From Knowledge Representation to Reality Representation Barry Smith

Institute for Formal Ontology and Medical Information Science (Germany) initially: work on formal ontology and on ontology-based quality control in medical terminologies (UMLS, SNOMED, NCI Thesaurus, etc.)

Fruit Orange Vegetable SimilarTo Apfelsine SynonymWith NarrowerThan Goble & Shadbolt Problem: Associative approach to word meanings

both testes is_a testis plant leaves is_a plant menopause part_of death bacterium causes experimental model of disease not normal cell is_a cell not abnormal cell is_a cell

move from associative relations between meanings to ontological relations between the entities themselves supplementing data mining approaches with 1)better data 2)better annotations 3)better integration 4)the possibility of strong logical reasoning

First crack in the wall Digital Anatomist Foundational Model of Anatomy (Department of Biological Structure, University of Washington, Seattle) Virtual Soldier Project: Reference Ontology of Anatomy Reference Ontology of Physiology Reference Ontology of Disease Pathways

Second Crack in the Wall Gene Ontology Consortium Open Biological Ontologies

NCOR: National Center for Ontological Research Buffalo Center of Excellence in Bioinformatics) Stanford Medical Informatics (Protégé 2000) Berkeley Drosophila Genome Project (Model Organism Phenotype Ontology Project)

NCOR: National Center for Ontological Research plus industrial parners Ontology Works...

NCOR Methodology work with content developers to ensure rigorous conformity with good principles of classification and definition use formally defined categories and relations to ensure interoperability and support automatic reasoning and to move beyond mere statistical / associative techniques

Goal in Biomedical Informatics use the methodology of formally defined relations and a common top-level ontology to bridge the granularity gap between genomics and proteomics data and phenotype (clinical, pharmacological, patient centered) data From molecules to diseases

Examples of simple formal- ontological structures is_a hierarchies part_of hierarchies dependence relations

A Window on Reality

Medical Diagnostic Hierarchy a hierarchy in the realm of diseases

Dependence Relations OrganismsDiseases

A Window on Reality OrganismsDiseases

Pleural Cavity Pleural Cavity Interlobar recess Interlobar recess Mesothelium of Pleura Mesothelium of Pleura Pleura(Wall of Sac) Pleura(Wall of Sac) Visceral Pleura Visceral Pleura Pleural Sac Parietal Pleura Parietal Pleura Anatomical Space Organ Cavity Organ Cavity Serous Sac Cavity Serous Sac Cavity Anatomical Structure Anatomical Structure Organ Serous Sac Mediastinal Pleura Mediastinal Pleura Tissue Organ Part Organ Subdivision Organ Subdivision Organ Component Organ Component Organ Cavity Subdivision Organ Cavity Subdivision Serous Sac Cavity Subdivision Serous Sac Cavity Subdivision part_of is_a

A Window on Reality

We can reason across such hierarchies and combinations but only if the top-level categories and associated formal-ontological relations are well-defined and used consistently

Formal-Ontological Categories object process site layer fragment quality function relation boundary region

Formal-Ontological Relations is_identical_to is_a part_of develops_ from derives_ from located_at depends_on is_boundary_of has_participant has_agent adjacent_to contained_in precedes is_functioning_of has_function intends

To support integration of ontologies relational expressions such as is_a part_of... should be used in the same way by all the ontologies to be integrated NCOR goal

to define these relations properly we need to take account of reality If we remain in the realm of concepts we will forever face problems of interoperability

to define these relations properly we need to take account not of concepts, but of universals and instances in reality

Tom Gruber “An ontology is a specification of a conceptualization”

The Concept Orientation Work on biomedical ontologies grew out of work on medical dictionaries and thesauri led to the assumption that all that need be said about concepts can be said without appeal to time or instances. & fostered an impoverished regime of definitions

‘Concept’ in ontology runs together: a)the meaning that is shared in common by a collection of synonymous terms b)an idea shared in common in the minds of those who use synonymous terms (psycho- linguistic view) c)a universal, feature or property shared by entities in the world which fall under the concept

Problem of evaluation if an ontology is a mere “specification of a conceptualization,” then the distinction between good and bad ontologies loses its foothold in reality

There are more word meanings than there are types of entities in reality unicorn devil cancelled performance avoided meeting prevented pregnancy imagined mammal...

A is_a B = def. ‘A’ is more specific in meaning than ‘B’

unicorn is_a one-horned mammal alien implant removal is_a surgical process Chios energy healing is_a therapeutic process

This linguistic reading yields a more or less coherent reading of relations like: ‘is_a’ ‘synonymous_with’ ‘associated_to’

but it fails miserably when it comes to relations of other types part_of = def. composes, with one or more other physical units, some larger whole contains =def. is the receptacle for fluids or other substances.

for how can concepts, on the linguistic reading, figure as relata of relations like: part_of adjacent_to connected_to

connected_to =def. Directly attached to another physical unit as tendons are connected to muscles. How can a meaning or concept be directly attached to another physical unit as tendons are connected to muscles ?

is_a human is_a mammal all instances of the universal human are as a matter of necessity instances of the universal mammal

Evaluation Good ontologies are those whose general terms correspond to universals in reality, and thereby also to corresponding instances.

Kinds of relations : is_a, part_of,... : this explosion instance_of the universal explosion : Mary’s heart part_of Mary

Instance-level relations part_of is_located_at has_participant has_agent earlier...

part_of For instances: part_of = instance-level parthood (for example between Mary and her heart) For universals: A part_of B =def. given any instance a of A there is some instance b of B such that a part_of b

C c at t c at t 1 C 1 transformation_of

transformation_of fetus transformation_of embryo adult transformation_of child C 2 transformation_of C 1 =def. any instance of C 2 was at some earlier time an instance of C 1

derives_from c derives_from c 1 =def c and c 1 are non-identical and exist in continuous succession

the new component detaches itself from the initial component, which itself continues to exist C c at t C c at t C 1 c 1 at t 1 c at t 1 C 1 c 1 at t the initial component ceases to exist with the formation of the new component

two initial components fuse to form a new component C c at t C 1 c 1 at t 1 C' c' at t

Functions your heart has the function: to pump blood =your heart is predisposed (has the potential or casual power) to realize a process of the type pumping blood. has_agent (instance-level relation) p is_functioning_of c  p has_agent c

Example: Spatially Coinciding Objects with thanks to Maureen Donnelly

Two entities coincide (partially) when they overlap (share parts) my hand coincides with my body the European Union coincides with the British Commonwealth (United Kingdom … Malta, Cyprus)

Some entities coincide even though they share no parts any material object coincides with its spatial region a portion of food coincides with my stomach cavity

Holes may coincide with material objects The hole in the chunk of amber coincides completely with, but does not overlap, the encapsulated insect which fills it Sometimes holes and objects are moving independently (a bullet flying through a railway carriage moving through a tunnel)

Layers layers co-located objects The region layer

Layered Ontology of Lakes L1. a region layer L2. a lake layer, consisting of a certain concave portion of the earth’s surface together with a body of water L3. a fish layer L4. a chemical contaminant layer

Layered Epidemiology Ontology L1. a two-dimensional region layer in some undisclosed location L2. a topographical layer, consisting of mountains, valleys, deserts, gullies L3. a storm-system occupying sub-regions of L2 L4: an airborne cloud of smallpox virus particles.

Layered Mereology = modified General Extensional Mereology (GEM)

Parthood (P) Parthood is a partial ordering: (P1) Pxx (reflexive) (P2) Pxy & Pyx  x = y (antisymmetric) (P3) Pxy & Pyz  Pxz (transitive) (P4) ~Pxy   z(Pzx & ~Ozy) (the remainder principle: if x is not part of y, then x has a part that does not overlap y)

layers co-located objects The region layer

The Region Function r(x) = the region at which x is exactly located. r is a new primitive r maps (collapses) entities on all higher layers onto the region layer

Axioms for the region function, e.g. (R3) Pxy  P r(x)r(y)

Some Theorems Ry  r(y) = y (every region is located at itself) (  x  &  x(   Rx) &  y (Oyz  x (  & Oyx)))  Rz (every sum of regions is a region)

Defined Relations ECxy =: Cxy & ~ Oxy (x and y are externally connected) Axy =: EC(r(x), r(y)) (x and y abut)

Towards Dynamic Spatial Ontology From spatial coincidence to spatio- temporal coincidence

Objects move through space An adequate ontology of motion requires at least two independent sorts of spatial entities: 1. locations, which remain fixed, 2. objects, which move relative to them.

Standard (RCC) approaches sparrow 152 moves from one location (region A) to another (region B) Becomes: each member of this continuous sequence of sparrow-shaped regions, starting with A and ending with B, has at successive times, rufous- winged (etc.) attributes. Instead of talking about sparrows flying through the sky, we talk of mappings of the form: Sparrow 152 : time  regular closed subsets of R 3.

Region-based approaches (RCC, etc.) have no means of distinguishing true overlap (i.e. the sharing of parts) from mere spatial co- location. They identify the relation of a fish to the lake it inhabits with the relation of a genuine part of a lake (a bay, an inlet) to the lake as a whole. They identify the genuine parts of the human body, such as the heart or lungs, with foreign occupants such as parasites or shrapnel.

The solution is to recognize both objects and locations, on separate layers and then we need a theory of coincidence and of layered mereotopology to do justice to the entities in these two categories

Some entities coincide spatially even though they share no parts a portion of food coincides with my stomach cavity at a certain time

Some entities coincide spatio- temporally even though they share no parts the course of a disease coincides with the treatment of the disease

Processes may coincide with each other The manouvres of the coalition troops coincide, but do not share parts in common, with the activities of the terrorists

Spatiotemporal Coincidence without Sharing of Parts The Great Plague of 1664 coincides with, but does not overlap, the history of Holland in the 17th century A process of deforestation coincides with, but does not overlap, the history of the forest

Objects and processes do not coincide For they are of different dimension: Objects are 3-dimensional Processes are 4-dimensional Object-layers are always 3-dimensional Process-layers are always 4-dimensional

Two ontologies of motion and change series of samples, or snapshots object x 1 is at region r 1 at time t 1 object x 2 is at region r 2 at time t 2 object x 3 is at region r 3 at time t 3  SNAP ontologies (ontologies indexed by times)

t 1

t 2

t 3

SNAP vs SPAN Continuants vs Occurrents (Sampling vs. Tracking)

SPAN ontology

SPAN ontology is an ontology which recognizes processes, changes, themselves = four-dimensional (spatio-temporal) entities not via a sequence of instantaneous samplings but via extended observations

Many different interconnections traverse the SNAP-SPAN divide But SNAP and SPAN entities are never related by part_of, connected_to or coincidence (layer) relations

SNAP

SPAN

There are layers in both the SNAP (object) ontology and the SPAN (process) ontology In SNAP the region layer = space In SPAN the region layer = spacetime

But distinguishing layers in the process realm of SPAN is a matter of gerrymandering (of fiat carvings) to a much greater degree than in the realm of SNAP

One big difference between SNAP and SPAN In SNAP, higher layers are categorially well- distinguished nicely separated (physical objects, holes, administrative entities …) In SPAN everything is flux

E N D E