1 VT

2 Ontology and Ontologies Barry Smith

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

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

5 Reality

6 is complicated

7 What is the best language to describe this complexity?

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

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

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

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

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

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

14 Substances demand 3-D partonomies space

15 Processes demand 4D-partonomies t i m e

16 Substances have spatial parts

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

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

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

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

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

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

23

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

25 Three views/partitions of the same reality

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

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

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

29 Ontological Zooming medicine cell biology

30 Ontological Zooming distinct partitions of one and the same reality

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

32 Projective relation to reality

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

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

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

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

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

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

39 Theory A Cells and Subcells

40 Species Genera as Tree canary animal bird fish ostrich

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

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)

43 Theory B Projection of Cells onto Reality

44 Projection and location Humans Apes Dogs Mammals

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

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)

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)

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

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

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

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

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.

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

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

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

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

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

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