1. ‫أكاديمية الحكومة اإللكترونية الفلسطينية‬
The Palestinian eGovernment Academy
www.egovacademy.ps
Tutorial 1: Data and Business Process Modeling
Session 7.1
Schema Equivalence and Optimization
Prof. Mustafa Jarrar
Sina Institute, University of Birzeit
mjarrar@birzeit.edu
www.jarrar.info
Reviewed by
Prof. Marco Ronchetti, Trento University, Italy
PalGov © 2011 1

2. About
This tutorial is part of the PalGov project, funded by the TEMPUS IV program of the
Commission of the European Communities, grant agreement 511159-TEMPUS-1-
2010-1-PS-TEMPUS-JPHES. The project website: www.egovacademy.ps
Project Consortium:
Birzeit University, Palestine
University of Trento, Italy
(Coordinator )
Palestine Polytechnic University, Palestine Vrije Universiteit Brussel, Belgium
Palestine Technical University, Palestine
Université de Savoie, France
Ministry of Telecom and IT, Palestine
University of Namur, Belgium
Ministry of Interior, Palestine
TrueTrust, UK
Ministry of Local Government, Palestine
Coordinator:
Dr. Mustafa Jarrar
Birzeit University, P.O.Box 14- Birzeit, Palestine
Telfax:+972 2 2982935 mjarrar@birzeit.eduPalGov © 2011
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3. © Copyright Notes
Everyone is encouraged to use this material, or part of it, but should properly
cite the project (logo and website), and the author of that part.
No part of this tutorial may be reproduced or modified in any form or by any
means, without prior written permission from the project, who have the full
copyrights on the material.
Attribution-NonCommercial-ShareAlike
CC-BY-NC-SA
This license lets others remix, tweak, and build upon your work non-
commercially, as long as they credit you and license their new creations
under the identical terms.
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4. Tutorial Map
Intended Learning Objectives
Topic Time
Module 1 (Conceptual Date Modeling)
Module I: Conceptual Data Modeling
A: Knowledge and Understanding
11a1: Demonstrate knowledge of conceptual modeling notations and concepts Session 0: Outline and Introduction
11a2: Demonstrate knowledge of Object Role Modeling (ORM) methodology. Session 1.1: Information Modeling 1
11a3: Explain and demonstrate the concepts of data integrity & business rules Session 1.2: Conceptual Data Modeling using ORM 1
B: Intellectual Skills Session 1.3: Conceptual Analyses 1
11b1: Analyze application and domain requirements at the conceptual level, Session 2: Lab- Conceptual Analyses 3
and formalize it using ORM. Session 3.1: Uniqueness Rules 1.5
11b2: Analyze entity identity at the application and domain levels. Session 3.2: Mandatory Rules 1.5
11b4: Optimize, transform, and (re)engineer conceptual models. Session 4: Lab- Uniqueness & Mandatory Rules 3
11b5: Detect &resolve contradictions & implications at the conceptual level. Session 5: Subtypes and Other Rules 3
C: Professional and Practical Skills Session 6: Lab- Subtypes and Other Rules 3
11c1: Using ORM modeling tools (Conceptual Modeling Tools). Session 7.1: Schema Equivalence &Optimization 1.5
Module 2 (Business Process Modeling) Session 7.2: Rules Check &Schema Engineering 1.5
A: Knowledge and Understanding Session 8: Lab- National Student Registry 3
12a1: Demonstrate knowledge of business process modeling notations and concepts.
Module II: Business Process Modeling
12a2: Demonstrate knowledge of business process modeling and mapping.
12a3: Demonstrate understand of business process optimization and re-engineering. Session 9: BP Management and BPMN: An Overview 3
B: Intellectual Skills Session 10: Lab - BP Management 3
12b1: Identify business processes. Session 11: BPMN Fundamentals 3
12b2: Model and map business processes. Session 12: Lab - BPMN Fundamentals 3
12b3: Optimize and re-engineer business processes. Session 13: Modeling with BPMN 3
C: Professional and Practical Skills Session 14: Lab- Modeling with BPMN 3
12c1: Using business process modeling tools, such as MS Visio. Session 15: BP Management & Reengineering 3
Session 16: Lab- BP Management & Reengineering 3
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5. Session ILOs
After completing this session students will be able to:
11a3: Explain and demonstrate the concepts of data integrity and
business rules.
11b5: Detect and resolve contradictions and implications at the
conceptual level.
11b4: Optimize, transform, and (re)engineer conceptual models.
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6. Conceptual Schema Design Steps
1. From examples to elementary facts
2. Draw fact types and apply population check
3. Combine entity types
4. Add uniqueness constraints
5. Add mandatory constraints
6. Add set, subtype, & frequency constraints
7. Final checks, & schema engineering issues
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7. Schema Equivalence and Optimization
• It is not surprising that people often come up with different ways (i.e.,
deferent conceptual models) of describing the same reality.
• Two conceptual schemas are equivalent if and only if whatever UoD
state or transition can be modeled in one can also be modeled in the
other.
• What is the difference between these two schemes:
 The act of reshaping two equivalent schemes like this is said to
be a conceptual schema transformation.
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8. Schema Equivalence and Optimization
• Skills of schema transformations helps us to see what different
design choices are possible.
• Moreover, if two independently developed schemas are to be either
fully or partly integrated, we often need to resolve the differences in
the ways that each schema models common UoD features.
• To do this, we need to know whether one representation can be
transformed into the other, and if so, how.
• Another use of conceptual schema transformations is to reshape the
original conceptual schema into one that maps directly to a more
efficient implementation, or to more conceptually elegant schema.
• This process is known as conceptual schema optimization.
There are two class of schema transformations:
Predicate Specialization, and Predicate Generalization
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9. Predicate Specialization and Generalization
If two or more predicates may be thought of as special cases of a more
general predicate, then we may replace them by the more general
predicate, so long as the original distinction can be preserved in some way.
We generalize smoking and drinking into indulging in a vice, where vice has
two specific cases. If we transform in the opposite direction, we specialize
indulging in a vice into two predicates, one for each case.
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10. Predicate Specialization and Generalization
If two or more predicates may be thought of as special cases of a more
general predicate, then we may replace them by the more general
predicate, so long as the original distinction can be preserved in some way.
?
Because there are exactly three kinds of medals, the ternary may be
specialized into three binaries, one for each medal kind,
Where m1, and each Si corresponds
to R where B = bi
Theory: R may be specialized into S1..Sn by absorbing B.
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11. Predicate Specialization and Generalization
The previous theorem always holds, but any constraint added to one of the
schemas must be translated into an equivalent, additional constraint on the
other schema.
Each Si corresponds to
R where B = bi
The UC on the left is equivalent to the UCs on the right.
 If a UC in R spans a combination of B’s role and other roles, a UC
spans the specialization of these other roles in S1,..,Sn, and conversely.
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12. Predicate Specialization and Generalization
?
The UC on the left is equivalent to the exclusion constraint on the right.
?
The UC on the left is equivalent to the exclusion constraint on the right.
Where m1, and each
Si corresponds to R
where B = bi
The UC on the left is equivalent to the exclusion constraint on the right.
If a UC spans all roles of R except for B’s role, then S1 .. Sn are mutually
exclusive, and conversely.
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13. Predicate Specialization and Generalization
?
if any medal results are recorded for a country, all three medal results (gold, silver,
and bronze) are required. To express, we add an equality constraint between the
medal winning roles played by Country.
 If R is a ternary with a UC spanning just B’s role and one other role, then
adding a frequency constraint of n to this other role is equivalent to adding an
equality constraint over the specialized versions of that role.
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14. Predicate Specialization and Generalization
The impact of adding mandatory role and frequency constraints.
?
Each S corresponds
to R where B = bi
 If A’s role (or role disjunction) in R is mandatory, then the disjunction of its
specialized roles is mandatory, and conversely (1 i  m).
 If R is a ternary with a UC spanning just B’s role and one other role, then adding a
mandatory role constraint and frequency constraint of n (the number of possible
values for B) to this other role is equivalent to making each specialized version of that
role mandatory. PalGov © 2011 14

15. Other Cases and Examples
?
Each car in the rally has two drivers (a main driver and a backup
driver), and each person drives exactly one car.
The drives predicate is specialized by absorbing Status.
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16. Other Cases and Examples
Each Si corresponds
to R where T is
restricted to B = bi
Theory: R may be specialized into S1..Sn by absorbing B.
 Corollary 1: If s roles are mandatory in the left-hand schema, the disjunction of s
roles in the right-hand schema is mandatory, and conversely.
 Corollary 2: If an external UC spans the roles of and in the left-hand schema, then a
UC applies to each of s roles in the right-hand schema, and conversely.
 Corollary 3: If s role in the left-hand schema is mandatory, then each of s roles in
the right-hand schema is mandatory, and conversely.
 Corollary 4: An equality constraint over s roles in the RHS is equivalent to a
frequency constraint of on s role in the left-hand schema; this constraint is
strengthened to if a UC exists on each of s roles in the right-hand schema.
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17. Other Cases and Examples
Can the predicate be specialized?
? ?
• Transforming from the original schema to one of those strengthens the
schema by adding information.
• Transforming in the opposite direction weakens the schema by losing
information.
 Any such transformations that add or lose information should be the result
of conscious decisions that are acceptable to the client (for which the
business domain is being modeled).
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18. Other Cases and Examples
Each Si corresponds to
one instance of R
Theory: The left-hand schema implies the right-hand schema.
Corollary 1:If an equality constraint applies over s roles in the left-hand schema, then
the frequency constraint in the right-hand schema is strengthened to , and conversely.
Corollary 2: Adding a UC to role in the right-hand schema is equivalent in the left-
hand schema to adding UCs to s roles (making the S 1:1) and strengthening the
exclusion constraint to an exclusion constraint over s roles.
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19. References
1. Information Modeling and Relational Databases: From
Conceptual Analysis to Logical Design, Terry Halpin (ISBN 1-
55860-672-6) – Chapter 12.
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