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Constituent ontologies and granular partitions

Constituent ontologies and granular partitions. Thomas Bittner and Barry Smith IFOMIS – Leipzig and Department of Philosophy, SUNY Buffalo. Overview. Constituent ontologies Levels of ontological theory The hierarchical structure of constituent ontologies

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Constituent ontologies and granular partitions

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  1. Constituent ontologies and granular partitions Thomas Bittner and Barry Smith IFOMIS – Leipzig and Department of Philosophy, SUNY Buffalo

  2. Overview • Constituent ontologies • Levels of ontological theory • The hierarchical structure of constituent ontologies • The projective relation of constituent ontologies and reality • Relations between constituent ontologies • Types of constituent ontologies

  3. The method of constituent ontology: • to study a domain ontologically • is to establish the parts and moments of the domain and • then to establish the interrelations between them

  4. Examples of constituent ontologies

  5. M ND M I SD W I W N Constituent ontologies

  6. Database tables Category trees Constituent ontologies

  7. Nice properties • Very simple structure • Very simple reasoning • Corresponds to the way people represent domains • In databases • Spreadsheets • Maps

  8. Meta-level relations between constituent ontologies

  9. M ND  M I SD W I W N x  y x is sub-constituent-ontology of y Meta level (sub-ontologies)

  10. Meta-level (granularity)

  11. Alabama Alaska Arkansas Arizona … Wyoming West Midwest Northeast South Meta-level (granularity)

  12. Alabama Alaska Arkansas Arizona … Wyoming West Midwest Northeast South Levels of granularity Coarse Intermediate Fine • USA

  13. USA physical Mountains Rivers Planes Meta-level (themes)

  14. USA physical Mountains Rivers Planes USA political Federal states Meta-level (themes)

  15. Constituent ontology2 Constituent ontologyn Constituent ontology1 Levels of ontological theory

  16. Level of foundation Formal relations: mereology, topology, location Space and time Basic categories: entities, regions, perdurants, endurants, … Constituent ontology2 Constituent ontologyn Constituent ontology1 Levels of ontological theory

  17. Object-level (Taxonomies, partonomies) Formal relations: mereology, topology, location Space and time Basic categories: entities, regions, perdurants, endurants, … Meta-level Granularity and selectivity (Theory of granular partitions) Relations between constituent ontologies Negation, Modality Constituent ontology2 Constituent ontologyn Constituent ontology1 Levels of ontological theory

  18. Object-level

  19. Object-level Formal relations: mereology, topology, location Space and time Basic categories: entities, regions, perdurants, endurants Meta-level Granularity and selectivity (Theory of granular partitions) Relations between constituent ontologies Levels of ontological theory Constituent ontology2 Constituent ontologyn Constituent ontology1

  20. Formal relations • Mereology (part-of) -- Partonomy • Mereotopology (is-connected-to) • Location (is-located-at) • Dependence (depends-on) • Subsumption (is-a) -- Taxonomy

  21. Constituent ontologies • A constituent ontology is an abstract entity • Has constituents as parts • Constituents are abstract entities that project onto something that is not a constituent itself

  22. Constituent ontologies asgranular partitions

  23. Level of foundation Formal relations: mereology, topology, location Space and time Basic categories: entities, regions, perdurants, endurants, … • Meta-level • Granularity and selectivity (Theory of granular partitions) Levels of ontological theory Constituent ontology2 Constituent ontologyn Constituent ontology1

  24. Database tables Category trees Granular partitions: Theory A Constituent ontologies have a simple hierarchical structure Maps

  25. Animal Bird Fish Canary Shark Salmon Ostrich Cell structures as Venn diagrams and trees

  26. minimal cells: H, He, … non-minimal cells:orange area, green area,yellow area (noble gases)... one maximal cell: the periodic table (PT) Constituent structures (1)

  27.  - subcell relation He  noble_gases (NG) NG  PT Partial ordering Cell structures (2)

  28. Granular partitions: Theory B Remember:Constituent ontologies • A constituent ontology is an abstract entity • Has constituents as parts • Constituents are abstract entities that project onto something that is not a constituent itself

  29. Projective relation to reality

  30. P(c, bug) Constituents project like a flashlight onto reality

  31. A constituent ontology is like an array of spotlights

  32. Pets in your kitchen Constituent 1 Constituent 2 Constituent 3 Constituent 4 Bug 1 Bug 2 Bug 3 Bug 4

  33. Pets in your kitchen Constituent 1 Constituent 2 Constituent 3 Constituent 4 Constituent ontology Projection Reality Bug 1 Bug 2 Bug 3 Bug 4

  34. constituent ontology Targets in reality Hydrogen Lithium Projection of constituents Projection

  35. North America Constituent ontology … Montana Idaho Wyoming … Projection of constituents (2) Projection

  36. I shall now use the notions cell and constituent synonymously! I shall also use the notions constituent ontology and granular partition synonymously!

  37. Projection and location

  38. L(bug,c) Location Being located is like being in the spotlight

  39. Projection does not necessarily succeed P(c, John) John John is not located in the spotlight! L(John, c)

  40. Mary Projection does not necessarily succeed P(c, John) John Mary is located in the spotlight! L(Mary, c)

  41. Misprojection P(‘Idaho’,Montana) butNOT L(Montana,’Idaho’) Location is what results when projection succeeds

  42. Transparency P(c1, Mary) P(c2, John) L(John, c2) L(Mary, c1) Transparency: L(x, c)  P(c, x)

  43. Humans Apes Dogs Mammals Projection and location

  44. Two cells projecting onto the same object Morning Star Venus Evening Star Functionality constraints (1) Location is functional: If an object is located in two cells then these cells are identical, i.e., L(o,z1) and L(o,z2)  z1 = z2

  45. The same cell (name) for the two different things: Republic of China China People’s Republic of China Functionality constraints (2) Projection is functional: If two objects are targeted by the same cell then they are identical, i.e., P(z,o1) and P(z,o2)  o1 = o2

  46. Neon Helium Noble gases Preserve mereological structure Potential of preserving mereological structure

  47. distortion Humans Apes Dogs Mammals Partitions should not distort mereological structure If a cell is a subcell of another cell then the object targeted by the first is a part of the object targeted by the second.

  48. Neon Helium Noble gases Mereological monotony Projection does not distort mereological structure Projection ignores mereological structure

  49. Well-formed constituent ontologies are granular partitions which are such that: • Projection and location are functions • Location is the inverse of projection wherever defined • Projection is order preserving If x  y then p(x)  p(y) If p(x)  p(y) then x  y

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