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Reference Ontologies, Application Ontologies, Terminology Ontologies. Barry Smith http://ontologist.com. GO: the Gene Ontology. 3 large telephone directories of standardized designations for gene functions and products Designed to cover the whole of biology Model for - PowerPoint PPT Presentation

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Page 1: Reference Ontologies, Application Ontologies, Terminology Ontologies

Reference Ontologies, Application Ontologies, Terminology Ontologies

Barry Smithhttp://ontologist.com

Page 2: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO: the Gene Ontology

3 large telephone directories of standardized designations for gene functions and productsDesigned to cover the whole of biologyModel for

fungal ontology, plant ontology,drosophila ontology,etc.

Page 3: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO: the Gene Ontology

GO organized into 3 hierarchies via is_a and part_of

Page 4: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO divided into three disjoint term hierarchies

cellular component ontology

molecular function ontology

biological process ontology

flagellum, chromosome, cell

ice nucleation, binding, protein stabilization

glycolysis, death

Page 5: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO’s is-a

sometimes called instance-ofGO states the law of transitivity for

subsumption as:If A is an instance of Band B is an instance of CThen A is an instance of C

Page 6: Reference Ontologies, Application Ontologies, Terminology Ontologies

The intended meaning of part-of

as explained in the GO Usage Guide is:

can be a part of

GO axiom: flagellum part-of cell, means: “a flagellum is part-of some cells”

Page 7: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO Usage Guide:

“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”

Page 8: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO, too, is centered around two foundational relations ‘is a’ and ‘part of’. The former it uses consistently and in a way which is in accord with our definition D1 above, though GO’s literature sometimes designates it, incorrectly, as ‘is an instance of’. The relation ‘part of’, in contrast, is used by GO in at least three ways. First, in assertions like ‘Cell Component part of Gene Ontology’, to represent inclusion relations between vocabularies. Second, to represent a time-dependent mereological relation between classes that is specified only informally:

Third, in examples such as flagellum part of cell, to stand for a variant of our part_for defined in D2 above.

GO’s first usage represents a simple inclusion relation between lists. Its second usage would seem to correspond formally to:

D10 A sometimes_part_ofGO B =def t x y ( inst(x, A, t) & inst(y, B, t) & part(x, y, t) ).

definitions in which the use of identical terms in different systems

Page 9: Reference Ontologies, Application Ontologies, Terminology Ontologies

A is part of B, on this reading, if there is some time at which an instance of A is an instance of B.

It’s third usage suggests a definition along the lines of:D11 A part_ofGO B =def C (C is_a B & A part_of C),according to which A is part of B means: there is some subclass C of B

for which A part_of C.Against this background GO’s Usage Guide [18] lists four ‘logical

relationships’ between its ‘is a’ and ‘part of’ relations, which can be summarized in our terms as follows:

(1) (A part_ofGO B & C is_a B) A part_ofGO C(2) is_a is transitive(3) part_ofGO is transitive(4) (A is_a B & C part_ofGO A) C part_ofGO B.

Page 10: Reference Ontologies, Application Ontologies, Terminology Ontologies

(1)–(3) are accepted by GO; (4), on the other hand, is rejected. Yet there are many cases for which (1) fails. For example:

hydrogenosome part_ofGO cytoplasm

sarcoplasm is_a cytoplasmBut not: hydrogenosome part_ofGO

sarcoplasm.

Page 11: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO: the Gene Ontology

3 large telephone directories of standardized designations for gene functions and productsDesigned to cover the whole of biologyModel for

fungal ontology, plant ontology,drosophila ontology,etc.

Page 12: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO: cell fate commitment

Definition: The commitment of cells to specific cell fates and their capacity to differentiate into particular kinds of cells.

Page 13: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO: asymmetric protein

localization involved in cell

fate commitment

Page 14: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO: the Gene Ontology

GO organized into 3 hierarchies via is_a and part_of(No links between hierarchies)

Page 15: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO divided into three disjoint term hierarchies

cellular component ontology

molecular function ontology

biological process ontology

flagellum, chromosome, cell

ice nucleation, binding, protein stabilization

glycolysis, death

Page 16: Reference Ontologies, Application Ontologies, Terminology Ontologies

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”

Page 17: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO Usage Guide:

But examples like Cellular Component Ontology is part-of Gene Ontology

and a flagellum is part-of some cells

make it clear that there are in fact two further uses of part-of in GO

Page 18: Reference Ontologies, Application Ontologies, Terminology Ontologies

Three meanings of part-of

1. inclusion relations between vocabularies (lists of terms)

2. A time-dependent mereological inclusion relation A sometimes_part_of B =def t x y

(inst(x, A, t) & inst(y, B, t) & part(x, y, t)).

3. Some (types of) Bs have As as parts: A part_ofGO B =def C (C is_a B & A part_of C)

Page 19: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO’s Usage Guide

lists four ‘logical relationships’ between its ‘is a’ and ‘part of’:

(1) (A part_ofGO B & C is_a B) A part_ofGO C(2) is_a is transitive(3) part_ofGO is transitive

(4) (A is_a B & C part_ofGO A) C part_ofGO B.

Page 20: Reference Ontologies, Application Ontologies, Terminology Ontologies

(1) (A part_ofGO B & C is_a B) A part_ofGO C

hydrogenosome part_ofGO cytoplasm

sarcoplasm is_a cytoplasmBut not: hydrogenosome part_ofGO

sarcoplasm.

Page 21: Reference Ontologies, Application Ontologies, Terminology Ontologies

(2) is_a is transitive

GO states the law of transitivity for subsumption as:

If A is an instance of Band B is an instance of CThen A is an instance of C

Page 22: Reference Ontologies, Application Ontologies, Terminology Ontologies

(3) part_ofGO is transitive

As concerns (3), consider:plastid part_ofGO cytoplasmcytoplasm part_ofGO cell (sensu

Animalia)But not: plastid part_ofGO cell (sensu Animalia).

Page 23: Reference Ontologies, Application Ontologies, Terminology Ontologies

(4) (A is_a B & C part_ofGO A) C part_ofGO B

GO justifies its rejection of (4) with the following:

meiotic chromosome is_a chromosome synaptonemal complex part_ofGO meiotic

chromosome But not necessarily:

synaptonemal complex part_ofGO chromosome

Page 24: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO’s Four Logical Relationships

(1) (A part_ofGO B & C is_a B) A part_ofGO C

(2) is_a is transitive(3) part_ofGO is transitive

(4) (A is_a B & C part_ofGO A) C part_ofGO B.

Page 25: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO’s Four Logical Relationships

(1) (A part_ofGO B & C is_a B) A part_ofGO C

(2) is_a is transitive(3) part_ofGO is transitive

(4) (A is_a B & C part_ofGO A) C part_ofGO B.

Page 26: Reference Ontologies, Application Ontologies, Terminology Ontologies

On the definitionA part_ofGO B =def C (C is_a B & A part_of C)

(4) can be proved as a matter of logic.

Page 27: Reference Ontologies, Application Ontologies, Terminology Ontologies

The problem of ontology alignment

GOSCOPSWISS-PROTSNOMEDMeSHFMA

…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

Page 28: Reference Ontologies, Application Ontologies, Terminology Ontologies

Formal Theory of Is_a and Part_of for Bioinformatics Ontology

Alignmententity two kinds of elite entities: instances and classesClasses are natural kindsInstances are natural exemplars of natural kinds(problem of non-standard instances)variables x, y for instances, A, B for classes

Page 29: Reference Ontologies, Application Ontologies, Terminology Ontologies

Two primitive relations: inst and part

inst(Jane, human being)part(Jane’s heart, Jane’s body)

A class is anything that is instantiatedAn instance as anything (any individual) that

instantiates some class

Page 30: Reference Ontologies, Application Ontologies, Terminology Ontologies

Two primitive relations: inst and part

Axioms governing inst : (1) it holds in every case between an instance and a

class, in that order; (2) that nothing can be both an instance and a class.

Axioms governing part (= ‘proper part’) (1) it is irreflexive (2) it is asymmetric (3) it is transitive (+ usual mereological axioms)

Page 31: Reference Ontologies, Application Ontologies, Terminology Ontologies

Further axioms (for ‘naturalness’)

In addition we need axioms specifying the properties of classes as natural kinds rather than arbitrary collections+ axioms dealing with the different sorts of classes (of objects, functions, processes, etc.) + axiom of extensionality: classes which share identical instances are identical

Page 32: Reference Ontologies, Application Ontologies, Terminology Ontologies

DefinitionsD1 A is_a B =def x (inst(x, A) inst(x, B))

D2 A part_for B =def x ( inst(x, A) y ( inst(y, B) & part(x, y) ) )

D3 B has_part A =def y ( inst(y, B) x ( inst(x, A) & part(x, y) ) )

human testis part_for human being, But not: human being has_part human testis.

human being has_part heart, But not: heart part_for human being.

Page 33: Reference Ontologies, Application Ontologies, Terminology Ontologies

part_of

D4 A part_of B =def A part_for B & B has_part A

This defines an Egli-Milner order It guarantees that As exist only as parts of

Bs and that Bs are structurally organized in such a way that As must appear in them as parts.

part_of NOT a relation between classes!

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Analogous distinctions required for nearly all foundational relations of ontologies and semantic

networks:A causes BA is associated with BA is located in Betc.

Reference to instances is necessary in defining mereotopological relations such as spatial occupation and spatial adjacency

Page 35: Reference Ontologies, Application Ontologies, Terminology Ontologies

We can prove: is_a is reflexive and antisymmetric

Axiom: part_of is irreflexive

We can prove that part_of is asymmetric

We can prove that both is_a and part_of are transitive

Page 36: Reference Ontologies, Application Ontologies, Terminology Ontologies

Classes vs. Sums

Classes are distinguished by granularity: they divide up the corresponding domain into whole units or members, whose interior parts and structure are traced over. The class of human beings is instantiated only by human beings as single, whole units.

A mereological sum is not granular in this sense.

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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”

Page 38: Reference Ontologies, Application Ontologies, Terminology Ontologies

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?)

Page 39: Reference Ontologies, Application Ontologies, Terminology Ontologies

Classes vs. SetsBoth classes and sets are marked by granularity –

but sets are timelessEach 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.

But 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 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.

A class is not determined by its instances as a state is not determined by its citizens.

Page 40: Reference Ontologies, Application Ontologies, Terminology Ontologies

Classes vs. Sets

A set with n members has in every case exactly 2n subsetsThe subclasses of a class are limited in number(which classes are subsumed by a larger class is a matter for empirical science to determine)

Page 41: Reference Ontologies, Application Ontologies, Terminology Ontologies

Classes vs. 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. A class can survive changes in the stock of its instances because classes exist in time. (An organism can similarly survive changes in the stock of cells or molecules by which it is constituted.)

D1* A is_a B =def t x ( inst(x, A, t) inst(x, B, t) ),

D1* will take care of false positives such as adult is_a child

Page 42: Reference Ontologies, Application Ontologies, Terminology Ontologies

ConclusionWork on biomedical ontologies and terminologies grew

out of work on medical dictionaries and nomenclatures, and has focused almost exclusively on classes (or ‘concepts’) atemporally conceived (IN FACT IT HAS FOCUSED ON TERMS).

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 of definitions in which the use of identical terms (like ‘part’) in different systems has been allowed to mask underlying incompatibilities.

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ConclusionMatters have not been helped by the fact that

description logic, the prevalent framework for terminology-based reasoning sys tems, has with some recent exceptions 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 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.

There are two complementary tasks: REFERENCE ONTOLOGY and APPLICATION ONTOLOGY

Page 44: Reference Ontologies, Application Ontologies, Terminology Ontologies

GO’s curators accordingly now consider removing the corresponding assertion from its Usage Guide.

As concerns (3), consider:plastid part_ofGO cytoplasmcytoplasm part_ofGO cell (sensu Animalia)

But not: plastid part_ofGO cell (sensu Animalia).While ‘cell (sensu Animalia)’ is not a term in GO, it does conform to GO’s rules

for term formation, and this suggests reason for some uncertainty also as to the validity of (3).

GO justifies its rejection of (4) with the following example:meiotic chromosome is_a chromosome

synaptonemal complex part_ofGO meiotic chromosome But not necessarily:

synaptonemal complex part_ofGO chromosome.

Page 45: Reference Ontologies, Application Ontologies, Terminology Ontologies

On the reading of GO’s ‘part of’ as meaning ‘can be part of’, however, it seems that synaptonemal complex is ‘part of’ chromosome. And if the reading of GO’s ‘part of’given in D11 is correct, then (4) can indeed be proved as a matter of logic.

We suggest that it is only by appeal to formal definitions that these and related uncertainties (detailed in [[19]]) can be resolved. Formal definitions would help to ensure also that when the terms of controlled vocabularies like GO are mapped into the UMLS Metathesaurus then this is done in ways that support the drawing of reliable inferences concerning relations between these terms and existing terms in the Metathesaurus.

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The growth of bioinformatics has led to an increasing number of evolving ontologies which must be correlated with the existing terminology systems developed for clinical medicine. A critical requirement for such correlations is the alignment of the fundamental ontological relations used in such systems, above all the relations of class subsumption (is_a) and partonomic inclusion (part_of). To achieve this end, however, existing clinical and evolving bioinformatics terminologies need to call upon formalisms whose significance was not evident at the time these resources were originally conceived.

Page 47: Reference Ontologies, Application Ontologies, Terminology Ontologies

Both is_a and part_of are ubiquitous in bioinformatics ontologies and terminologies. Yet their treatment is inconsistent and problematic, and in some cases the two relations are not clearly distinguished at all. SNOMED-RT, for example, has: both testes is_a testis. UMLS has: plant leaves is_a plant.

In this communication we argue that a coherent treatment of is_a and part_of must be based on explicit formal definitions which take into account not only the classes involved as terms of these relations but also the instances of these classes. We base our arguments on the lessons we learned during the evolution of the Digital Anatomist Foundational Model of Anatomy (FMA, for short [[1]]) in which we have refined the treatment of these relations over time and distinguished between classes and instances in terms of canonical and instantiated anatomy. [[2]]

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Our objectives are to define canonical and instantiated anatomy before giving formal definitions of is_a and part_of in terms of a theory of instantiation. We then discuss in this light issues of universal relevance to ontologies, such as classes vs. wholes and sets, granularity, idealization, and the role of time and change. After illustrating problematic usage of is_a and part_of we draw conclusions for ontology alignment, pointing to the need for supplementing Description Logic-based reasoning implementations with rigorous manual auditing of underlying data-sources based on formal analyses in terms of instance-level relations and on clear and intuitive principles of curation.

Canonical and Instantiated Anatomy

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Canonical anatomy is a field of anatomy (science) that comprises the synthesis of generalizations based on anatomical observations that describe idealized anatomy (structure). These generalizations have been implicitly sanctioned by their usage in anatomical discourse. Instantiated anatomy is a field of anatomy (science) that comprises anatomical data pertaining to individual instances of organisms and their parts. Instantiated anatomy is needed to support the application of biomedical knowledge in clinical care and in fields such as image analysis. The corresponding instance-data is not incorporated into the FMA, which deals with idealizations at a higher level of abstraction. In introducing the relation between canonical and instantiated anatomy, however, the FMA provides the key to an adequate formal treatment of is_a and part_of, for the latter can be defined and formally interrelated only when the relation of instantiation between instances and classes is taken into account.

Page 50: Reference Ontologies, Application Ontologies, Terminology Ontologies

Formal Theory of Is_a and Part_ofWe use the term entity as a universal ontological term of art

embracing objects, processes, functions, structures, times and places, and we distinguish among entities in general two special sub-totalities, called instances and classes, respectively. Instances are individuals (particulars, tokens) of special sorts. Thus each is a simply located entity, bound to a specific (normally topologically connected) location in space and time. [[3]] Classes (also called universals, kinds, types) are multiply located; they exist in their respective instances.

Page 51: Reference Ontologies, Application Ontologies, Terminology Ontologies

To formalize these notions we use standard first-order logic with variables x, y, x1, etc. ranging over instances, and A, B, A1, etc. ranging over classes. Our system rests on two primitive relations of inst and part. Inst is the relation of instantiation between instances and classes, illustrated by: Jane is an instance of human being. Part is the relation of parthood among instances, illustrated by: Jane’s heart is part of Jane’s body. We define a class as anything that is instantiated; an instance as anything (any individual) that instantiates some class.

The principal axioms governing inst are: (1) that it holds in every case between an instance and a class, in that order; and (2) that nothing can be both an instance and a class.

The axioms governing part (also called ‘proper part’) can be specified as follows [[4]]. It is (1) irreflexive (no entity is part of itself), (2) asymmetric (if part(x, y) then not-part(y, x)), and (3) transitive (if part(x, y) and part(y, z), then part(x, z)). In addition, it satisfies: (4) a principle governing the formation of sums of parts (for example of binary sums x+y), and (5) a remainder axiom, to the effect that if part(x, y) then there is some part z of y which does not share parts in common with x.

We use the standard quantifiers of first-order logic: , abbreviating for some value of, and , abbreviating for all values of. The device of quantification allows us to take account of instantiation in generic fashion, i.e. without the need to take specific instances into account. The full formalism requires general axioms specifying the properties of classes as natural kinds (rather than arbitrary collections) [[5]], together with more specific axioms dealing with the different sorts of classes (of objects, functions, processes, pathways, sites, etc.) in the different domains of biomedical ontology. It also requires an axiom of extensionality, to the effect that classes which share identical instances are themselves identical.

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We can now define is_a, the relation of class subsumption:D1A is_a B =def x ( inst(x, A) inst(x, B) ) where ‘’ abbreviates: if ... then .... To say that A is_a B is to say that

every instance of A is an instance of B. To define part_of is more tricky. We start by defining:D2A part_for B =def

x ( inst(x, A) y ( inst(y, B) & part(x, y) ) ).D2 provides information primarily about As; it tells us that As do not

exist except as instance-level parts of Bs. Conversely:D3B has_part A =def

y ( inst(y, B) x ( inst(x, A) & part(x, y) ) )provides information primarily about Bs; it tells us that Bs do not exist

except with As as instance-level parts.

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Because there are female as well as male human beings, we can state: human testis part_for human being, but we cannot state: human being has_part human testis. Because non-human vertebrates also have hearts, we can state human being has_part heart, but not: heart part_for human being.

We now define the relation part_of by combining D2 and D3:D4 A part_of B =def A part_for B & B has_part A Thus A part_of B if and only if: (i) for any instance x of A there is some instance

y of B which is such that x stands to y in the instance-level part relation, and vice versa: (ii) for any instance y of B there is some instance x of A which is such that x stands to y in this same relation. This yields a strong structural mereological tie between the classes A and B (defining a so-called Egli-Milner order [[6]]). It guarantees that As exist only as parts of Bs and that Bs are structurally organized in such a way that As must appear in them as parts. That partonomies like those associated with the FMA are structured by the full part_of relation is ensured by the fact that here all terms for body parts are assumed to have an implicit prefix designating the type of organism involved.

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Sometimes we need to capture mereological relations involving specific numbers of instances. Thus in a case like human being has_part brain, we need to express that each instance of human being has exactly one instance of brain as part:

inst(x, human) yz((inst(z, brain) & part(z, x)) z = y)

with generalizations to represent a human being’s canonical organization as having two lungs, ten fingers, and so on.

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Both is_a and part_of are standardly treated as relations between classes. The formal structure of D4 makes it clear, however, that the latter does not signify that classes stand in some special class-level mereological inclusion relation. Rather, it expresses more fundamental part-relations – captured in D2 and D3 – between the underlying instances.

A distinction analogous to that between D2, D3 and D4 is indispensable to the formal definition of many other foundational relations of biomedical ontologies – including 53 of the 54 relations contained in the UMLS Semantic Network (UMLS-SN, Version 2003AB) [[7]]. In particular, reference to instances is a necessary first step in the rigorous implementation, in systems like the FMA, of mereotopological relations such as spatial occupation and spatial adjacency, as also of concepts such as junction, boundary, cluster, and the like. [1,[8],[9]]

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We can then prove that is_a is reflexive (for every class A we have: A is_a A), and antisymmetric (if A is_a B and B is_a A, then A and B are identical).

We need to add as axiom that part_of is irreflexive (that no class is part_of itself). From this we can prove that part_of is also asymmetric (if A part_of B then not-B part_of A).

We can prove also that both is_a and part_of are transitive: thus if A is_a B and B is_a C, then A is_a C, and if A part_of B and B part_of C then A part_of C.

Classes vs. Wholes: Granularity and Idealizationhas 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. [[20]]) 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.

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A rigorous system of formal definitions to support biomedical ontology alignment must clarify also the relations between the concept of class, mereological whole and set. Here, too, the reference to instances is indispensable. For classes are distinguished by the fact that they capture their instances in a way which involves the factor of granularity, which means: in such a way as to divide up the corresponding domain into whole units or members, whose interior parts and structure are traced over. [[10]] A mereological sum is not granular in this sense. The mereological sum of human beings comprehends also all instance-level parts (including organs, cells, molecules, and so on). The class of human beings, in contrast, is instantiated only by human beings as single, whole units.

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The instances (units, members) in a class are marked out by the fact that, in the Aristotelian terms used by the FMA, they share a common essence. [[11],[12]] Which classes exist in a given domain is a matter for empirical research. Hence a good first clue to the existence of a class is provided by the fact that there exists a corresponding term that has either been sanctioned by (in our case anatomical) science or can be inferred from terms so sanctioned by the need to fill gaps in the taxonomy or partonomy (for example terms for higher-level classes and for not previously named classes instantiated by macroscopic parts of the body) [[13]]. In anatomy and related disciplines a supplementary clue may be provided through the association of given classes with the structural genes whose coordinated expression gives rise to the corresponding instances.

Each class-definition in the FMA specifies the essence shared by the corresponding instances via the specification of (i) a genus, which is some wider class to which the given class belongs, together with (ii) the differentiae which mark out its instances within this wider class.

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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.

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Classes vs. Sets: Granularity and TimeSets 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.

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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.

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Taxonomy and PartonomyA 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).

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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]]

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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.

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ConclusionPractitioners 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 des crip tion logic, the pre valent frame work for ter mi no logy-based reas on ing sys tems, 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 frame work like that of description logic. At the same time, however, we must ensure that the data that serves as input to such sys tems is organized formally in a way that sus tains 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.

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WordNetI just read the Smith/Rosse paper and am thrilled that it addresses several very specific questions that WordNet has never faced.

While we do have subsumption and meronymy relations in the same sense that S&R define them (nicely and formally), WordNet could never deal with what I jokingly call "optional" body parts, like warts, freckles, etc. Nor "temporaray optional" body parts like fetus or "five-o'clock shadow."S&R can deal nicely with these.

ALso, WN has artificial lexical nodes like "female_body" and "male_body," which would be instances in S&R?

To be sure that I understand the granularity question right: Would that be the way to deal with statements that "a fingernail is part of an arm," which, though true, are linguistically odd, because people tend to restrict partonymy to more or less adjacent parts and wholes. However, it is *not* odd to say "a fingernail is a part of the human body."Perhaps we don't have to worry about linguistically odd sentences when we want to explore probability judgements.

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WordNetMeronymy builds a pair of lexical relations together with holonymy. Some morenaive lexicon theories would specify

wheel   IS A MERYNYME OF / IS A PART OF   carcar   IS A HOLONYME OF / HAS A PART CALLED   wheel

I haven't heard Christiane's opinion about this, but I'm sure that WordNetrepresents holonymy quite sparingly since it is not the inversion of meronymy.For monotonic reasoning purpose, holonymy could only be used to representsomething like 'essential parthood' = 'an A always has a B as its part'. SoWordNet normally gives trivial holonymic relations which, in my opinion, arejust analytically true (in Kant's sense: true by definition). Note that they donot dare for instance to give 'car' or 'vehicle' as a holonyme of wheel:

wheel -- PART OF: wheeled vehiclesteering wheel, wheel -- PART OF: steering system, steering mechanism

You see, that's like saying 'an aggregate of a stone and an egg has a stone asone of its parts'

Representing meronymes, they rightly are much more generous:

car, auto, automobile, machine, motorcar --    HAS PART: air bag    HAS PART: glove compartment    etc.

(The way of presenting the data in Online-WordNET is quite confusing. Theywrite:

A -- HAS PART: B

but what they really mean is

B -- IS A PART OF: A

It's just due to the fact that user query for a wordform A, and then look forall the B's that are meronymes of A. I think they should write something like'A -- IS THE WHOLE OF: B'.)

In non-lexical semantics, the mereological asymmetry has hardly any effects, asfar as I know... There are some rumors though that bridging via mereologicalrelations is easier from PART to WHOLE than vice versa:

Two years ago, Peter bought a farm. He restored THE BARN last fall.     PART ->WHOLELast year, Peter restored a barn. He bought THE FARM two years ago.  WHOLE ->PART

If  this is due to asymmetry of part/whole there should be psycholinguisticevidence for that...

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FMA1. All of the slots whose names begin with a colon, and whose names are inall capital letters, are system slots. These are part of the Protégé 2000frame-based system that we use. We did not create these.2. Not all of the relationships in this list are currently in use. Some areold, while others we have not began entering values. I will try and generateanother list for you soon that contains only slots that are in use.3. Some of these relations are attributes on relations themselves (i.e. the'adjacency' relation has several sub-relationships that serve to qualify themain relationship such as 'value', 'coordinate', and 'laterality'). Imention this just to explain that not all relationships in the FMA relateclasses to classes, naturally. Some relate slots to slots, or classes toprimitives, or instances to primitives, for example.

Now, as for definitions of these relationships, we have not yet formalizedthese. Although we know in our heads what these relationships mean (so thatwe can populate them) we have not written concise, human readable,descriptions. This is a high priority on our to-do list. We would like tohave precise definitions both as plain text and in a formal logicalrepresentation for each of these relationships. Please let me know what elsewe can provide you with now.

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UMLS-SN

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FMAclinical part ofconstitutional part offormsgeneral part ofmember ofnecessary partnecessary wholepart ofpossible partregional part ofrelated partsecondary segmental supply ofsegmental composition ofsegmental contribution tosystemic part of

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UMLS-SN Semantic Relations

Semantic Relation: affectsTUI: T151Definition: 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

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UMLS-SN Semantic Relations

Semantic Relation: associated_withTUI: T166Definition: has a significant or salient relationship to.Inverse: associated_with

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UMLS-SN Semantic Relations

Semantic Relation: carries_outTUI: T141Definition: Executes a function or performs a procedure or activity. This includes transacts, operates on, handles, and executes.Inverse: carried_out_by

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UMLS-SN Semantic Relations

Semantic Relation: causesTUI: T147Definition: 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

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UMLS-SN Semantic Relations

Semantic Relation: conceptual_part_ofTUI: T160Definition: Conceptually a portion, division, or component of some larger whole.Inverse: has_conceptual_part

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UMLS-SN Semantic Relations

Semantic Relation: conceptually_related_toTUI: T158Definition: Related by some abstract concept, thought, or idea.Inverse: conceptually_related_to

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UMLS-SN Semantic Relations

Semantic Relation: consists_ofTUI: T172Definition: 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

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UMLS-SN Semantic Relations

Semantic Relation: containsTUI: T134Definition: Holds or is the receptacle for fluids or other substances. This includes is filled with, holds, and is occupied by.Inverse: contained_in

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UMLS-SN Semantic Relations

Semantic Relation: derivative_ofTUI: T178Definition: 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

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UMLS-SN Semantic Relations

Semantic Relation: developmental_form_ofTUI: T179Definition: An earlier stage in the individual maturation of.Inverse: has_developmental_form

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UMLS-SN Semantic Relations

Semantic Relation: evaluation_ofTUI: T161Definition: Judgment of the value or degree of some attribute or process.Inverse: has_evaluation

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UMLS-SN Semantic Relations

Semantic Relation: exhibitsTUI: T145Definition: Shows or demonstrates.Inverse: exhibited_by

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UMLS-SN Semantic Relations

Semantic Relation: functionally_related_toTUI: T139Definition: Related by the carrying out of some function or activity.Inverse: functionally_related_to

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UMLS-SN Semantic Relations

Semantic Relation: indicatesTUI: T156Definition: Gives evidence for the presence at some time of an entity or process.Inverse: indicated_by

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UMLS-SN Semantic Relations

Semantic Relation: ingredient_ofTUI: T202Definition: Is a component of, as in a constituent of a preparation.Inverse: has_ingredient

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UMLS-SN Semantic Relations

Semantic Relation: isaTUI: T186Definition: The basic hierarchical link in the Network. If one item "isa" another item then the first item is more specific in meaning than the second item.Inverse: inverse_isa

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UMLS-SN Semantic Relations

Semantic Relation: issue_inTUI: T165Definition: Is an issue in or a point of discussion, study, debate, or dispute.Inverse: has_issue

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UMLS-SN Semantic Relations

Semantic Relation: location_ofTUI: T135Definition: The position, site, or region of an entity or the site of a process.Inverse: has_location

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UMLS-SN Semantic Relations

Semantic Relation: manifestation_ofTUI: T150Definition: 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

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UMLS-SN Semantic Relations

Semantic Relation: occurs_inTUI: T152Definition: Takes place in or happens under given conditions, circumstances, or time periods, or in a given location or population. This includes appears in, transpires, comes about, is present in, and exists in.Inverse: has_occurrence

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UMLS-SN Semantic Relations

Semantic Relation: part_ofTUI: T133Definition: Composes, with one or more other physical units, some larger whole. This includes component of, division of, portion of, fragment of, section of, and layer of.Inverse: has_part

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UMLS-SN Semantic Relations

Semantic Relation: performsTUI: T188Definition: Executes, accomplishes, or achieves an activity.Inverse: performed_by

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UMLS-SN Semantic Relations

Semantic Relation: physically_related_toTUI: T132Definition: Related by virtue of some physical attribute or characteristic.Inverse: physically_related_to

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UMLS-SN Semantic Relations

Semantic Relation: preventsTUI: T148Definition: Stops, hinders or eliminates an action or condition.Inverse: prevented_by

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UMLS-SN Semantic Relations

Semantic Relation: process_ofTUI: T140Definition: Action, function, or state of.Inverse: has_process

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UMLS-SN Semantic Relations

Semantic Relation: producesTUI: T144Definition: Brings forth, generates or creates. This includes yields, secretes, emits, biosynthesizes, generates, releases, discharges, and creates.Inverse: produced_by

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UMLS-SN Semantic Relations

Semantic Relation: property_ofTUI: T159Definition: Characteristic of, or quality of.Inverse: has_property

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UMLS-SN Semantic Relations

Semantic Relation: result_ofTUI: T157Definition: 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

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UMLS-SN Semantic Relations

Semantic Relation: surroundsTUI: T176Definition: Establishes the boundaries for, or defines the limits of another physical structure. This includes limits, bounds, confines, encloses, and circumscribes.Inverse: surrounded_by

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UMLS-SN Semantic Relations

Semantic Relation: traversesTUI: T177Definition: Crosses or extends across another physical structure or area. This includes crosses over and crosses through.Inverse: traversed_by