2. 1 VT

3. 2 Ontology and Ontologies Barry Smith

4. 3 IFOMIS Strategy get real ontology right first and then investigate ways in which this real ontology can be translated into computer- usable form later NOT ALLOW ISSUES OF COMPUTER- TRACTABILITY TO DETERMINE THE CONTENT OF ONTOLOGY

5. 4 BFO Basic Formal Ontology (BFO) BFO as an ontological theory of reality designed as a real constraint on domain ontologies

6. 5 Reality

7. 6 is complicated

8. 7 What is the best language to describe this complexity?

9. 8 Unfortunately … there are problems with the use of English as a formal representation language

10. 9 Nouns and verbs Substances and processes Continuants and occurrents In preparing an inventory of reality we keep track of these two different categories of entities in two different ways

11. 10 Natural language glues them together indiscriminately substance t i m e process

12. 11 SNAP vs. SPAN (roughly: Snapshot vs. Video) substance t i m e process

13. 12 SPAN Ontology of Processes unfolding (messily) in time t i m e

14. 13 Substances and processes t i m e process demand different sorts of inventories

15. 14 Substances demand 3-D partonomies space

16. 15 Processes demand 4D-partonomies t i m e

17. 16 Substances have spatial parts

18. 17 Processes have temporal parts The first 5 minutes of my headache is a temporal part of my headache The first game of the match is a temporal part of the whole match

19. 18 Substances do not have temporal parts The first 5-minute phase of my existence is not a temporal part of me It is a temporal part of that complex process which is my life

20. 19 You are a substance Your life is a process You are 3-dimensional Your life is 4-dimensional

21. 20 Two alternative basic ontologies SNAP and SPAN SNAP = substances plus qualities, functions, roles, conditions, etc. SPAN = processes

22. 21 These represent two views of the same rich and messy reality

23. 22 SNAP: Time-Stamped Ontologies t1t1 t3t3 t2t2 here time exists outside the ontology, as an index or time-stamp

24. 23

25. 24 SPAN: Here time exists within the ontology itself t i m e

26. 25 Three views/partitions of the same reality

27. 26 BFO’s two main components 1. SNAP and SPAN 2. The Theory of Granular Partitions

28. 27 Theory of granular partitions There is a projective relation between cognitive subjects and reality Major assumptions: Humans see reality as through a grid The grid is usually not regular and raster shaped

29. 28 Projection of cells … Wyoming Idaho Montana … Cell structure North America Projection

30. 29 Ontological Zooming medicine cell biology

31. 30 Ontological Zooming distinct partitions of one and the same reality

32. 31 When viewing reality in terminology systems, maps, inventories, descriptions, or in simple perception and reasoning WE ALWAYS CHOOSE SOME LEVEL OF GRANULARITY AT WHICH TO WORK

33. 32 Projective relation to reality

34. 33 Crisp and vague projection … Montana … crisp The Himalayas Everest vague P1P1 PnPn

35. 34 Theory of granular partitions Major assumptions –Projection is an active process: it brings certain features of reality into the foreground of our attention (and leaves others in the background) –The projective relation can reflect the mereological structure of reality

36. 35 Projection of cells (1) Cell structureTargets in reality Hydrogen Lithium Projection

37. 36 Projection of cells (2) … Wyoming Idaho Montana … Cell structure North America Projection

38. 37 Multiple ways of projecting County partition Highway partition Big city partition

39. 38 Two core components of the theory of granular partitions –Cell structures (Theory A) –Projective relation to reality (Theory B)

40. 39 Theory A Cells and Subcells

41. 40 Species Genera as Tree canary animal bird fish ostrich

42. 41 Species-Genera as Map/Partition animal bird canary ostrich fish canary

43. 42 Systems of cells Subcell relation –Reflexive, transitive, antisymmetric The cell structure of a granular partition has a unique maximal cell (top-most node, root) Each cell is connected to the root by a finite chain Every pair of cells stands either in a subcell or a disjointness relation (tree structure)

44. 43 Theory B Projection of Cells onto Reality

45. 44 Projection and location Humans Apes Dogs Mammals

46. 45 Misprojection … Montana Wyoming … P(‘Montana’,Montano) and L(Montana,’Montana’) P(‘Wyoming’,Sicily) but not L(Sicily,’Wyoming’)

47. 46 A granular partition projects transparently onto reality if and only if Transparency of projection (1) –Location presupposes projection L(o,z)  P(z,o) –There is no misprojection P(z,o)  L(o,z)

48. 47 Transparency of projection (2) Still: there may be irregularities of correspondence –There may be cells that do not project (e.g. ‘unicorn’) –Multiple cells may target the same object –There may be ‘forgotten’ objects (e.g. the species dog above)

49. 48 Functionality constraints (1) Morning Star Evening Star Venus Location is functional: If an object is located in two cells then these cells are identical, i.e., L(o,z 1 ) and L(o,z 2 )  z 1 = z 2 Two cells projecting onto the same object

50. 49 Functionality constraints (2) China Republic of China (Formosa) People’s Republic of China The same name for two different things: Projection is functional: If two objects are targeted by the same cell then they are identical, i.e., P(z,o 1 ) and P(z,o 2 )  o 1 = o 2

51. 50 Morning Star/Evening Star/Venus and other problems solved by providing a formal framework for dealing with the ways in which partitions are refined and corrected with increases in our knowledge about misprojections about ambiguity about multiple terms designating the same object about hitherto unknown objects/types

52. 51 Preserve mereological structure Helium Noble gases Neon Potential of preserving mereological structure

53. 52 Partitions should not distort mereological structure Humans Apes Dogs Mammals distortion If a cell is a proper subcell of another cell then the object targeted by the first is a proper part of the object targeted by the second.

54. 53 Features of granular partitions Selectivity –Only a few features are in the foreground of attention Granularity –Recognizing a whole without recognizing all of its parts Preserve mereological structure

55. 54 Classification of granular partitions according to Degree of preservation of mereological structure Degree of completeness of correspondence Degree of redundancy

56. 55 Mereological monotony … Helium Noble gases Neon … Helium Noble gases Neon Projection does not distort mereological structureProjection preserves mereological structure

57. 56 Projective completeness Empty cells Every cell has an object located within it:

58. 57 Exhaustiveness Humans Apes Dogs Mammals Everything of kind  in the domain of the partition A is recognized by some cell in A HumansApes Cats Mammals

59. 58 Science = the endeavour to construct partitions of reality which satisfy the conditions of mereological monotony (tree structure) exhaustiveness (every object recognized) functionality (one object per cell) …but no God’s eye partition – every partition we create has some granularity