On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages

Computing as a discipline is maturing rapidly. However, with maturity often comes a plethora of subdisciplines, which, as time progresses, can become isolationist. The subdisciplines of modelling, metamodelling, ontologies and modelling languages within software engineering e.g. have, to some degree, evolved separately and without any underpinning formalisms. Introducing set theory as a consistent underlying formalism, Brian Henderson-Sellers shows how a coherent framework can be developed that clearly links these four, previously separate, areas of software engineering. In particular, he shows how the incorporation of a foundational ontology can be beneficial in resolving a number of controversial issues in conceptual modelling, especially with regard to the perceived differences between linguistic metamodelling and ontological metamodelling. An explicit consideration of domain-specific modelling languages is also included in his mathematical analysis of models, metamodels, ontologies and modelling languages. This encompassing and detailed presentation of the state-of-the-art in modelling approaches mainly aims at researchers in academia and industry. They will find the principled discussion of the various subdisciplines extremely useful, and they may exploit the unifying approach as a starting point for future research.

[1]  Steven Kelly,et al.  Worst Practices for Domain- Specific Modeling domain-sp ec ific m o d eling , 2009 .

[2]  Peter Höfferer,et al.  Achieving Business Process Model Interoperability Using Metamodels and Ontologies , 2007, ECIS.

[3]  Gerd Wagner,et al.  An Ontologically Well-Founded Profile for UML Conceptual Models , 2004, CAiSE.

[4]  Ed Seidewitz,et al.  What Models Mean , 2003, IEEE Softw..

[5]  Jeannette M. Wing,et al.  A behavioral notion of subtyping , 1994, TOPL.

[6]  Mark A. Musen,et al.  Ontology versioning in an ontology management framework , 2004, IEEE Intelligent Systems.

[7]  Ferdinand de Saussure.  Course in General Linguistics , 1916 .

[8]  John F. Sowa,et al.  Ontology, Metadata, and Semiotics , 2000, ICCS.

[9]  Ron Weber,et al.  On the ontological expressiveness of information systems analysis and design grammars , 1993, Inf. Syst. J..

[10]  Alan L. Rector,et al.  Frames and OWL Side by Side , 2006 .

[11]  H. Kaiya,et al.  On Relationships among Models , Meta Models and Ontologies , 2006 .

[12]  Oscar Pastor,et al.  An Ontological-Based Approach to Analyze Software Production Methods , 2008, UNISCON.

[13]  Bernhard Rumpe,et al.  Meaningful modeling: what's the semantics of "semantics"? , 2004, Computer.

[14]  Terry Halpin,et al.  Higher-Order Types and Information Modeling , 2005 .

[15]  Simon K. Milton,et al.  Using a Common-Sense Realistic Ontology: Making Data Models Better Map the World , 2005 .

[16]  Michael Jackson,et al.  Some Basic Tenets of Description , 2002, Software and Systems Modeling.

[17]  Jean Bézivin,et al.  KM3: A DSL for Metamodel Specification , 2006, FMOODS.

[18]  Brian Henderson-Sellers,et al.  Bridging metamodels and ontologies in software engineering , 2011, J. Syst. Softw..

[19]  Bran Selic,et al.  The Pragmatics of Model-Driven Development , 2003, IEEE Softw..

[20]  B. L. Whorf.  The Relation of Habitual Thought and Behavior to Language , 1997 .

[21]  Ron Weber,et al.  An Ontological Model of an Information System , 1990, IEEE Trans. Software Eng..

[22]  C. K. Ogden,et al.  The Meaning of Meaning , 1923 .

[23]  C. Maria Keet.  A taxonomy of types of granularity , 2006, 2006 IEEE International Conference on Granular Computing.

[24]  Jeffrey G. Gray,et al.  Using Ontologies in the Domain Analysis of Domain-Specific Languages , 2009, TWOMDE@MoDELS.

[25]  Timothy W. Finin,et al.  Enabling Technology for Knowledge Sharing , 1991, AI Mag..

[26]  George Lakoff,et al.  Women, Fire, and Dangerous Things , 1987 .

[27]  Giancarlo Guizzardi,et al.  Towards Ontological Foundations for Agent Modelling Concepts Using the Unified Fundational Ontology (UFO) , 2004, AOIS.

[28]  Brian Henderson-Sellers,et al.  The rationale of powertype-based metamodelling to underpin software development methodologies , 2005 .

[29]  James Odell,et al.  Power Types , 1994, J. Object Oriented Program..

[30]  Boris Motik,et al.  Bridging the gap between OWL and relational databases , 2007, WWW '07.

[31]  Daniel L. Moody,et al.  The “Physics” of Notations: Toward a Scientific Basis for Constructing Visual Notations in Software Engineering , 2009, IEEE Transactions on Software Engineering.

[32]  Brian Henderson-Sellers,et al.  Random Thoughts on Multi-level Conceptual Modelling , 2008, The Evolution of Conceptual Modeling.

[33]  Brian Henderson-Sellers,et al.  Uses and abuses of the stereotype mechanism in UML 1.x and 2.0 , 2006, MoDELS'06.

[34]  Terry A. Halpin,et al.  Information modeling and relational databases (2. ed.) , 2008 .

[35]  Thomas Kühne.  Contrasting Classification with Generalisation , 2009, APCCM.

[36]  Thomas Kühne,et al.  Matters of (Meta-) Modeling , 2006, Software & Systems Modeling.

[37]  Brian Henderson-Sellers,et al.  Connecting Powertypes and Stereotypes , 2005, J. Object Technol..

[38]  Stephen Ullmann,et al.  Semantics: An Introduction to the Science of Meaning , 1962 .

[39]  Stijn Hoppenbrouwers,et al.  A Fundamental View on the Process of Conceptual Modeling , 2005, ER.

[40]  Brian Henderson-Sellers,et al.  An Ontological Evaluation of the OML Metamodel , 2000, ISCO.

[41]  Giancarlo Guizzardi,et al.  Towards an Ontological Account of Agent-Oriented Goals , 2007, SELMAS.

[42]  Brian Henderson-Sellers,et al.  Granularity in Conceptual Modelling: Application to Metamodels , 2010, ER.

[43]  Brian Henderson-Sellers,et al.  Towards the Use of Granularity Theory for Determining the Size of Atomic Method Fragments for Use in Situational Method Engineering , 2011, ME.

[44]  Alfons Laarman,et al.  Ontological Metamodeling with Explicit Instantiation , 2009, SLE.

[45]  Steffen Schulze-Kremer,et al.  The Ontology of the Gene Ontology , 2003, AMIA.

[46]  Jochen Ludewig,et al.  Models in software engineering - an introduction , 2004, Informatik Forschung und Entwicklung.

[47]  Barbara Liskov,et al.  Data Abstraction and Hierarchy , 1987 .

[48]  Wolfgang Hesse,et al.  More matters on (meta-)modelling: remarks on Thomas Kühne’s “matters” , 2006, Software & Systems Modeling.

[49]  Ron Weber,et al.  An Ontological Analysis of some Fundamental Information Systems Concepts , 1988, ICIS.

[50]  Yair Wand,et al.  Ontology as a foundation for meta-modelling and method engineering , 1996, Inf. Softw. Technol..

[51]  Luís Ferreira Pires,et al.  An ontology-based approach for evaluating the domain appropriateness and comprehensibility appropriateness of modeling languages , 2005, MoDELS'05.

[52]  Ron Weber,et al.  On the deep structure of information systems , 1995, Inf. Syst. J..

[53]  Roland H. Kaschek,et al.  A little theory of abstraction , 2004, Modellierung.

[54]  Brian Henderson-Sellers,et al.  Ontological Evaluation of the UML Using the Bunge–Wand–Weber Model , 2002, Software and Systems Modeling.

[55]  Stijn Hoppenbrouwers,et al.  Focused Conceptualisation: Framing Questioning and Answering in Model-Oriented Dialogue Games , 2010, PoEM.

[56]  Thomas Kühne.  Clarifying matters of (meta-) modeling: an author’s reply , 2006, Software & Systems Modeling.

[57]  Inge van de Weerd,et al.  Exploring Intuitive Modelling Behaviour , 2010, BMMDS/EMMSAD.

[58]  Dimitris Karagiannis,et al.  Metamodelling Platforms , 2002, EC-Web.

[59]  Stijn Hoppenbrouwers,et al.  Formal Modelling as a Grounded Conversation , 2005 .

[60]  Michael Jackson.  Some Notes on Models and Modelling , 2009, Conceptual Modeling: Foundations and Applications.

[61]  Brian Henderson-Sellers,et al.  Open Modeling with UML , 2000 .

[62]  José Ramón Hilera,et al.  Using Ontologies in Software Engineering and Technology , 2006, Ontologies for Software Engineering and Software Technology.

[63]  Scott A. Whitmire,et al.  Object-Oriented Design Measurement , 1997 .

[64]  Yanchun Zhang,et al.  An analytical evaluation of NIAM'S grammar for conceptual schema diagrams , 1996, Inf. Syst. J..

[65]  Stephen J. Mellor,et al.  MDA Distilled Principles Of Model-Driven Architecture , 2004 .

[66]  Marian H. Nodine,et al.  Facilitating Open Communication in Agent Systems: The InfoSleuth Infrastructure , 1997, ATAL.

[67]  Ivar Jacobson,et al.  The unified modeling language reference manual , 2010 .

[68]  C. Maria Keet.  Enhancing Comprehension of Ontologies and Conceptual Models Through Abstractions , 2007, AI*IA.

[69]  Giancarlo Guizzardi,et al.  Representing and reasoning over a taxonomy of part-whole relations , 2008, Appl. Ontology.

[70]  Steffen Staab,et al.  OntoDSL: An Ontology-Based Framework for Domain-Specific Languages , 2009, MoDELS.

[71]  Inderjeet Mani,et al.  A Theory of Granularity and its Application to Problems of Polysemy and Underspecification of Meaning , 1998, KR.

[72]  Christopher Menzel,et al.  Reference Ontologies - Application Ontologies: Either/Or or Both/And? , 2003, KI Workshop on Reference Ontologies and Application Ontologies.