Mereotopology

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The mereotopology is a formal theory that mereology and topology together. It examines the topological relationships between wholes, parts and the edges of parts. Although the theory is essentially mathematical, it was developed entirely by logicians and theoretical computer scientists . Mereotopology has proven useful for formal ontology purposes (Smith 1996).

Alfred North Whitehead began in 1916 to develop theories of the part-whole relation, which culminated in his work Process and Reality . For an easy-to-read introduction to this, see Kneebone (2001), Chapter 12. Despite Whitehead's proven mathematical acumen, these theories were informal and contained errors. Bowman Clarke (1981, 1985) showed how Whitehead's theories could be corrected and fully formalized. Clarke's work forms the basis of current mereotopology. Their mathematical capabilities come to light in the advanced presentation by Roeper (1997). The relevant university textbook is Casati and Varzi (1999).

literature

  • R. Casati, AC Varzi: Parts and places: the structures of spatial representation . MIT Press 1999.
  • Bowman Clarke: A calculus of individuals based on 'connection'. In: Notre Dame Journal of Formal Logic. Volume 22, 1981, pp. 204-218.
  • Bowman Clarke: Individuals and Points. In: Notre Dame Journal of Formal Logic. Volume 26, 1985, pp. 61-75.
  • Geoffrey Kneebone: Mathematical Logic and the Foundation of Mathematics . Dover 2001 (1963).
  • Peter Roeper: Region-Based Topology. In: Journal of Philosophical Logic. Volume 26, 1997, pp. 251-309.
  • Barry Smith: Mereotopology: A Theory of Parts and Boundaries . In: Data and Knowledge Engineering. Volume 20, 1996, pp. 287-303.
  • Barry Smith: Boundaries: An Essay in Mereotopology . In: L. Hahn (Ed.): The Philosophy of Roderick Chisholm . Open Court, 1997, pp. 534-561.
  • AC Varzi: Parts, wholes, and part-whole relations: the prospects of mereotopology. In: Data and Knowledge Engineering. Volume 20, 1996, pp. 259-286.
  • AC Varzi: Basic Problems of Mereotopology. In: N. Guarino (Ed.): Formal Ontology in Information Systems. IOS Press, Amsterdam 1998, pp. 29-38.

Individual evidence

  1. ↑ Peter Simons: Whitehead and Mereology. In: Guillaume Durand, Michel Weber (eds.): Les principes de la connaissance naturelle d'Alfred North Whitehead - Alfred North Whitehead's Principles of Natural Knowledge. Ontos Verlag, Frankfurt / Paris / Lancaster 2007, ISBN 978-3-938793-64-0 , pp. 215-234.