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On Mereologies in Computing Science

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Reflections on the Work of C.A.R. Hoare

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Abstract

In this paper we solve the following problems: ∙ We give a formal model of a large class of mereologies, with simple entities modelled as parts and their relations by connectors. ∙ We show that class applies to a wide variety of societal infrastructure component domains. ∙ We show that there is a class of CSP channel and process structures that correspond to the class of mereologies where mereology parts become CSP processes and connectors become channels; and where simple entity attributes become process states. We have yet to prove to what extent the models satisfy the axiom systems for mereologies of, for example, [12] and a calculus of individuals [13]. Mereology is the study, knowledge and practice of part-hood relations: of the relations of part to whole and the relations of part to part within a whole. By parts we shall here understand simple entities – of the kind illustrated in this paper. Manifest simple entities of domains are either continuous (fluid, gaseous) or discrete (solid, fixed), and if the latter, then either atomic or composite. It is how the sub-entities of a composite entity are “put together” that “makes up” a mereology of that composite entity – at least such as we shall study the mereology concept. In this paper, we shall study some ways of modelling the mereology of composite entities. One way of modelling mereologies is using sorts, observer functions and axioms (McCarthy style), another is using CSP.

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Notes

  1. 1.

    Our notation now is not RSL but some conventional first-order predicate logic notation.

  2. 2.

    This paper is most likely not published with colours, so red will be shown as darker colour.

  3. 3.

    Shown as lighter coloured connections.

  4. 4.

    http://www2.imm.dtu.dk/\~db/container-paper.pdf

  5. 5.

    http://www2.imm.dtu.dk/\~db/fsi.pdf

  6. 6.

    http://www2.imm.dtu.dk/\~db/pipeline.pdf

  7. 7.

    http://www2.imm.dtu.dk/\~db/transport.pdf

  8. 8.

    http://www.railwaydomain.org/

  9. 9.

    We use the name “simple entities” in contrast to “entities” which we see as comprising all of simple entities, functions, events and behaviours. “Interesting” functions and normal events involve all forms of entities.

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Acknowledgements

I thank University of Saarland for hosting me during some of the time when I wrote this paper.

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  1. Fredsvej 11, DK-2840, Holte, Denmark

    Dines Bjørner

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  1. Dines Bjørner
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Correspondence to Dines Bjørner .

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  1. Oxford University Computing Laboratory, Parks Road, Oxford, OX13QD, United Kingdom

    A.W. Roscoe

  2. Dept. Computing Science, University of Newcastle upon Tyne, Newcastle upon Tyne, NE17RU, United Kingdom

    Cliff B. Jones

  3. Microsoft Research Ltd., J. J. Thomson Avenue 7, Cambridge, CB30FB, United Kingdom

    Kenneth R. Wood

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Bjørner, D. (2010). On Mereologies in Computing Science. In: Roscoe, A., Jones, C., Wood, K. (eds) Reflections on the Work of C.A.R. Hoare. Springer, London. https://doi.org/10.1007/978-1-84882-912-1_3

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