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Objectification

Terry HalpinNorthface University, USA

terry.halpin@northface.eduwww.orm.net

www.northface.edu

© 2005, T. A. Halpin & Northface University

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Contents

Objectification in ORM, UML, and ER

Two Kinds of Nominalization

Objectification and Composite Reference

Schemes

Objectification of Unary Facts

Objectification of Fact Types with Non-spanning

UCs

Propositional Nominalization and Communication

Acts

Conclusion

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Objectification in ORM, UML, and ER

Roughly speaking, objectification (a.k.a. nesting), treats a relationship instance as an object in its own right, so it may be talked about like any other object.

ORM example(ORM 2 notation):

Country(Code)

Sport(Name)plays

“Playing !”

AU cricketAU tennisNZ cricketUS tennis

Rank(Nr)

is at

(AU, cricket) 1

(US, tennis) 1(AU, tennis) 4

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UML usually calls this reification, allowing association instances to be objectifiedas instances of an association class.

Unfortunately the name of the association class must matchthe name of the association (whether displayed or not).

UML example, augmented by non-standard notationfor preferred identification scheme “{P}” :

code {P}

Country

name {P}

Sport

rank [0..1]

Playing

**

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Industrial Entity Relationship Modeling (ER)(e.g. IE, IDEF1X, Barker ER) does not support objectification at all.

Some academic versions of ER do support objectification,typically with restrictions (e.g. objectified relationships may have attributes but not play in other relationships)

Example in Elmasri-Navathe ER notation(unable to specify attribute optionality):

COUNTRY SPORTPLAYS

CountryCode

M N

SportNameRank

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Two Kinds of Nominalization

Nominalization replaces a declarative sentence by a noun phrase,enabling the nominalized object to be referenced like any other object.

Two basic kinds of nominalization may be distinguished:

• Circumstantial -- nominalized object is a state of affairs/event/activity

• Propositional -- nominalized object is a proposition

Elvis sang the song ‘Hound Dog’. -- original proposition

Elvis’s singing of the song ‘Hound Dog’ is popular. -- actual state of affairs

That Elvis sang the song ‘Hound Dog’ is well known. -- true proposition

That Elvis sang the song ‘Hound Dog’ is debatable. -- false proposition

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It’s snowing outside. -- original proposition

It’s true that it’s snowing outside. -- proposition

That snowing is beautiful. -- state of affairs

In ordinary speech, “fact” (i.e. fact instance) often means “true proposition”.

ORM uses “fact” in the weaker sense of

“proposition taken to be true”

(epistemic commitment by users in the business being modeled)

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Country(Code)

Sport(Name)plays

“Playing !”

AU cricketAU tennisNZ cricketUS tennis

Rank(Nr)

is at

(AU, cricket) 1

(US, tennis) 1(AU, tennis) 4

code {P}

Country

name {P}

Sport

rank [0..1]

Playing

**

(a) (b)

Consider an object instance resulting from the objectification to Playing,

e.g. Australia’s playing of cricket.

Is this object a state of affairs/event/activity or is it a proposition?

Australia’s playing of cricket is at rank 1.

Makes sense if playing is an activity, but not if it’s a proposition.

Australia’s playing of cricket is true. -- Nonsense.

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This is typical of objectification examples in information models.

“Objectified relationships” are typically states of affairs in 1:1 correspondence with the relationships (facts in the ORM sense)that they objectify,but are not identical with those facts.

So we reject this aspect of the UML metamodel,where AssociationClass is a subclass of Association and Class.

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Objectification andComposite Reference Schemes

To facilitate conceptual declaration of business rules (constraints or derivation rules) and queries on information modelsORM includes (implicitly or explicitly) link fact typesto support navigation betweenthe objectification result and the objects in the fact being objectified.

Country(Code)

Sport(Name)plays

“Playing !”Rank(Nr)

is at

<< is by is of

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If needed, default readings are assigned for link predicates, e.g.

The modelermay assignbetter readings,e.g.

Company(Name)

acquired

“Acquisition !”

was friendly

involves1 << involves2

Company(Name)

acquired

“Acquisition !”

was friendly

was by << is of

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Company(Name)

acquired“Acquisition !” was friendly

was by /was acquirer in

<< is of

was acquired in

Microsoft Visio Microsoft Navision Visio InfoModelers

[acquisitionBySelf]

[acquirer] [target]

[acquisitionOfSelf]

[acquirer] [target]

ORM 2 supports multiple predicate readings and role nameswhose screen or print display may be suppressed individually.

ORM 2 allows rules and navigation paths to be declared in • relational style -- using predicate names• attribute style -- using role names• mixed style -- using both

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Country(Code)

Sport(Name)plays

“Playing !”Rank(Nr)

is at

<< is by is of

Playing !

Country(Code)

Sport(Name)

Rank(Nr)is at

<< is by << is of

plays

ORM 2 allowsobjectificationto be displayedin this way

but interprets this as shorthand for:

Asserting theequality constraintis the critical stepin treating thisas objectification.

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Playing !

Country(Code)

Sport(Name)

Rank(Nr)is at

<< is by << is of

plays1.1 1.2

2.1 2.2

ORM 2 allows role sequences participating in constraintsto be disambiguated by role sequence numbers whose display may be toggled on/off.

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Playing !

Country(Code)

Sport(Name)

Rank(Nr)is at

<< is by << is of

plays1.1 1.2

2.1 2.2

This model may be arrived at in different ways, e.g.

(1) Start with the fact type Country plays Sport, then objectify it as Playing.

(2) Start with the fact types Playing is by Country and Playing is of Sport, then define Country plays Sport as fully derived from them.

(3) Start with the 3 fact types Country plays Sport, Playing is by Country,

and Playing is of Sport, then assert the equality constraint.

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These 3 ways may be formalized as equivalences thus:

E1: x [Playing x y:Country z:Sport (x is by y & x is of z & y plays z)]

E2: x:Country y:Sport [x plays y z:Playing (z is by x & z is of y)]

E3: x:Country y:Sport z:Playing [x plays y (z is by x & z is of y)]

Regardless of which way is used to arrive at the model, the same basic structure is used to capture the model in the metamodel,and the same basic mapping procedures are used to transform itto implementation targets (e.g. Rmap, Omap, Xmap) -- under development

ORM 2 includes a formal, high level textual languagefor all its graphical rules as well as additional business rulese.g. the derivation rule E2 may be rendered as:

Country plays Sport iff some Playing is by Country and is of Sport.

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Objectification of Unary Facts

ORM previously forbad objectification of unary facts.For ORM 2, we removed this restriction, by extending the previous analysis toobjectified types with simple reference schemes.

Consider the unary fact:

The President named ‘Abraham Lincoln’ died.

We may objectify this event using the nominalization “that death”, and declare the following additional fact:

That death occurred in the Country with country code ‘US’.

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President(Name)

Abraham Lincoln

George W. Bush Ronald Reagan

died

Abraham Lincoln Ronald Reagan

“Death !”

occurred in

Country(Code)

Abraham Lincoln US Ronald Reagan US

AU

US CA

...

The schema is interpreted as shorthand for:

President(Name)

occurred in

Country(Code)

Death !

met / is of

died

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The earlier analysis for objectificationmay now be generalized by allowing the arity to be unrestricted (1 or more)and the reference scheme to be simple or composite.

The result of objectifying a relationship typemay be viewed asan entity type that has a reference schemewhose reference projectionbears an equality constraintto the fact type being objectified.

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FCO-IM also supports objectification of unaries,but in a very different way and for a different purpose.

FCO-IM uses defines non-lexical objectsas objectifications of roles played by lexical objects, e.g.

CountryCoderefers to a country

Country

While this approach is interesting, and is supported by twoDutch tools (CaseTalk and Infagon), this seems to conflate reference with referent,and to make it awkward to deal with multiple inheritance,context-dependent reference, and changes to reference schemes.

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Objectification of Fact Typeswith Non-spanning UCs

Previously, ORM allowed an association to be objectified only if either• it has just one uniqueness constraint, and this spans all its roles, • or it is a binary 1:1 association.

This restriction forbids objectification of 2 kinds of associations:

• An n:1 (or 1:n) binary association; • A ternary or longer association whose longest uniqueness constraint spans exactly n-1 roles.

The above cases are allowed in UML, and those academic versionsof ER that support objectification.

ORM 2 allows these cases, subject to modeling guidelines.

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AIRPORTLEG

INSTANCEDEPARTS

DepTime

N1

Usually, objectifying an n:1 association is just bad modeling, e.g. consider this Elmasri-Navathe ER example1:

It’s simpler to remodel the departure timeas an attribute of just LegInstance.

1 Example from Elmasri, R. & Navathe, S. 1989, Fundamentals of Database Systems, Benjamin/Cummings Publishing, Figure 3.18, p. 63.

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GovtHead(Name)

Country(Code)was born in

“Birth”

Bill Clinton US George W. Bush US John Howard AU

Birth

GovtHead(Name)

Country(Code)

has /is of

<< is in

was born in

To support thiskind of examplein ORM 2(whether or notit is the best way to model)

we interpretthe schema thus:

The 1:1 nature of the left-hand link fact type avoids denormalization on Rmapping.

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Birth

GovtHead(Name)

Country(Code)

was born in

Bill Clinton US George W. Bush US John Howard AU

has /is of is in

Bill Clinton b1 George W. Bush b2 John Howard b3 Helen Clark b4

b1 US b2 US b3 AU

For objectification, mandatory constraints are needed on all link rolesof the objectified type.e.g. if we remove a mandatory role constraint as shown below, Birth is no longer an objectification of GovtHead was born in Country.

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The main case where it makes sense to objectify associationswith non-spanning uniqueness constraints, is when the UC(s) mayevolve over time (e.g. from non-spanning to spanning)and we wish to minimize the impact of such changes to the model.

A set of modeling guidelines, which also covers other cases is presented on the next slide.

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Modeling heuristic.1

A fact type may be objectified only if:

(a) it has only a spanning uniqueness constraint; or

(b) its uniqueness constraint pattern is likely to evolve over time, e.g. from n:1 to m:n, or m:n:1 to m:n:p; or

(c) it has at least two uniqueness constraints spanning n-1 roles (n > 1), and there is no obvious choice as to which of the n-1 role uniqueness constraints is the best basis for a smaller objectification based on a spanning uniqueness constraint; or

(d) the objectification significantly improves the display of semantic affinity between fact types attached to the objectified type.

1 For further discussion, see Halpin, T. 2003, ’Uniqueness Constraints on Objectified Associations’, Journal of Conceptual Modeling, October 2003. Online at: http://www.orm.net/pdf/JCM2003Oct.pdf.

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Propositional Nominalization and Communication Acts

The Business Rules Team submission to the OMG RFP onBusiness Semantics for Business Rules includes business rules thatmay be treated directly as cases of propositional nominalization, e.g.

If a waiter earns an amount of money as a tip from serving a meal, the waiter must report that fact.

Rather than introducing a second kind of objectification into ORM 2to deal directly with propositional nominalization, we recommend recasting such cases in terms ofcircumstantial nominalization (e.g. as shown on the next slide).

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If a waiter earns an amount of money as a tip from serving a meal, the waiter must report that fact.

Waiter(EmpNr)

Meal(Nr)served

“Service !”

earned a tip of

MoneyAmount(USD)

… for serving … reported a tip of ...

2.1 2.2 2.3

1.1 1.2

1.3

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As regards modeling of communication acts, when it is of interest to model these acts, they are best modeled directly like any other business domain objects. e.g. in a genealogy model we might be interested in not just descriptions of states of affairs, but assertion acts made by researchers about states of affairs. Such a model might include fact types such as:

AssertionAct reported Proposition;

AssertionAct was made by Researcher with ConfidenceLevel; etc.

These comments relate to the information model only. For modeling communication processes, the information model should be supplemented by other kinds of model(e.g. interaction or workflow models) that provide a more intuitive and direct way of understandingessential business processes/services.

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Conclusion

For information modeling, objectification may be restricted tocircumstantial nominalization, where the nominalized object is a state of affairs (event, activity …) rather than a proposition.

Objectification of facts (unary, binary, or longer)may then be interpreted in terms of entities whose reference schemesare constrained by equality constraintsinvolving reference projections from linking predicates.

Objectification of facts with non-spanning uniqueness constraintsshould be permitted, but subject to proposed modeling guidelines.

Communication acts may be included as domain entities in informationmodels, but some communication aspects are best specified withother kinds of model (e.g. interaction or workflow diagrams).

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www.orm.net -- my ORM websitewww.brcommunity.com/ -- Business Rules Journal: article series

on Verbalizing Business Ruleswww.inConcept.com -- Journal of Conceptual Modeling, …www.ORMcentral.com -- ORM tool COM API details, …www.objectrolemodeling.com/ -- orthogonal toolbox, …www.omg.org/uml -- UML specification

Halpin, T. A. 2001, Information Modeling and Relational Database

Design, Morgan Kaufmann.Halpin, T. A. et al. 2003, Database Modeling with Microsoft Visio

for Enterprise Architects, Morgan Kaufmann.

Further resources