Pal gov.tutorial1.session7 1.schema equivalence and optimization
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Here are the key points about predicate specialization and generalization: - Predicate specialization replaces a general predicate with more specific predicates when the general predicate can be thought of as covering specific cases. - Predicate generalization replaces multiple specific predicates with a single more general predicate, while preserving the original distinctions, such as through subtypes. - Specialization adds detail, while generalization reduces detail in exchange for a more concise representation. Both aim to transform a schema into a logically equivalent but structurally different form.
Pal gov.tutorial1.session7 1.schema equivalence and optimization
- 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 2
- 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. PalGov © 2011 3
- 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 PalGov © 2011 4
- 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. PalGov © 2011 5
- 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 PalGov © 2011 6
- 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. PalGov © 2011 7
- 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 PalGov © 2011 8
- 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. PalGov © 2011 9
- 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 m1, and each Si corresponds to R where B = bi Theory: R may be specialized into S1..Sn by absorbing B. PalGov © 2011 10
- 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. PalGov © 2011 11
- 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 m1, 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. PalGov © 2011 12
- 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. PalGov © 2011 13
- 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. PalGov © 2011 15
- 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. PalGov © 2011 16
- 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). PalGov © 2011 17
- 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. PalGov © 2011 18
- 19. References 1. Information Modeling and Relational Databases: From Conceptual Analysis to Logical Design, Terry Halpin (ISBN 1- 55860-672-6) – Chapter 12. PalGov © 2011 19