Compositionality: Ontology and Mereology of Domains

In this discursive paper we discuss compositionality of (i) simple entities, (ii) operations, (iii) events, and (iv) behaviours. These four concepts, (i)–(iv), together define a concept of entities. We view entities as “things” characterised by properties. We shall review some such properties. Mereology, the study of part-whole relations is then applied to a study of composite entities. We then speculate on compositionality of simple entities, operations, events and behaviours in the light of their mereologies. entities. We end the paper with some speculations on the role of Galois connections in the study of compositionality and domain mereology.

[1]  D. Millen,et al.  New Journal , 1967, Nature.

[2]  Anne Elisabeth Haxthausen,et al.  Casl - The Common Algebraic Specification Language: Semantics and Proof Theory , 2003, Comput. Artif. Intell..

[3]  Daniel Jackson,et al.  Software Abstractions - Logic, Language, and Analysis , 2006 .

[4]  Zohar Manna,et al.  Introduction to mathematical theory of computation , 1972 .

[5]  Timothy Williamson,et al.  Parts. A Study in Ontology , 1990 .

[6]  John McCarthy,et al.  Towards a Mathematical Science of Computation , 1962, IFIP Congress.

[7]  Barry Smith,et al.  SNAP and SPAN: Towards Dynamic Spatial Ontology , 2004, Spatial Cogn. Comput..

[8]  Thomas P. Sachse This ` paper is one of a series of research syntheses commissioned by the , 2007 .

[9]  Dines Bjørner,et al.  Software Engineering 3 - Domains, Requirements, and Software Design , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[10]  Jean-Raymond Abrial,et al.  The B-book - assigning programs to meanings , 1996 .

[11]  Michael J. Loux Metaphysics: A Contemporary Introduction , 1997 .

[12]  Martin C. Henson,et al.  Logics of Specification Languages (Monographs in Theoretical Computer Science. An EATCS Series) , 2007 .

[13]  Bobby Woolf,et al.  Null object , 1997 .

[14]  Andrew William Roscoe,et al.  The Theory and Practice of Concurrency , 1997 .

[15]  Dines Bjørner,et al.  Construction informatics - Issues in engineering, computer science and ontology , 2004 .

[16]  Anne Elisabeth Haxthausen,et al.  The Logic of the RAISE Specification Language , 2003, Comput. Artif. Intell..

[17]  Anne Elisabeth Haxthausen,et al.  The Raise Specification Language , 1992 .

[18]  Jonathan P. Bowen,et al.  Formal Methods: State of the Art and New Directions , 2009 .

[19]  Robert W. Taylor,et al.  Proceedings of the 1976 conference on Data : Abstraction, definition and structure , 1976 .

[20]  Dines Bjørner Software Engineering 1: Abstraction and Modelling (Texts in Theoretical Computer Science. An EATCS Series) , 2005 .

[21]  Dines Bjørner Software Engineering 2 - Specification of Systems and Languages , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[22]  Dines Bjørner Abstraction and modelling , 2006 .

[23]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[24]  Peter D. Mosses,et al.  CASL: the Common Algebraic Specification Language , 2002, Theor. Comput. Sci..

[25]  Wolfgang Reisig,et al.  The Expressive Power of Abstract-State Machines , 2003, Comput. Artif. Intell..

[26]  Dines Bjørner,et al.  Software Engineering, vol. 3: Domains, Requirements and Software Design , 2006 .

[27]  I. Mitchell,et al.  Proving Safety of a Railway Signalling System Incorporating Geographic Data , 1992 .

[28]  P. Simons Parts: A Study in Ontology , 1991 .

[29]  Bowman L. Clarke,et al.  A calculus of individuals based on "connection" , 1981, Notre Dame J. Formal Log..

[30]  Dines Bjørner,et al.  Software Engineering, vol 2: Specification of Systems and Languages , 2006 .

[31]  Dines Bjørner,et al.  Believable Software Management ∗ , 2007 .

[32]  M. Leng,et al.  Platonism and Anti-Platonism in Mathematics , 2001 .

[33]  Nelson Goodman,et al.  The calculus of individuals and its uses , 1940, Journal of Symbolic Logic.

[34]  C. Lejewski A note on Leśniewski's axiom system for the mereological notion of ingredient or element , 1983 .

[35]  Dave Roberts,et al.  Developing Software Using OVID , 1997, IEEE Softw..

[36]  Takeo Kanade,et al.  Unifying Theories of Programming , 2010, Lecture Notes in Computer Science.

[37]  Asger Eir Relating Domain Concepts Intensionally by Ordering Connections , 2007, Formal Methods and Hybrid Real-Time Systems.

[38]  Dines Bjørner Programming in the META-Language: A Tutorial , 1978, The Vienna Development Method: The Meta-Language.

[39]  Dines Bjørner The Vienna development method (VDM): Software specification & program synthesis , 1978, Mathematical Studies of Information Processing.

[40]  Dines Bjørner,et al.  The Vienna Development Method: The Meta-Language , 1978, Lecture Notes in Computer Science.

[41]  Steffen Staab,et al.  Handbook on Ontologies (International Handbooks on Information Systems) , 2004 .

[42]  Jim Woodcock,et al.  Theoretical Aspects of Computing - ICTAC 2007, 4th International Colloquium, Macau, China, September 26-28, 2007, Proceedings , 2007, ICTAC.

[43]  Leslie Lamport,et al.  Time, clocks, and the ordering of events in a distributed system , 1978, CACM.

[44]  Roberto Casati,et al.  Parts and Places: The Structures of Spatial Representation , 1999 .

[45]  Dines Bjørner,et al.  Triptych Process Model , 2010, Encyclopedia of Software Engineering.

[46]  Jim Woodcock,et al.  Formal Methods and Hybrid Real-Time Systems, Essays in Honor of Dines Bjørner and Chaochen Zhou on the Occasion of Their 70th Birthdays, Papers presented at a Symposium held in Macao, China, September 24-25, 2007 , 2007, Formal Methods and Hybrid Real-Time Systems.

[47]  Wolfgang Reisig Abstract State Machines for the Classroom , 2008 .

[48]  Dines Bjørner,et al.  Formal specification and software development , 1982 .

[49]  Dines Bjørner Specification of systems and languages , 2006 .

[50]  LamportLeslie Time, clocks, and the ordering of events in a distributed system , 1978 .

[51]  Dines Bjørner,et al.  Software Engineering, vol. 1: Abstraction and Modelling , 2006 .

[52]  Steffen Staab,et al.  International Handbooks on Information Systems , 2013 .

[53]  Douglas T. Ross,et al.  Toward foundations for the understanding of type , 1976, Conference on Data: Abstraction, Definition and Structure.

[54]  John Fitzgerald The Typed Logic of Partial Functions and the Vienna Development Method , 2006 .

[55]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[56]  Dines Bjørner,et al.  Logics of Specification Languages , 2007, Monographs in Theoretical Computer Science. An EATCS Series.

[57]  Kazuhiro Ogata,et al.  CafeOBJ: Logical Foundations and Methodologies , 2003, Comput. Artif. Intell..

[58]  J. Michael Spivey,et al.  The Z notation - a reference manual , 1992, Prentice Hall International Series in Computer Science.

[59]  S. Shapiro Philosophy of mathematics : structure and ontology , 1997 .

[60]  Dines Bjørner Software Abstraction Principles: Tutorial Examples of: An Operating System Command Language Specification, and a PL/I-like On-Condition Language Definition , 1978, The Vienna Development Method: The Meta-Language.

[61]  Jonathan P. Bowen,et al.  Z Logic and its Consequences , 2003, Comput. Artif. Intell..

[62]  Dines Bjørner,et al.  From Domain to Requirements , 2008, Concurrency, Graphs and Models.

[63]  Dines Bjørner Domain Theory: Practice and Theories A Discussion of Possible Research Topics , 2007, ICTAC.

[64]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[65]  John McCarthy,et al.  Mathematical Theory of Computation , 1991 .

[66]  J. Michael Spivey,et al.  Understanding Z : A specification language and its formal semantics , 1985, Cambridge tracts in theoretical computer science.

[67]  Răzvan Diaconescu A Methodological Guide to the CafeOBJ Logic , 2008 .

[68]  Stephan Merz,et al.  On the Logic of TLA+ , 2003, Comput. Artif. Intell..

[69]  Dines Bjørner Domains, requirements, and software design , 2006 .

[70]  Michael A. Jackson,et al.  Software requirements and specifications - a lexicon of practice, principles and prejudices , 1995 .

[71]  Chris Fox,et al.  The ontology of language - properties, individuals and discourses , 2000, CSLI lecture notes series.

[72]  C. A. R. Hoare,et al.  Unifying Theories for Parallel Programming , 1997, Euro-Par.