Medical Ontologies: An Overview Barry Smith http://ifomis.de
Three levels of ontology formal (top-level) ontology dealing with categories employed in every domain: object, event, whole, part, instance, class 2) domain ontology, applies top-level system to a particular domain cell, gene, drug, disease, therapy 3) terminology-based ontology large, lower-level system Dupuytren’s disease of palm, nodules with no contracture http:// ifomis.de
Three levels of ontology formal (top-level) ontology dealing with categories employed in every domain: object, event, whole, part, instance, class 2) domain ontology, applies top-level system to a particular domain cell, gene, drug, disease, therapy 3) terminology-based ontology large, lower-level system Dupuytren’s disease of palm, nodules with no contracture http:// ifomis.de
Three levels of ontology formal (top-level) ontology dealing with categories employed in every domain: object, event, whole, part, instance, class 2) domain ontology, applies top-level system to a particular domain cell, gene, drug, disease, therapy 3) terminology-based ontology large, lower-level system Dupuytren’s disease of palm, nodules with no contracture http:// ifomis.de
Three levels of ontology formal (top-level) ontology dealing with categories employed in every domain: object, event, whole, part, instance, class 2) domain ontology, applies top-level system to a particular domain cell, gene, drug, disease, therapy 3) terminology-based ontology large, lower-level system Dupuytren’s disease of palm, nodules with no contracture http:// ifomis.de
Institute for Formal Ontology and Medical Information Science IFOMIS Institute for Formal Ontology and Medical Information Science Leipzig http://ifomis.de philosophers and medical informaticians attempting to build and test a Basic Formal Ontology for applications in biomedical and related domains http:// ifomis.de
IFOMIS use basic principles of philosophical ontology for quality assurance and alignment of biomedical ontologies http:// ifomis.de
Compare: pure mathematics (theories of structures such as order, set, function, mapping) employed in every domain applied mathematics, applications of these theories = re-using the same definitions, theorems, proofs in new application domains physical chemistry, biophysics, etc. = adding detail http:// ifomis.de
Three levels of ontology ????? formal (top-level) ontology = medical ontology has nothing like the technology of definitions, theorems and proofs provided by pure mathematics 2) domain ontology = UMLS Semantic Network, GALEN CORE 3) terminology-based ontology = UMLS, SNOMED-CT, GALEN, FMA http:// ifomis.de
Strategy Part 1: Provide an overview of medical ontologies and of the top-level ontologies which they implicitly define Part 2: Show how principles of classification and definition derived from top-level ontology can help in quality assurance of terminology-based ontologies and in ontology alignment Parts 3 and 4: IFOMIS Collaboration with L&C http:// ifomis.de
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part of the UMLS Semantic Network http:// ifomis.de
UMLS Semantic Network entity event physical conceptual object entity http:// ifomis.de
UMLS Semantic Network entity event physical conceptual object entity http:// ifomis.de
Occupation or Discipline conceptual entity Organism Attribute Finding Idea or Concept Occupation or Discipline Organization Group Group Attribute Intellectual Product Language http:// ifomis.de
Conceptual Entity Idea or Concept Functional Concept Qualitative Concept Quantitative Concept Spatial Concept Body Location or Region Body Space or Junction Geographic Area Molecular Sequence Amino Acid Sequence Carbohydrate Sequence Nucleotide Sequence http:// ifomis.de
Fairfax County is an Idea or Concept http:// ifomis.de
Why is Fairfax County a Conceptual Entity for UMLS-SN? UMLS-SN Spatial Concepts share the following characteristics: a) they are extended in space b) their boundaries are determined not by any underlying physical discontinuities but rather by human fiat. The referent of ‘Fairfax County’ satisfies these conditions, but so also does hand, which is not classified by UMLS as a conceptual entity. http:// ifomis.de
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fully formed anatomical structure gene part_of cell component body system conceptual_part_of fully formed anatomical structure http:// ifomis.de
conceptual entity idea or concept functional concept body system http:// ifomis.de
But: Gene or Genome is defined as: “A specific sequence … of nucleotides along a molecule of DNA or RNA …” and nucleotide sequence is_a conceptual entity http:// ifomis.de
confusion of entity and concept entity physical conceptual object entity idea or concept functional concept body system confusion of entity and concept http:// ifomis.de
Functional Concept: Body system is_a Functional Concept. but: Concepts do not perform functions or have physical parts. http:// ifomis.de
This: is not a concept http:// ifomis.de
Problem: Confusion of Is_A and Has_Role Physical Entity Chemical Entity Chemical Chemical Viewed Viewed Structurally Functionally http:// ifomis.de
Chemical Viewed Structurally vs. Chemical Viewed Functionally reflects a distinction between types of classification – not between types of entity compare a classificationof people into: tall people, people who play tennis, people who look like flies from a distance etc. http:// ifomis.de
Confusion of Is_A and Has_Role Physical Object Substance Food Chemical Body Substance http:// ifomis.de
Roles A box used for storage is not (ipso facto) a special kind of box An animal belonging to the emperor is not a special kind of animal http:// ifomis.de
The Hydraulic Equation BP = CO*PVR arterial blood pressure is directly proportional to the product of blood flow (cardiac output, CO) and peripheral vascular resistance (PVR) http:// ifomis.de
Confusion of Ontology and Epistemology blood pressure is an Organism Function, cardiac output is a Laboratory or Test Result or Diagnostic Procedure BP = CO*PVR thus asserts that blood pressure is proportional either to a laboratory or test result or to a diagnostic procedure http:// ifomis.de
Disease History is classified by UMLS under Health Care Activity This runs together the history or course of a disease on the side of the patient (ontology) with the act of eliciting that history (epistemology). http:// ifomis.de
Object vs. Process = Continuant vs. Occurrent Continuant entities = endure through time organisms, cells, molecules exist in full in every instant at which you exist at all Occurrent entities (processes, events, activities, changes, histories) unfold themselves in time; never exist in full in any single instant http:// ifomis.de
Dependent vs. Independent Entities Dependent entities require support from other entities in order to exist: there is no mass or shape without some body Independent entities are themselves the substrates for qualities, dispositions, motions, functions and other dependent entities http:// ifomis.de
entities independent dependent occurrents continuants continuants (always dependent) ORGANISMS ROLES PROCESSES CELLS FUNCTIONS HISTORIES MOLECULES CONDITIONS LIVES (diseases) (courses of diseases) http:// ifomis.de
entities independent dependent occurrents continuants continuants (always dependent) ORGANISMS ROLES PROCESSES CELLS FUNCTIONS HISTORIES MOLECULES CONDITIONS LIVES (diseases) (courses of diseases) classes instances http:// ifomis.de
A three-category ontology along these lines accepted by DOLCE = first module of Semantic Web Wonderweb Foundational Ontologies Library BFO = IFOMIS Basic Formal Ontology UMLS-SN, GO http:// ifomis.de
GALEN independent dependent occurrents continuants continuants (always dependent) GENERALISED MODIFIER GENERALISED STRUCTURES + CONCEPT PROCESS GENERALISED (features, SUBSTANCES states, roles) http:// ifomis.de
GALEN independent dependent occurrents continuants continuants (always dependent) GENERALISED MODIFIER GENERALISED STRUCTURES + CONCEPT PROCESS GENERALISED (features, SUBSTANCES states, cell + sputum roles) http:// ifomis.de
GALEN independent dependent occurrents continuants continuants (always dependent) GENERALISED MODIFIER GENERALISED STRUCTURES + CONCEPT PROCESS GENERALISED (features, SUBSTANCES states, roles) http:// ifomis.de
GALEN independent dependent occurrents continuants continuants (always dependent) GENERALISED ASPECT GENERALISED STRUCTURES + PROCESS GENERALISED (features, SUBSTANCES states, roles) http:// ifomis.de
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immune system is_a logical structure http:// ifomis.de
GALEN CORE (1996) Phenomenon = those categories which can be observed http:// ifomis.de
GALEN CORE (1996) Phenomenon = categories whose instances can be observed http:// ifomis.de
SNOMED-CT Concept Substance Body Structure Specimen Context-Dependent Categories Attribute Finding Staging and Scales Organism Physical Object Events Environments and Geographic Locations Qualifier Value Special Concept Pharmaceutical / Biological Product Social Context Disease Procedure Physical Force http:// ifomis.de
SNOMED-CT Concept Substance Body Structure Specimen Context-Dependent Categories Attribute Finding Staging and Scales Organism Physical Object Events Environments and Geographic Locations Qualifier Value Special Concept Pharmaceutical / Biological Product Social Context Disease Procedure Physical Force http:// ifomis.de
SNOMED-CT Concept Substance Body Structure Specimen Context-Dependent Categories Attribute Finding Staging and Scales Organism Physical Object Events Environments and Geographic Locations Qualifier Value Special Concept Pharmaceutical / Biological Product Social Context Disease Procedure Physical Force http:// ifomis.de
An unintuitive top-level with unintuitive rules for classification leads to coding errors difficulties in training of curators obstacles to alignment with other ontology and terminology systems obstacles to harvesting content in automatic reasoning systems http:// ifomis.de
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Principles for Building Medical Ontologies Barry Smith http://ifomis.de
Examples Don’t confuse entities with concepts Don’t confuse domain entities with logical structures Don’t confuse ontology with epistemology Don’t confuse is_a with has_role http:// ifomis.de
Methodological Principles Formal Principles (Axioms, Definitions and Theorems of a Formal Ontology for Biomedical Classification) http:// ifomis.de
Further Principles univocity: terms should have the same meanings (and thus point to the same referents) on every occasion of use UMLS-SN: ‘organization’ = body plan ‘organization’ = social organization http:// ifomis.de
univocity Gene Ontology: ‘part_of’ = ‘can be part of’ (flagellum part_of cell) ‘part_of’ = ‘is sometimes part of’ (replication fork part_of the nucleoplasm) ‘part_of’ = ‘is included as a sublist in’ http:// ifomis.de
don’t forget instances part_of as a relation between classes vs. part as a relation between instances A part_of B every instance of A is part of some instance of B every instance of B has some instance of A as part http:// ifomis.de
Part_of as a relation between classes is more problematic than is standardly supposed testis part_of human being ? heart part_of human being ? http:// ifomis.de
UMLS-SN Semantic Relations prevents Definition: Stops, hinders or eliminates an action or condition. Inverse: prevented_by contraception prevents pregnancy pregnancy prevented by contraception http:// ifomis.de
UMLS-SN Semantic Relation produces Definition: Brings forth, generates or creates. Inverse: produced_by artificial insemination produces pregnancy pregnancy produced by artificial insemination http:// ifomis.de
positivity complements of classes are not themselves classes. (Terms such as ‘non-mammal’ or ‘non-membrane’ do not designate natural kinds.) http:// ifomis.de
objectivity which classes exist is not a function of our biological knowledge. (Terms such as ‘unknown’ or ‘unclassified’ or ‘unlocalized’ do not designate biological natural kinds.) http:// ifomis.de
rules governing levels the terms in a classificatory hierarchy should be divided into predetermined levels (analogous to the levels of kingdom, phylum, class, order, etc., in traditional biology). the terms in a partonomic hierarchy should be divided into predetermined granularity levels (organism, organ, cell, molecule, etc.) http:// ifomis.de
JEPD (jointly exhaustive and pairwise disjoint) single inheritance: no class in a classifi-catory hierarchy should have more than one parent on the immediate higher level exhaustiveness: the classes on any given level should exhaust the domain of the classificatory hierarchy (difficult to satisfy in biomedicine but is accepted as a goal by every scientist) http:// ifomis.de
Shortfalls from single inheritance are often clues as to bad coding, since they mark deviations from is_a relations which also block ontology alignment http:// ifomis.de
Is_a Overloading The success of ontology alignment depends crucially on the degree to which basic ontological relations such as is a and part of can be relied on as having the same meanings in the different ontologies to be aligned. http:// ifomis.de
Use of multiple inheritance involves the assignment to the is_a relation of a plurality of different meanings within a single ontology. The resultant mélange makes coherent integration across ontologies achievable (at best) only under the guidance of human beings with relevant biological knowledge http:// ifomis.de
rules for definitions intelligibility: the terms used in a definition should be simpler (more intelligible) than the term to be defined otherwise the definition provides no assistance to the understanding (for humans) or is unprocessable (for machines) http:// ifomis.de
substitutability in all so-called extensional contexts a defined term should be substitutable by its definition in such a way that the result is both grammatically correct and has the same truth-value as the sentence with which we begin GO:0015070: toxin activity Definition: Acts as to cause injury to other living organisms. http:// ifomis.de
substitutability There is toxin activity here There is acts as to cause injury to other living organisms here http:// ifomis.de
modularity: you can’t define everything isolate primitive terms (= level 0) define terms on level n + 1, for each n 0 using only: terms taken from levels n and below plus logical and ontological constants such as ‘and’, ‘all’, ‘is_a’ and ‘part_of’ http:// ifomis.de
univocity and modularity if these rules are not satisfied then error checking and ontology alignment can be achieved, at best, only with human intervention http:// ifomis.de
The Foundational Model of Anatomy follows formal rules for definitions laid down by Aristotle. A definition is the specification of the essence (nature, invariant structure) shared by all the members of a class or natural kind. http:// ifomis.de
The Foundational Model of Anatomy Topmost node are the undefinable primitives. The definition of a class lower down in the hierarchy is provided by specifying the parent of the class together with the relevant differentia, which tells us what marks out instances of the defined class within the wider parent class, as in: human = rational animal. http:// ifomis.de
FMA Examples Cell is an anatomical structure that consists of cytoplasm surrounded by a plasma membrane with or without a cell nucleus Plasma membrane is a cell part that surrounds the cytoplasm, http:// ifomis.de
The FMA regimentation brings the advantage that each definition reflects the position in the hierarchy to which a defined term belongs. The position of a term within the hierarchy enriches its own definition by incorporating automatically the definitions of all the terms above it. The entire information content of the FMA’s term hierarchy can be translated very cleanly into a computer representation http:// ifomis.de
These Rules are Rules of Thumb The world of biomedical research is a world of difficult trade-offs the benefits of formal (logical and ontological) rigor need to be balanced 1. against the constraints of computer tractability, 2. against the needs of biomedical practitioners. But automatic alignment biomedical information resources will be achieved only to the degree that such resources conform to the standard principles of classification and definition http:// ifomis.de
Formal Principles genus(A)=def class(A) B (B is a A B A) species(A)=def class(A) B (A is a B B A) lowestspecies(A)=def species(A) genus(A) highestgenus(A)=def genus(A) species(A) class(A) (genus(A) lowestspecies(A)) class(A) (species (A) highestgenus(A)) (A is a B B is a C) A is a C (A is a B B is a A) A = B nearestspecies(A,B) =def A is a B AB C((A is a C C is a B) (C=A C=B)) (nearestspecies(A, B) nearestspecies (A, C)) B = C lowestspecies(A) lowestspecies(B) A B x(inst(x, A) inst(x, B)) genus(A) inst(x, A) B nearestspecies(B, A) inst(x, B) nearestspecies(A, B) x(inst(x, B) inst(x, A)) nearestspecies(B, A) C (nearestspecies(C, A) B C) (nearestspecies(B, A) nearestspecies(C, A) x(inst(x, B) inst(x, C))) B = C genus(A) BC(nearestspecies(B, A) nearestspecies (C, A) B C)) (genus(A) inst(x, A)) B (lowestspecies(B) B is a A inst(x, B)) http:// ifomis.de
Axioms Every class has at least one instance Distinct classes on the same level never share instances Distinct leaf classes within a classification never share instances http:// ifomis.de
Axioms Every genus has an instantiated species Each species has a smaller class of instances than its genus http:// ifomis.de
Axioms Every genus has at least two children http:// ifomis.de
Theorems Every instance is also an instance of some leaf class Classes which share a child in common are either identical or one is subordinated to the other http:// ifomis.de
Mathematical Structure Each class hierarchy constitutes a supremum-semilattice with respect to is_a http:// ifomis.de
Classes vs. Sets Both classes and sets are marked by granularity – but sets are timeless A class endures through time and survives the turnover in its instances A set is determined by its members A class is not determined by its instances (as a state is not determined by its citizens and as an organism is not determined by its molecules) http:// ifomis.de
Classes vs. Sums Classes are marked by granularity: they divide up the corresponding domain into whole units or members The class of human beings is instantiated only by human beings as single, whole units. The sum of human beings includes also all cells and molecules existing inside human beings as parts http:// ifomis.de
Classes sets A set is an abstract structure, existing outside time and space. The set of human beings existing at t is (timelessly) a different entity from the set of human beings existing at t because of births and deaths. http:// ifomis.de
Classes vs. Sets A set with n members has in every case exactly 2n subsets The subclasses of a class are limited in number (which classes are subsumed by a larger class is a matter for empirical science to determine) http:// ifomis.de
Conclusion The analogue of pure mathematics for biomedical informatics (the theory of biomedical classification) must look very different from standard mathematical set theory (and from its progeny, including Description Logic) The formal theory of biological classification is still in its infancy http:// ifomis.de
Biological classes are marked always by an opposition between standard or prototypical instances and a surrounding penumbra of non-standard instances (not all instances of the class human being are marked by the presence of amputation stumps or pituitary tumors). To do justice to these matters FMA introduces the factor of idealization, which means (in first approximation) that the classes of the FMA’s Anatomy Taxonomy AT include only those instances to which canonical anatomy applies. This means that we need to revise definitions D1–D4 by restricting the range of variables x, y, ... to the realm of individuals which satisfy the generalizations of canonical anatomy, so that the same abstraction of anatomy (structure) will be represented in all the instances of any given AT-class. This device of specifying different ranges of variables gives us the means also to represent the generalizations belonging to the different branches of canonical anatomy, for example to canonical anatomy for male vs. female human beings, for human beings at various developmental stages, and for organisms in other species. It can allow us also to represent the generalizations governing the anatomical variants yielded by the presence of, for example, coronary arteries or bronchopulmonary segments, which deviate from canonical anatomical patterns of organization. http:// ifomis.de
http:// ifomis.de Classes vs. Sets: Granularity and Time Sets in the mathematical sense, too, are marked by the factor of granularity, which means that each set comprehends its members as single, whole units. A class or set is laid across reality like a grid consisting (1) of a number of slots or pigeonholes each (2) occupied by some member. (This informal talk of grids and slots is formalized in [[14]] in terms of the theory of granular partitions.) Classes are distinguished from sets, however, by the fact that a set is determined by its members. This means that it is (1) associated with a specific number of slots, each of which (2) must be occupied by some specific member. A set is thus specified in a double sense. A class, in contrast, survives the turnover in its instances, and so it is specified in neither of these senses, since both (1) the number of associated slots and (2) the individuals occupying these slots may vary with time. Sets are distinguished from classes also in this: a set with n members has in every case exactly 2n subsets, constituted by all the combinations of these members. The subclasses of a class, on the other hand, are limited in number, and which classes are subsumed by a larger class is a matter for empirical science to determine. Leaves (lowest nodes) in the taxonomy are (changing) collections of instances. As we move up the taxonomy we encounter in succession collections of such collections of instances, collections of collections of such collections, etc., organized in a nested hierarchy reaching up to the maximal class or ‘root’. We can visualize the classes at different levels as being analogous to geopolitical entities (towns, counties, states) as represented on a map. Instances correspond in this analogy to the corresponding populations: a class is not determined by its instances as a state is not determined by its citizens. http:// ifomis.de
Classes are distinguished from sets also by their relation to time Classes are distinguished from sets also by their relation to time. A set is an abstract structure, existing outside time and space, and this is so even when its members are parts of concrete reality. Since each set is determined by its members, the set of human beings existing at t is (timelessly) a different entity from the set of human beings existing at t because of births and deaths. Matters are different with regard to classes. The class human being can survive the change in the stock of its instances which occurs when John and Jane die, because classes exist in time. John and Jane themselves can similarly survive changes in the stock of cells or molecules by which they are constituted. To do justice to the fact that classes in the biological domain endure even when their extensions change, a full definition of the is_a relation must involve a temporally indexed reading of inst (with variables t, t, etc., ranging over times): D1* A is_a B =def t x ( inst(x, A, t) inst(x, B, t) ), so that A is_a B means: at all times t, if x is an instance of A at t then x is an instance of B at t. D1* will also take care of false positives such as adult is_a child, which an untensed reading of D1 would otherwise allow. In general, all statements of inst and part relations involving objects in biomedical ontologies, like all the data of instantiated anatomy, are indexed by times. http:// ifomis.de
Taxonomy and Partonomy A taxonomy such as AT is formally speaking a tree in the mathematical sense. It satisfies axioms to the effect that (1) it has a root or unique maximal genus (here: anatomical entity) and (2) all other classes are connected to this root via finite chains of is_a relations satisfying a principle of single inheritance. A partonomy, in contrast, is a partial order in the mathematical sense, with top (here: organism – the class instantiated by mereologically maximal entities), to which all other classes are connected via chains of part_of relations. We can then define the concepts of root and leaf of a taxonomy and top and bottom of a partonomy as follows. D5 root(A) =def B (B is_a A) D6 leaf(A) =def B (B is_a A A = B) D7 top(A) =def B (A = B or B part_of A) & not-B (A part_of B) D8 bottom(A) =def not-B (B part_of A). http:// ifomis.de
We can then postulate axioms to the effect that every class includes some leaf as subclass, and that every instance of every class instantiates some leaf: AB ( leaf(B) & B is_a A ) Ax ( inst(x, A) B (leaf(B) & inst(x, B) ) ) The taxonomical union AÈB of classes A and B is defined as the minimal class satisfying the condition that it contains both A and B as subclasses. Such a class always exists, since A and B are in any case subclasses of the root. The taxonomic union of femur and liver, for example, is organ. The partonomic union of two classes A+B is the class, if it exists, whose instances are sums x+y of instances of classes A and B respectively. While every pair of classes has a taxonomic union, only some classes have a partonomic union, since entities of the form x+y are instances of classes only in some highly restricted cases, for example: left lung = upper-lobe-of-left-lung + lower-lobe-of-left-lung. Such examples characteristically involve the phenomenon of fiat boundaries. [[15],[16]] http:// ifomis.de
As concerns taxonomic intersection, a class is never immediately subordinated to more than one higher class within a tree. This means that if two classes overlap in sharing some common sub-class, then this is because one is a subclass of the other. AB, the taxonomic intersection of A and B, if it exists, is then simply the smaller of these two classes. We can add further an axiom to the effect that, if two classes are such as to overlap in sharing some common instances, then this, too, is because one is a subclass of the other: x (inst(x, A) Ù inst(x, B)) A is_a B or B is_a A. Classes can overlap partonomically, on the other hand, in such a way that there is a class which stands in the part_of relation to both, though neither stands in this relation to the other: D9 A1 partonomic_overlap A2 = def A (A part_of A1 & A part_of A2). For example: pelvis and vertebral column overlap in the sacrum and coccyx. Most classes in the biomedical domain do not overlap partonomically in this sense, yet it is this difference in behavior between taxonomic and partonomic overlap which captures the essential difference between the tree structure of taxonomies and the partial order structure of partonomies. http:// ifomis.de
http:// ifomis.de Conclusion Practitioners in the biomedical sciences move easily between the realm of classes and the realm of instances existing in time and space. For historical reasons, however, work on biomedical ontologies and terminologies – which grew out of work on medical dictionaries and nomenclatures – has focused almost exclusively on classes (or ‘concepts’) atemporally conceived. This class-orientation is common in knowledge representation, and its predominance has led to the entrenchment of an assumption according to which all that need be said about classes can be said without appeal to formal features of instantiation of the sorts described above. This, however, has fostered an impoverished regime ofof definitions in which the use of identical terms in different systems has been allowed to mask underlying incompatibilities. Matters have not been helped by the fact that description logic, the prevalent framework for terminology-based reasoning systems, has with some recent exceptions (e.g. [[i]]) been oriented primarily around reasoning with classes. Certainly if we are to produce information systems with the requisite computational properties, then this entails recourse to a logical framework like that of description logic. At the same time, however, we must ensure that the data that serves as input to such systems is organized formally in a way that sustains rather than hinders successful alignment with other systems. The way forward is to recognize, as does the FMA, that these are two distinct tasks, both of which are equally important to the construction of biomedical ontologies and terminologies. http:// ifomis.de
The problem of ontology alignment GO SCOP SWISS-PROT SNOMED MeSH FMA … all remain at the level of TERMINOLOGY (two reasons: legacy of dictionaries + DL) What we need is a REFERENCE ONTOLOGY = a formal theory of the foundational relations which hold TERMINOLOGY ONTOLOGIES and APPLICATION ONTOLOGIES together http:// ifomis.de
A causes B A is associated with B A is located in B etc. Analogous distinctions required for nearly all foundational relations of ontologies and semantic networks: A causes B A is associated with B A is located in B etc. Reference to instances is necessary in defining mereotopological relations such as spatial occupation and spatial adjacency http:// ifomis.de
Instances are elite individuals Which classes (and thus which instances) exist in a given domain is a matter for empirical research. Cf. Lewis/Armstrong “sparse theory of universals” http:// ifomis.de
D extension(A) = {x | inst(x, A)} D9 differentia(A) =def BC nearestspecies(B, C) & A B & A C & extension(C) = extension(B) extension(C) http:// ifomis.de
differentia (A) not-class(A) The genus together with the differentia of a species constitutes the essence of the species. differentia (A) not-class(A) http:// ifomis.de
Axioms (Berg) A1 lowestspecies(A) x inst(x, A) A2 lowestspecies(A) & lowestspecies(B) & A B (not-x inst(x, A) & inst(x, B)) A3 nearestspecies(A, B) & nearestspecies (A, C) B = C A4 genus(A) & inst(x, A) B nearestspecies(B, A) & inst(x, B) A5 nearestspecies(A, B) the extension of A is a subset of the extension of B http:// ifomis.de
Axioms (Berg) genus(A) & inst(x, A) B nearestspecies(B, A) & inst(x, B) EVERY GENUS HAS AN INSTANTIATED SPECIES nearestspecies(A, B) the extension of A is a subset of the extension of B EACH SPECIES HAS A SMALLER CLASS OF INSTANCES THAN ITS GENUS http:// ifomis.de
Axioms (Berg) 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 A8 There is no infinite sequence <A1, A2, …> such that nearestspecies(Ai, Ai+1) for all i 1 A9 There is no infinite sequence <A1, A2, …> such that nearestspecies(Ai+1, Ai) for all i 1 http:// ifomis.de
Theorems (Berg) T1 nearestspecies(A, B) the extension of A is a proper subset of the extension of B T2 A x inst(x, A) T3 nearestspecies(A, B) not-C (nearestspecies(A, C) & nearestspecies(C, B)) T4 lowestspecies(A1) & lowestspecies(A2) & nearestspecies(A1, B) not-C(nearestspecies (B, C) & nearestspecies (C, A2) http:// ifomis.de
Theorems (Berg) T5 (genus(A) & inst(x, A)) B (lowestspecies(B) & B is_a A & inst(x, B)) T6 (genus(A) & lowestspecies(B) & x (inst(x, A) & inst(x, B)) B is_a A T7 A is_a B & A is_a C (B = C or B is_a C or C is_a B T8 (genus(A) & genus(B) & x(inst(x, A) & inst(x, B))) C(C is_a A & C is_a B) T9 class(A) & class(B) (A = B or A is_a B or B is_a A or not-x(inst(x, A) & inst(x, B))) http:// ifomis.de
WordNet NOT: wheel PART OF car WordNet represents part-of quite sparingly It normally gives trivial holonymic relations which are just true by definition). wheel PART OF wheeled vehicle steering wheel PART OF steering system http:// ifomis.de
WordNet With has_part relations it is more generous: car, auto, automobile, machine, motorcar -- HAS PART: air bag HAS PART: glove compartment etc. http:// ifomis.de
Circular definitions and associated problems in general endemic in biomedical terminology systemsConfusion of use and mention Confusion of concepts and objects Confusion of concepts and classes Confusion of terms and objects Confusion knowledge with what is known Confusion of object-level with machine-level Simple stupidity … all of which lead to poor coding http:// ifomis.de
UMLS-SN http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: affects TUI: T151 Definition: Produces a direct effect on. Implied here is the altering or influencing of an existing condition, state, situation, or entity. This includes has a role in, alters, influences, predisposes, catalyzes, stimulates, regulates, depresses, impedes, enhances, contributes to, leads to, and modifies. Inverse: affected_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: carries_out TUI: T141 Definition: Executes a function or performs a procedure or activity. This includes transacts, operates on, handles, and executes. Inverse: carried_out_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: causes TUI: T147 Definition: Brings about a condition or an effect. Implied here is that an agent, such as for example, a pharmacologic substance or an organism, has brought about the effect. This includes induces, effects, evokes, and etiology. Inverse: caused_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: consists_of TUI: T172 Definition: Is structurally made up of in whole or in part of some material or matter. This includes composed of, made of, and formed of. Inverse: constitutes http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: contains TUI: T134 Definition: Holds or is the receptacle for fluids or other substances. This includes is filled with, holds, and is occupied by. Inverse: contained_in http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: derivative_of TUI: T178 Definition: In chemistry, a substance structurally related to another or that can be made from the other substance. This is used only for structural relationships. This does not include functional relationships such as metabolite of, by product of, nor analog of. Inverse: has_derivative http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: developmental_form_of TUI: T179 Definition: An earlier stage in the individual maturation of. Inverse: has_developmental_form http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: evaluation_of TUI: T161 Definition: Judgment of the value or degree of some attribute or process. Inverse: has_evaluation http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: exhibits TUI: T145 Definition: Shows or demonstrates. Inverse: exhibited_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: functionally_related_to TUI: T139 Definition: Related by the carrying out of some function or activity. Inverse: functionally_related_to http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: indicates TUI: T156 Definition: Gives evidence for the presence at some time of an entity or process. Inverse: indicated_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: ingredient_of TUI: T202 Definition: Is a component of, as in a constituent of a preparation. Inverse: has_ingredient http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: issue_in TUI: T165 Definition: Is an issue in or a point of discussion, study, debate, or dispute. Inverse: has_issue http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: manifestation_of TUI: T150 Definition: That part of a phenomenon which is directly observable or concretely or visibly expressed, or which gives evidence to the underlying process. This includes expression of, display of, and exhibition of. Inverse: has_manifestation http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: property_of TUI: T159 Definition: Characteristic of, or quality of. Inverse: has_property http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: result_of TUI: T157 Definition: The condition, product, or state occurring as a consequence, effect, or conclusion of an activity or process. This includes product of, effect of, sequel of, outcome of, culmination of, and completion of. Inverse: has_result http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: surrounds TUI: T176 Definition: Establishes the boundaries for, or defines the limits of another physical structure. This includes limits, bounds, confines, encloses, and circumscribes. Inverse: surrounded_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: traverses TUI: T177 Definition: Crosses or extends across another physical structure or area. This includes crosses over and crosses through. Inverse: traversed_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: performs TUI: T188 Definition: Executes, accomplishes, or achieves an activity. Inverse: performed_by http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: physically_related_to TUI: T132 Definition: Related by virtue of some physical attribute or characteristic. Inverse: physically_related_to http:// ifomis.de
UMLS-SN Semantic Relations Semantic Relation: conceptually_related_to Definition: Related by some abstract concept, thought, or idea. Inverse: conceptually_related_to http:// ifomis.de
Prototypicality Biological classes are marked always by an opposition between standard or prototypical instances and a surrounding penumbra of non-standard instances How solve this problem: restrict range of instance variables x, y, to standard instances? Recognize degrees of instancehood? (Impose topology/theory of vagueness on classes?) http:// ifomis.de
Example: joint anatomy joint HAS-HOLE joint space joint capsule IS-OUTER-LAYER-OF joint meniscus IS-INCOMPLETE-FILLER-OF joint space IS-TOPO-INSIDE joint capsule IS-NON-TANGENTIAL-MATERIAL-PART-OF joint joint IS-CONNECTOR-OF bone X IS-CONNECTOR-OF bone Y synovia synovial membrane IS-BONAFIDE-BOUNDARY-OF joint space http:// ifomis.de
SNOMED RT (2000) already has description logic definitions but it also has some bad coding, which derives from failure to pay attention to ontological principles: e.g. both testes is_a testis http:// ifomis.de
organism anatomical structure fully formed anatomical structure entity physical conceptual object entity organism anatomical structure fully formed anatomical structure body part, organ or organ component http:// ifomis.de
Musculo-Skeletal System etc. Body System Circulatory System Nervous System Immune System Musculo-Skeletal System etc. http:// ifomis.de
UMLS Semantic Network entity event physical conceptual object entity http:// ifomis.de
P1. entities in different highest-level categories (independent continuant, dependent continuant, occurrent) should not be combined within a single class; P2. objects should not be combined within a single class with the roles they play or with the functions they exercise; P3. entities in reality should not be combined within a single class with our knowledge about or with our concepts of such entities; P4. what is concrete (what exists in space and time and enters into causal relations) should not be combined within a single class with what is abstract (for example with abstract spatial regions, measures, and the like); P5. classifications should respect the factor of time; for example classes should be assigned in a way that is consistent with the fact that continuant entities endure through time. http:// ifomis.de
Anatomical Structure – (Embryonic Structure; Fully Formed Anatomical Structure; Anatomical Abnormality): Anatomical Structure is defined as: “A normal or pathological part of the anatomy or structural organization of an organism.” Note that in the phrase ‘structural organization’, the term ‘organization’ is not used in conformity with SN’s own definition (see below) as meaning ‘social organization’. Rather it is used to mean an entity’s Bauplan. The latter, however, would be, not a concrete three-dimensionally extended independent thing but rather some dependent abstract feature which gives shape and functionality to an entity of this sort. Then, however, it should not subsume liver or leukocyte. http:// ifomis.de
The UMLS Semantic Network is ‘an upper-level ontology … in which all concepts are given a consistent and semantically coherent representation’. Alexa McCray, “An upper level ontology for the biomedical domain”. Comp Functional Genomics 2003; 4: 80-84. http:// ifomis.de
BUT THEY NEVER IN FACT LOOK AT THE REFERENTS AT ALL! Concepts CEN/TC251 ENV 12264 : This ENV is applicable to the description of the categorial structure of systems of concepts supporting computer-based terminological systems, including coding systems, for health-care. concept : “unit of thought constituted through abstraction on the basis of properties common to a set of one or more referents” BUT THEY NEVER IN FACT LOOK AT THE REFERENTS AT ALL! ISO/TC215/N142: Health informatics —Vocabulary of terminology The purpose of this International Standard is to define a set of basic concepts required to describe and discuss formal representation of concepts and characteristics, for use especially in formal computer based concept representation systems. concept: “unit of knowledge created by a unique combination of characteristics” THEY ARE ALREADY TWO LEVELS REMOVED FROM THE REFERENT! http:// ifomis.de
Chemical Chemical Chemical Viewed Viewed Structurally Functionally Inorganic Organic Enzyme Biomedical or Chemical Chemical Dental Material http:// ifomis.de
Genbank gene =df DNA region of biological interest with a name and that carries a genetic trait or phenotype http:// ifomis.de
Why is this a problem? All biomedical ontologies and terminology systems must make themselves conform to the UMLS Semantic Network Foundational Model of Anatomy divides body parts into physical entities and conceptual entities ‘with some regret’ … http:// ifomis.de
Entities http:// ifomis.de
Entities universals (classes, types, roles …) particulars (individuals, tokens, instances …) Axiom: Nothing is both a universal and a particular http:// ifomis.de
Two Kinds of Elite Entities classes, within the realm of universals instances within the realm of particulars http:// ifomis.de
Entities classes http:// ifomis.de
Entities classes* *natural, biological http:// ifomis.de
Entities classes of objects different axioms for classes of functions, processes, etc. http:// ifomis.de
Entities classes instances http:// ifomis.de
Classes are natural kinds Instances are natural exemplars of natural kinds (problem of non-standard instances must be dealt with also) http:// ifomis.de
Entities classes instances instances penumbra of borderline cases http:// ifomis.de
Entities classes junk junk instances junk example of junk: beachball desk http:// ifomis.de
Primitive opposition between universals and particulars variables A, B, … range over universals variables x, y, … range over particulars http:// ifomis.de
Primitive relations: inst and 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 http:// ifomis.de
Entities human inst Jane http:// ifomis.de
Entities human Jane’s heart part Jane http:// ifomis.de
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 http:// ifomis.de
Definitions Theorem: Nothing can be both an instance and a class class(A) =def x inst(x, A) instance(x) = defA inst(x, A) Theorem: Nothing can be both an instance and a class http:// ifomis.de
Axiom of Extensionality Classes which share identical instances are identical (need to take care of the factor of time) http:// ifomis.de
differentiae (roles, qualities…) Entities classes differentiae (roles, qualities…) x, y, … http:// ifomis.de
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 http:// ifomis.de
role http:// ifomis.de
A is_a B genus(A) species(A) instances http:// ifomis.de
A is_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 http:// ifomis.de
nearest species nearestspecies(A, B)=def A is_a B & C ((A is_a C & C is_a B) (C = A or C = B) http:// ifomis.de
Definitions lowest species http:// ifomis.de
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) http:// ifomis.de