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Introduction to the Workshop

Introduction to the Workshop. Parts and Classes in Biomedical Ontology. Barry Smith http://ontologist.com. GO:0003673: cell fate commitment. Definition: The commitment of cells to specific cell fates and their capacity to differentiate into particular kinds of cells. .

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Introduction to the Workshop

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  1. Introduction to the Workshop

  2. Parts and Classes in Biomedical Ontology Barry Smith http://ontologist.com

  3. GO:0003673: cell fate commitment • Definition: The commitment of cells to specific cell fates and their capacity to differentiate into particular kinds of cells.

  4. GO: asymmetric protein localization involved in cell fate commitment

  5. The intended meaning of part-of • as explained in the GO Usage Guide is: • “part of means can be a part of, not is always a part of: the parent need not always encompass the child. For example, in the component ontology, replication fork is a part of the nucleoplasm; however, it is only a part of the nucleoplasm at particular times during the cell cycle”

  6. So, GO ‘part of’ • means: • can be a part of, not is always a part of

  7. But what about: • GO: a flagellum is part-of cells • here ‘part of’ means: • some kinds of cells always have flagella as parts

  8. And what about:

  9. GO: Cellular Component Ontology is part-of Gene Ontology • GO: Biological Process Ontology is part-of Gene Ontology • GO: Molecular Process Ontology is part-of Gene Ontology • here ‘part of’ means: one vocabulary is included in another vocabulary

  10. GO’s three meanings of part-of • 1. A time-dependent mereological inclusion relation between instances • Asometimes_part_of B =def t x y • (inst(x, A, t) & inst(y, B, t) & part(x, y, t)). • 2. Some (types of) Bs have As as parts: • Apart_ofGO B =defC (C is_a B & A part_of C) • 3. Inclusion relations between vocabularies

  11. GO’s use of ‘part of’ illustrates the following problems • One term being used to represent a plurality of different relations • One lexically simple term being used to represent lexically complex concept • A term with an established use (inside and outside biomedical ontology) being used with a new non-standard use WHY SHOULD WE CARE?

  12. Because we want to use GO • to support reasoning

  13. GO’s Usage Guide • lists four ‘logical relationships’ between ‘is a’ and ‘part of’: • (1) (A part_of B & C is_a B) A part_of C • (2) is_a is transitive • (3) part_of is transitive • (4) NOT: (A is_a B & C part_of A) C part_of B

  14. Of these four logical relationships, only • (2) is_a is transitive • is valid, and even this law is mis-expressed by GO as: • if A is an instance of B • and B is an instance of C • then A is an instance of C • so that GO confuses classes with instances

  15. (3) part_ofGOis transitive • fails because of • plastid part_ofGO cytoplasm • cytoplasm part_ofGO cell (sensu Animalia) • But not: plastid part_ofGO cell (sensu Animalia).

  16. GO built by biologists • who deliberately did not want to take account of any of the results of non-biologists working in fields such as ‘ontology’ • But still: GO belongs to the world of KR • The ‘K’ of KR is characteristically a very odd fragment of what (e.g. scientists) would recognize as ‘knowledge’

  17. The world of KR is world of classes exclusively (e.g. WordNet) • Dictionary makers live in a world of classes exclusively • Terminologists live in a world of classes exclusively • Description logic lives in a world of classes (almost) exclusively

  18. GO’s confusion about part-of • 1. A time-dependent mereological inclusion relation between instances • Asometimes_part_of B =def t x y • (inst(x, A, t) & inst(y, B, t) & part(x, y, t)). • 2. Some (types of) Bs have As as parts: • Apart_ofGO B =defC (C is_a B & A part_of C) • 3. Inclusion relations between vocabularies illustrate the need to take not just classes but also instancesinto account

  19. Entities

  20. Entities universals (classes, types, roles …) particulars (individuals, tokens, instances …) Axiom: Nothing is both a universal and a particular

  21. Two Kinds of Elite Entities • classes, within the realm of universals • instances within the realm of particulars

  22. Entities classes

  23. Entities classes* *natural, biological

  24. Entities classes of objects different axioms for classes of functions, processes, etc.

  25. Entities classes instances

  26. Classes are natural kinds • Instances are natural exemplars of natural kinds • (problem of non-standard instances must be dealt with also)

  27. penumbra of borderline cases Entities classes instances instances

  28. Entities classes junk junk instances junk example of junk: beachball desk

  29. Primitive opposition between universals and particulars • variables A, B, … range over universals • variables x, y, … range over particulars

  30. Primitive relations: instand part • inst(Jane, human being) • part(Jane’s heart, Jane’s body) • A class is anything that is instantiated • An instance as anything (any individual) that instantiates some class

  31. Entities human inst Jane

  32. Entities human Jane’s heartpartJane

  33. Axioms for part • Axioms governing part (= ‘proper part’) • (1) it is irreflexive • (2) it is asymmetric • (3) it is transitive • (+ usual mereological axioms) • part is the usual mereological relation among individuals

  34. Definitions • class(A) =def x inst(x, A) • instance(x) = defAinst(x, A) • Theorem: Nothing can be both an instance and a class

  35. Axiom of Extensionality • Classes which share identical instances are identical • (need to take care of the factor of time)

  36. Entities classes differentiae (roles, qualities…) x, y, …

  37. Differentiae • Aristotelian Definitions An A is a B which exemplifies C • C is a differentia • No differentia is a class • exemp(individual, differentia) • exemp(Jane, rationality) • objects exemplify roles

  38. role

  39. Ais_a B • genus(A) • species(A) instances

  40. Ais_a B =def x (inst(x, A) inst(x, B)) • genus(A)=def B (B is_a A & BA) • species(A)=def B (A is_a B & BA) instances

  41. nearest species • nearestspecies(A, B)=defA is_a B & • C ((A is_a C & C is_a B)  (C = A or C = B)

  42. Definitions lowest species

  43. lowest species and highest genus • lowestspecies(A)=def • species(A) & not-genus(A) • highestgenus(A)=def • genus(A) & not-species(A) • Theorem: • class(A) genus(A) or lowestspecies(A)

  44. Axioms • Every class has at least one instance • Distinct lowest species never share instances • SINGLE INHERITANCE: • (nearestspecies(A, B) & nearestspecies (A, C)) B = C

  45. Axioms governing inst • genus(A) & inst(x, A)  • B nearestspecies(B, A) & inst(x, B) • EVERY GENUS HAS AN INSTANTIATED SPECIES • nearestspecies(A, B) A’s instances are properly included in B’s instances • EACH SPECIES HAS A SMALLER CLASS OF INSTANCES THAN ITS GENUS

  46. Axioms • nearestspecies(B, A) • C (nearestspecies(C, A) & B C) • EVERY GENUS HAS AT LEAST TWO CHILDREN • nearestspecies(B, A) & nearestspecies(C, A) & BC)  not-x (inst(x, B)& inst(x, C)) • SPECIES OF A COMMON GENUS NEVER SHARE INSTANCES

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