epistemological status of the value (defined by the facet)  Precisely known, default, possibilistic, plausibilistic, probabilistic  Generic Relations:  With or without generalization hierarchy running parallel to concept generalization hierarchy  Correspond to:  Associations, aggregations, compositions and complex object filled attributes of OO models  Relations of relational model  Predicates of logical models

5. Elements of an Ontology: Constraints and Derivation Rules  Constraints:  On the domain values of attributes from  One concept (type constraints)  Several related concepts (integrity constraints)  To prohibit semantically invalid concepts instances or semantically inconsistent concept instance set  Correspond to:  Class signatures and invariants in OO models  Typing predicates, sorts (partition of constant symbol alphabet) and integrity constraints in logical models  Typing and integrity constraints in database schemas  Rules to derive:  The value of attribute concepts from set of other such values  The existence of concept instances from the existence of other such instances  Correspond to:  Declarative methods in OO models  Implicative clauses of logical models  Database views

6. Elements of an Ontology: Constraints x Derivation Rules  As a constraint, the formula:   C, person(C)   ! M, person(M)  mother(M,C)  prohibits the creation of person concept instances with zero or multiple mothers;  As a derivation rule, this same formula allows inferring: - From the existence of each instance C of the person concept the existence of another instance M of that concept, related to C by an instance of the mother relation; - From the existence of two instances M and M’ of the person concept, both related to the same third instance C of that concept by the mother relation, that M = M’  Concept instances generally not part of an ontology  Exception: special values that correspond to constant value declaration in programming language as opposed to variable binding

7. Computation Services to Provide to Make an Ontology Useful  Insertion or deletion of element:  Entity class, generic relation, constraint, derivation rule  Simple queries:  Entity attribute value local retrieval  Relation navigation  Queries involving automated reasoning:  Entity attribute value retrieval with inheritance  Instance classification from its attribute values  Subsumption between two entity or relation classes  Input constraint verification over an entity class  Search for entity classes that satisfy a given input constraint  Verification of instance sets against ontology constraints  Overall ontology consistency  Derivability of given formula

8. Cross-Disciplinary History of Ontologies Organization Knowledge Management since 1990 Data Integration since 1995 Multi-Agent Systems since 1995 Web Information Retrieval since 2000 Cognitive Psychology since 1960 Linguistics since 1960 Expert Systems since 1980 Natural Language Processing since 1980 Ontologies Philosophy since 350 A.C. Software Engineering (Business Modeling) since 1990

9. Ontology Classification Dimensions  Specialist x General  Specialist:  Specialist: Models a restricted domain or field  ex. geometry, stock market, soccer, viral infections, etc.  General:  Models common sense knowledge  Most generic cognitive categories, reusable in multiple domains, with domain- specific concepts specializing  Common sense ontology provide sound guidance to avoid  Conceptual x Linguistic:  Conceptual:  Based on distinctions useful for automated reasoning executing variety of tasks  Linguistic:  Based on the vocabulary of one or several natural languages  A concept is defined by the synonyms to express it  A relation is defined by recurrent, deep thematico-lexical relations among these synonyms

10. Ontology Classification Dimensions  Structural x Behavioral  Behavioral ontology reify as concepts reasoning and problem solving methods  Domain-Level x Meta-Level  Meta-Level ontology defines the computational concepts with which to model the domain or common sense concepts

11. Skeleton of a Top-Level Common Sense Ontology

12. Ontology Engineering Issues  Domain partitioning:  How to delimit concepts?  What are the distinctions that bring added value?  Scope:  What knowledge to include?  What is the domain frontier?  Granularity:  Down to which level to detail the model?  Validation:  How to evaluate the model quality?  Why to prefer one modeling solution over another?  How to identify key missing concepts?  Since an ontology is by definition meant to be application independent, application requirements cannot be used as guidance  These issues are particularly vexing for conceptual, common sense ontology that can neither fall back on linguistics nor on common requirement of application family for guidance

13. What is OCL? Definition and Role  A textual specification language to adorn UML and MOF diagrams and make them far more semantically precise and detailed  OCL2 integral part of the UML2 standard  OCL complements UML2 diagrams to make UML2:  A domain ontology language that is self-sufficient at the knowledge level to completely specify both structure and behaviors  A complete input for the automated generation of a formal specification at the formalization level to be verified by theorem provers  A complete input for the automated generation of source code at the implementation level to be executed by a deployment platform  OCL complements MOF2 diagrams to make MOF2:  An object-oriented declarative abstract syntax and semantics specification language that is self-sufficient at the meta-knowledge/meta-modeling level  OCL forms the basis of model transformation languages  such as Atlas Transformation Language (ATL) or Query-View-Transform (QVT)  which declaratively specify through rewrite transformation rules the automated generation of formal specifications and implementations from a knowledge level ontology  OCL expressions are reused in the left-hand side and right-hand side of such rules  To specify objects to match in the source ontology of the transformation  To specify objects to create in the target formal specification or code of the transformation

14. What is OCL? Characteristics  Formal language with well-defined semantics based on set theory and first- order predicate logic, yet free of mathematical notation and thus friendly to mainstream programmers  Object-oriented functional language: constructors syntactically combined using functional nesting and object-oriented navigation in expressions that take objects and/or object collections as parameters and evaluates to an object and/or an object collection as return value  Strongly typed language where all expression and sub-expression has a well-defined type that can be an UML primitive data type, a UML model classifier or a collection of these  Semantics of an expression defined by its type mapping  Declarative language that specifies what properties the software under construction must satisfy, not how it shall satisfy them  Side effect free language that cannot alter model elements, but only specify relations between them (some possibly new but not created by OCL expressions)  Pure specification language that cannot alone execute nor program models but only describe them  Both a constraint and query language for UML models and MOF meta- models

15. What is OCL? How does it complement UML?  Structural adornments:  Specify complex invariant constraints (value, multiplicity, type, etc) between multiple attributes and associations  Specify deductive rules to define derived attributes, associations and classes from primitive ones  Disambiguates association cycles  Behavioral adornments:  Specify operation pre-conditions  Specify write operation post-conditions  Specify read/query operation bodies  Specify read/query operation initial/default value

16. OCL: Motivating Examples  Diagram 1 allows Flight with unlimited number of passengers  No way using UML only to express restriction that the number of passengers is limited to the number of seats of the Airplane used for the Flight  Similarly, diagram 2 allows:  A Person to Mortgage the house of another Person  A Mortgage start date to be after its end date  Two Persons to share same social security number  A Person with insufficient income to Mortgage a house 1 2

17. OCL: Motivating Examples 1 2 context Flight inv: passengers -> size() <= plane.numberOfSeats context Mortgage inv: security.owner = borrower inv: startDate < endDate context Person inv: Person::allInstances() -> isUnique(socSecNr) context Person::getMortgage(sum:Money,security:House) pre: self.mortgages.monthlyPayment -> sum() <= self.salary * 0.3

18. OCL Expression Contexts Operation

19. OCL Contexts: Default Value and Query Specifications Initial values:  context LoyaltyAccount::points : integer init: 0  context LoyaltyAccount::transactions : Set(Transaction) init: Set{} Query operations:  context LoyaltyAccount::getCustomerName() : String body: Membership.card.owner.name  context LoyaltyProgram::getServices(): Set(Services) body: partner.deliveredServices -> asSet()

20. OCL Contexts: Specifying Invariants on Attributes The context of an invariant constraint is a class When it occurs as navigation path prefix, the self keyword can be omitted:  context Customer inv: self.name = ‘Edward’  context Customer inv: name = ‘Edward’ Invariants can be named:  context Customer inv myInvariant23: self.name = ‘Edward’  context LoyaltyAccount inv oneOwner: transaction.card.owner -> asSet() -> size() = 1 In some context self keyword is required:  context Membership inv: participants.cards.Membership.includes(self)

21. Association Navigation  Association navigation:  context Transaction def getCustomer():Customer = self.card.owner  Attribute access:  context Transaction def getCustomerName():String = self.card.owner.name  Abbreviation of collect operator that creates new collection from existing one, for example result of navigating association with plural multiplicity:  context LoyaltyAccount inv: transactions -> collect(points) -> exists(p:Integer | p=500)  context LoyaltyAccount inv: transactions.points -> exists(p:Integer | p=500)  Use target class name to navigate roleless association:  context LoyaltyProgram inv: levels -> includesAll(Membership.currentLevel)  Call UML model and OCL library operations

22. Generalization Navigation  OCL constraint to limit points earned from single service to 10,000  Cannot be correctly specified using association navigation: context ProgramPartner inv totalPoints: deliveredServices.transactions.points -> sum() < 10,000 adds both Earning and Burning points  Operator oclIsTypeOf allows hybrid navigation following associations and specialization links context ProgramPartner inv totalPoints: deliveredServices.transactions -> select(oclIsTypeOf(Earning)).points -> sum() < 10,000

23. OCL Contexts: Specifying Attribute Derivation Rules  context CustomerCard::printedName derive: owner.title.concat(‘ ‘).concat(owner.name)  context TransactionReportLine: String derive self.date = transaction.date ...  context TransactionReport inv dates: lines.date -> forAll(d | d.isBefore(until) and d.isAfter(from)) ...

24. OCL Contexts: Specifying Pre and Post Conditions  context LoyaltyAccount::isEmpty(): Boolean pre: -- none post: result = (points = 0) Keyword @pre used to refer in post-condition to the value of a property before the execution of the operation:  context LoyaltyProgram::enroll(c:Customer) pre: c.name <> ‘ ‘ post: participants = participants@pre -> including(c) Keyword oclIsNew used to specify creation of a new instance (objects or primitive data):  context LoyaltyProgram:: enrollAndCreateCustomer(n:String,d:Date):Cust omer post: result.oclIsNew() and result.name = n and result.dateOfBirth = d and participant -> includes(result) oclIsNew only specifies that the operation created the new instance, but not how it did it which cannot be expressed in OCL

25. Links Between OCL and UML Meta-Models

26. The OCL Expressions Meta-Model

27. The OCL Types Meta-Model OCL MetaclassUML Metaclass

28. OCL Types  Value Types:  UML primitive types (including user-defined enumerations)  OCL collection types (even of user-defined classifiers ?)  Their instances never change value  ex, Integer instance 1 cannot be changed to instance 2, nor can string instance “Lew Alcindor” be changed to string instance “Kareem Abdul-Jabbar”, nor can enumeration Grade instance A can be changed to enumeration instance C.  Object types: UML classifiers  Their instances can change value, i.e., the Person instance p1 can have its name attribute “Lew Alcindor” changed to “Kareem Abdul-Jabbar” yet remain the same instance p1  OclAny:  Most generic OCL type, subsuming all others  General reflective operations are defined for this type and inherited by all other OCL types

29. OCL Types  Primitive data types (from UML): boolean, string, integer, real  Type conformance rules:  t 1 conforms to t 2 if t 1 <= t 2 in type hierarchy  t 1 = collection(t 2 ) conforms to t 3 = collection(t 4 ) if t 2 conforms to t 4  integer <= real  Type casting:  Operation oclAsType(s) can be invoked on an expression of type g to recast it as a type s  s must conform to g  OclVoid:  Undefined value (similar to null values of SQL)  Tested by oclIsUndefined operation of OclAny type

30. OCL Types: Collections  Collection constants can be specified in extension:  Set{1, 2, 5, 88}, Set{‘apple’, ‘orange’, ‘strawberry’}  OrderedSet{‘black’, ‘brown’, ‘red’, ‘orange’, ‘yellow’, ‘green’, ‘blue’, ‘purple’}  Sequence{1, 3, 45, 2, 3}, Bag{1, 3, 4, 3, 5}  Sequence of consecutive integers can be specified in intension:  Sequence{1..4} = Sequence{1,2,3,4}  Collection operations are called using -> instead of.  Collection operations have value types:  They do not alter their input only output a new collection which may contain copies of some input elements  Most collections operations return flattened collections  ex, flatten{Set{1,2},Set{3,Set{4,5}}} = Set{1,2,3,4,5}  Operation collectNested must be used to preserve embedded sub- structures  Navigating through several associations with plural multiplicity results in a bag

31. OCL Semantics: Encapsulation and Inheritance  By default, OCL expressions ignore attribute visibility  i.e., an expression that access a private attribute from another class is not syntactically rejected  OCL constraints are inherited down the classifier hierarchy  OCL constraints redefined down the classifier hierarchy must follow substituability principle  Invariants and post-condition can only become more restrictive  Preconditions can only become less restrictive Examples violating substituability principle: context Stove inv: temperature <= 200 context ElectricStove inv: temperature <= 300 context Stove::open() pre: status = StoveState::off post: status = StoveState::off and isOpen context ElectricStove::open() pre: status = StoveState::off and temperature <= 100 post: isOpen

32. OCL Expressions: Local Variables  Let constructor allows creation of aliases for recurring sub-expressions context CustomerCard inv: let correctDate : Boolean = validFrom.isBefore(Date::now) and goodThru.isAfter(Date::now) in if valid then correctDate = false else correctDate = true endif  Syntactic sugar that improves constraint legibility

33. OCL Library: Generic Operators  Operators that apply to expressions of any type  Defined at the top-level of OclAny

34. OCL Library: Primitive Type Operators  Boolean: host, parameter and return type boolean  Unary: not  Binary: or, and, xor, =, <>, implies  Ternary: if-then-else  Arithmetic: host and parameters integer or real  Comparison (return type boolean): =, <>, =,  Operations (return type integer or real): +, -, *, /, mod, div, abs, max, min, round, floor  String: host string  Comparison (return type boolean): =, <>  Operation: concat(String), size(), toLower(), toUpper(), substring(n:integer,m:integer)

35. OCL Library: Generic Collection Operators

36. OCL Library: Specialized Collection Operators

37. OCL Constraints vs. UML Constraints context ElectricGuitar inv: strings -> forAll(s \ s.oclIsType(MetalStrings)) context: ClassicalGuitar inv: strings -> forAll(s | s.oclIsType(plasticStrings)) context ElectricGuitar inv: strings -> forAll(type = StringType::metal) context ClassicGuitar inv: strings -> forAll(type = StringType::plastic) context Guitar inv: type = GuitarType::classic implies strings -> forAll(type = StringType::plastic inv: type = GuitarType::classic implies strings -> forAll(type = StringType::plastic

38. OCL vs. Java  Declarative specification of operation post-conditions in OCL is far more concise than corresponding implementation in mainstream imperative OO language such as Java  This is due mainly to OCL’s powerful collection operators  Example: OCL expression self.parters -> select(deliveredServices -> forAll(pointsEarned = 0))  Corresponding Java code: 1.Iterator it = this.getPartners().iterator(); 2.Set selectResult = new HashSet(); 3.while( it.hasNext() ){ 4. ProgramPartner p = (ProgramPartner) it.next(); 5. Iterator services = p.getDeliveredServices().iterator(); 6. boolean forAllresult = true; 7. while( services.hasNext() ){ 8. Service s = (Service) services.next(); 9. forAllResult = forAllResult && (s.getPointsEarned() == 0); 10. } 11. if ( forAllResult ){ 12. selectResult.add(p); 13. } 14.} 15.return result;