SlideShare uma empresa Scribd logo
1 de 6
1Jarrar © 2015
(Chapter 6)
Quick Mathematical Background
for Conceptual Modeling
Reference:
Mustafa Jarrar: Lecture Notes on Mathematics for Conceptual Modeling
Birzeit University, Palestine, 2015
Mustafa Jarrar
Birzeit University, Palestine
mjarrar@birzeit.edu
www.jarrar.info
2Jarrar © 2015
Watch this lecture and download the slides from
http://jarrar-courses.blogspot.com/2015/01/dataandbusinessprocessmodelling.html
Some diagrams in this lecture are based on [1]
Keywords: Mandatory, Role Mandatory, Disjunctive Mandatory, Cardinality, Business Rules,‫اجباري‬ ،‫ضرورة‬
Slides And Videos - Download, Watch, Interact
3Jarrar © 2015
Mathematical Background
Hypothetical Euler diagrams for set comparisons.
4Jarrar © 2015
Venn diagrams for three set-forming operations.
Mathematical Background
5Jarrar © 2015
Mathematical Background
Venn diagrams for (a) A is a proper subset of B and (b)
four sets.
6Jarrar © 2015
References
1. Terry Halpin, Tony Morgan: Information Modeling and Relational Databases, Second Edition. 2nd
Edition. The Morgan Kaufmann Series in Data Management Systems. ISBN: 0123735688
2. Mustafa Jarrar and Stijn Heymans: Towards Pattern-Based Reasoning For Friendly Ontology
Debugging. Journal of Artificial Intelligence Tools. Volume 17. No.4. World Scientific Publishing. Aug
2008.
3. Mustafa Jarrar: Mapping ORM Into The SHOIN/OWL Description Logic- Towards A Methodological
And Expressive Graphical Notation For Ontology Engineering. In OTM 2007 workshops:
Proceedings of the International Workshop on Object-Role Modeling (ORM'07). Pages (729-741), LNCS
4805, Springer. ISBN: 9783540768890. Portogal. November, 2007
4. Mustafa Jarrar: Towards Automated Reasoning On ORM Schemes. -Mapping ORM Into The
DLR_idf Description Logic. In proceedings of the 26th International Conference on Conceptual
Modeling (ER 2007). Pages (181-197). LNCS 4801, Springer. Auckland, New Zealand. ISBN
9783540755623. November 2007
5. Mustafa Jarrar and Stijn Heymans: Unsatisfiability Reasoning In ORM Conceptual Schemes. In
Current Trends in Database Technology - EDBT 2006: Proceeding of the IFIP-2.6 International
Conference on Semantics of a Networked. Pages (517-534). LNCS 4254, Springer. Munich, Germany.
ISBN: 3540467882. March 2006.
6. Mustafa Jarrar, Maria Keet, and Paolo Dongilli: Multilingual Verbalization Of ORM Conceptual Models
And Axiomatized Ontologies. Technical eport. STARLab, Vrije Universiteit Brussel, Feb 2006.
7. Mustafa Jarrar: Modularization And Automatic Composition Of Object-Role Modeling (ORM)
Schemes. OTM 2005 Workshops: Proceedings of the Object-Role Modeling (ORM'05). Pages (613-
625). LNCS 3762, Springer. Larnaca, Cyprus. ISBN: 3540297391. November 2005.

Mais conteúdo relacionado

Mais de Mustafa Jarrar

Introduction to Business Process Management
Introduction to Business Process ManagementIntroduction to Business Process Management
Introduction to Business Process ManagementMustafa Jarrar
 
Customer Complaint Ontology
Customer Complaint Ontology Customer Complaint Ontology
Customer Complaint Ontology Mustafa Jarrar
 
Subset, Equality, and Exclusion Rules
Subset, Equality, and Exclusion RulesSubset, Equality, and Exclusion Rules
Subset, Equality, and Exclusion RulesMustafa Jarrar
 
Schema Modularization in ORM
Schema Modularization in ORMSchema Modularization in ORM
Schema Modularization in ORMMustafa Jarrar
 
On Computer Science Trends and Priorities in Palestine
On Computer Science Trends and Priorities in PalestineOn Computer Science Trends and Priorities in Palestine
On Computer Science Trends and Priorities in PalestineMustafa Jarrar
 
Lessons from Class Recording & Publishing of Eight Online Courses
Lessons from Class Recording & Publishing of Eight Online CoursesLessons from Class Recording & Publishing of Eight Online Courses
Lessons from Class Recording & Publishing of Eight Online CoursesMustafa Jarrar
 
Presentation curras paper-emnlp2014-final
Presentation curras paper-emnlp2014-finalPresentation curras paper-emnlp2014-final
Presentation curras paper-emnlp2014-finalMustafa Jarrar
 
Jarrar: Future Internet in Horizon 2020 Calls
Jarrar: Future Internet in Horizon 2020 CallsJarrar: Future Internet in Horizon 2020 Calls
Jarrar: Future Internet in Horizon 2020 CallsMustafa Jarrar
 
Habash: Arabic Natural Language Processing
Habash: Arabic Natural Language ProcessingHabash: Arabic Natural Language Processing
Habash: Arabic Natural Language ProcessingMustafa Jarrar
 
Adnan: Introduction to Natural Language Processing
Adnan: Introduction to Natural Language Processing Adnan: Introduction to Natural Language Processing
Adnan: Introduction to Natural Language Processing Mustafa Jarrar
 
Riestra: How to Design and engineer Competitive Horizon 2020 Proposals
Riestra: How to Design and engineer Competitive Horizon 2020 ProposalsRiestra: How to Design and engineer Competitive Horizon 2020 Proposals
Riestra: How to Design and engineer Competitive Horizon 2020 ProposalsMustafa Jarrar
 
Bouquet: SIERA Workshop on The Pillars of Horizon2020
Bouquet: SIERA Workshop on The Pillars of Horizon2020Bouquet: SIERA Workshop on The Pillars of Horizon2020
Bouquet: SIERA Workshop on The Pillars of Horizon2020Mustafa Jarrar
 
Jarrar: Sparql Project
Jarrar: Sparql ProjectJarrar: Sparql Project
Jarrar: Sparql ProjectMustafa Jarrar
 
Jarrar: Logical Foundation of Ontology Engineering
Jarrar: Logical Foundation of Ontology EngineeringJarrar: Logical Foundation of Ontology Engineering
Jarrar: Logical Foundation of Ontology EngineeringMustafa Jarrar
 
Jarrar: Stepwise Methodologies for Developing Ontologies
Jarrar: Stepwise Methodologies for Developing OntologiesJarrar: Stepwise Methodologies for Developing Ontologies
Jarrar: Stepwise Methodologies for Developing OntologiesMustafa Jarrar
 
Jarrar: Ontology Modeling using OntoClean Methodology
Jarrar: Ontology Modeling using OntoClean MethodologyJarrar: Ontology Modeling using OntoClean Methodology
Jarrar: Ontology Modeling using OntoClean MethodologyMustafa Jarrar
 
Jarrar: Informed Search
Jarrar: Informed Search  Jarrar: Informed Search
Jarrar: Informed Search Mustafa Jarrar
 
Jarrar: Un-informed Search
Jarrar: Un-informed SearchJarrar: Un-informed Search
Jarrar: Un-informed SearchMustafa Jarrar
 
Introduction to Artificial Intelligence
Introduction to Artificial Intelligence Introduction to Artificial Intelligence
Introduction to Artificial Intelligence Mustafa Jarrar
 

Mais de Mustafa Jarrar (20)

Introduction to Business Process Management
Introduction to Business Process ManagementIntroduction to Business Process Management
Introduction to Business Process Management
 
Customer Complaint Ontology
Customer Complaint Ontology Customer Complaint Ontology
Customer Complaint Ontology
 
Subset, Equality, and Exclusion Rules
Subset, Equality, and Exclusion RulesSubset, Equality, and Exclusion Rules
Subset, Equality, and Exclusion Rules
 
Schema Modularization in ORM
Schema Modularization in ORMSchema Modularization in ORM
Schema Modularization in ORM
 
On Computer Science Trends and Priorities in Palestine
On Computer Science Trends and Priorities in PalestineOn Computer Science Trends and Priorities in Palestine
On Computer Science Trends and Priorities in Palestine
 
Lessons from Class Recording & Publishing of Eight Online Courses
Lessons from Class Recording & Publishing of Eight Online CoursesLessons from Class Recording & Publishing of Eight Online Courses
Lessons from Class Recording & Publishing of Eight Online Courses
 
Presentation curras paper-emnlp2014-final
Presentation curras paper-emnlp2014-finalPresentation curras paper-emnlp2014-final
Presentation curras paper-emnlp2014-final
 
Jarrar: Future Internet in Horizon 2020 Calls
Jarrar: Future Internet in Horizon 2020 CallsJarrar: Future Internet in Horizon 2020 Calls
Jarrar: Future Internet in Horizon 2020 Calls
 
Habash: Arabic Natural Language Processing
Habash: Arabic Natural Language ProcessingHabash: Arabic Natural Language Processing
Habash: Arabic Natural Language Processing
 
Adnan: Introduction to Natural Language Processing
Adnan: Introduction to Natural Language Processing Adnan: Introduction to Natural Language Processing
Adnan: Introduction to Natural Language Processing
 
Riestra: How to Design and engineer Competitive Horizon 2020 Proposals
Riestra: How to Design and engineer Competitive Horizon 2020 ProposalsRiestra: How to Design and engineer Competitive Horizon 2020 Proposals
Riestra: How to Design and engineer Competitive Horizon 2020 Proposals
 
Bouquet: SIERA Workshop on The Pillars of Horizon2020
Bouquet: SIERA Workshop on The Pillars of Horizon2020Bouquet: SIERA Workshop on The Pillars of Horizon2020
Bouquet: SIERA Workshop on The Pillars of Horizon2020
 
Jarrar: Sparql Project
Jarrar: Sparql ProjectJarrar: Sparql Project
Jarrar: Sparql Project
 
Jarrar: Logical Foundation of Ontology Engineering
Jarrar: Logical Foundation of Ontology EngineeringJarrar: Logical Foundation of Ontology Engineering
Jarrar: Logical Foundation of Ontology Engineering
 
Jarrar: Stepwise Methodologies for Developing Ontologies
Jarrar: Stepwise Methodologies for Developing OntologiesJarrar: Stepwise Methodologies for Developing Ontologies
Jarrar: Stepwise Methodologies for Developing Ontologies
 
Jarrar: Ontology Modeling using OntoClean Methodology
Jarrar: Ontology Modeling using OntoClean MethodologyJarrar: Ontology Modeling using OntoClean Methodology
Jarrar: Ontology Modeling using OntoClean Methodology
 
Jarrar: Games
Jarrar: GamesJarrar: Games
Jarrar: Games
 
Jarrar: Informed Search
Jarrar: Informed Search  Jarrar: Informed Search
Jarrar: Informed Search
 
Jarrar: Un-informed Search
Jarrar: Un-informed SearchJarrar: Un-informed Search
Jarrar: Un-informed Search
 
Introduction to Artificial Intelligence
Introduction to Artificial Intelligence Introduction to Artificial Intelligence
Introduction to Artificial Intelligence
 

Último

AWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of TerraformAWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of TerraformAndrey Devyatkin
 
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)Zilliz
 
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemkeProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemkeProduct Anonymous
 
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...apidays
 
Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​Bhuvaneswari Subramani
 
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...apidays
 
How to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected WorkerHow to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected WorkerThousandEyes
 
Mcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot Model
Mcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot ModelMcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot Model
Mcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot ModelDeepika Singh
 
[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdfSandro Moreira
 
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024Victor Rentea
 
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, AdobeApidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobeapidays
 
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers:  A Deep Dive into Serverless Spatial Data and FMECloud Frontiers:  A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FMESafe Software
 
ICT role in 21st century education and its challenges
ICT role in 21st century education and its challengesICT role in 21st century education and its challenges
ICT role in 21st century education and its challengesrafiqahmad00786416
 
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...Jeffrey Haguewood
 
Boost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdfBoost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdfsudhanshuwaghmare1
 
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc Webinar - Unlock the Power of AI-Driven Data DiscoveryTrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc Webinar - Unlock the Power of AI-Driven Data DiscoveryTrustArc
 
MINDCTI Revenue Release Quarter One 2024
MINDCTI Revenue Release Quarter One 2024MINDCTI Revenue Release Quarter One 2024
MINDCTI Revenue Release Quarter One 2024MIND CTI
 
DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 AmsterdamDEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 AmsterdamUiPathCommunity
 

Último (20)

AWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of TerraformAWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of Terraform
 
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)
 
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemkeProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
 
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
 
Understanding the FAA Part 107 License ..
Understanding the FAA Part 107 License ..Understanding the FAA Part 107 License ..
Understanding the FAA Part 107 License ..
 
Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​
 
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
 
How to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected WorkerHow to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected Worker
 
Mcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot Model
Mcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot ModelMcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot Model
Mcleodganj Call Girls 🥰 8617370543 Service Offer VIP Hot Model
 
[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf
 
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
 
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, AdobeApidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
 
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers:  A Deep Dive into Serverless Spatial Data and FMECloud Frontiers:  A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
 
ICT role in 21st century education and its challenges
ICT role in 21st century education and its challengesICT role in 21st century education and its challenges
ICT role in 21st century education and its challenges
 
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
 
Boost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdfBoost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdf
 
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
 
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc Webinar - Unlock the Power of AI-Driven Data DiscoveryTrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
 
MINDCTI Revenue Release Quarter One 2024
MINDCTI Revenue Release Quarter One 2024MINDCTI Revenue Release Quarter One 2024
MINDCTI Revenue Release Quarter One 2024
 
DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 AmsterdamDEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
 

Jarrar.lecture notes.mathbachgroundforconceptualmodeling

  • 1. 1Jarrar © 2015 (Chapter 6) Quick Mathematical Background for Conceptual Modeling Reference: Mustafa Jarrar: Lecture Notes on Mathematics for Conceptual Modeling Birzeit University, Palestine, 2015 Mustafa Jarrar Birzeit University, Palestine mjarrar@birzeit.edu www.jarrar.info
  • 2. 2Jarrar © 2015 Watch this lecture and download the slides from http://jarrar-courses.blogspot.com/2015/01/dataandbusinessprocessmodelling.html Some diagrams in this lecture are based on [1] Keywords: Mandatory, Role Mandatory, Disjunctive Mandatory, Cardinality, Business Rules,‫اجباري‬ ،‫ضرورة‬ Slides And Videos - Download, Watch, Interact
  • 3. 3Jarrar © 2015 Mathematical Background Hypothetical Euler diagrams for set comparisons.
  • 4. 4Jarrar © 2015 Venn diagrams for three set-forming operations. Mathematical Background
  • 5. 5Jarrar © 2015 Mathematical Background Venn diagrams for (a) A is a proper subset of B and (b) four sets.
  • 6. 6Jarrar © 2015 References 1. Terry Halpin, Tony Morgan: Information Modeling and Relational Databases, Second Edition. 2nd Edition. The Morgan Kaufmann Series in Data Management Systems. ISBN: 0123735688 2. Mustafa Jarrar and Stijn Heymans: Towards Pattern-Based Reasoning For Friendly Ontology Debugging. Journal of Artificial Intelligence Tools. Volume 17. No.4. World Scientific Publishing. Aug 2008. 3. Mustafa Jarrar: Mapping ORM Into The SHOIN/OWL Description Logic- Towards A Methodological And Expressive Graphical Notation For Ontology Engineering. In OTM 2007 workshops: Proceedings of the International Workshop on Object-Role Modeling (ORM'07). Pages (729-741), LNCS 4805, Springer. ISBN: 9783540768890. Portogal. November, 2007 4. Mustafa Jarrar: Towards Automated Reasoning On ORM Schemes. -Mapping ORM Into The DLR_idf Description Logic. In proceedings of the 26th International Conference on Conceptual Modeling (ER 2007). Pages (181-197). LNCS 4801, Springer. Auckland, New Zealand. ISBN 9783540755623. November 2007 5. Mustafa Jarrar and Stijn Heymans: Unsatisfiability Reasoning In ORM Conceptual Schemes. In Current Trends in Database Technology - EDBT 2006: Proceeding of the IFIP-2.6 International Conference on Semantics of a Networked. Pages (517-534). LNCS 4254, Springer. Munich, Germany. ISBN: 3540467882. March 2006. 6. Mustafa Jarrar, Maria Keet, and Paolo Dongilli: Multilingual Verbalization Of ORM Conceptual Models And Axiomatized Ontologies. Technical eport. STARLab, Vrije Universiteit Brussel, Feb 2006. 7. Mustafa Jarrar: Modularization And Automatic Composition Of Object-Role Modeling (ORM) Schemes. OTM 2005 Workshops: Proceedings of the Object-Role Modeling (ORM'05). Pages (613- 625). LNCS 3762, Springer. Larnaca, Cyprus. ISBN: 3540297391. November 2005.