towards the ontological foundations of symbolic biological theories

Artificial Intelligence in Medicine (2007) 39, 237—250

http://www.intl.elsevierhealth.com/journals/aiim

Towards the ontological foundations of symbolicbiological theories

Stefan Schulz a,*, Udo Hahn b

aDepartment of Medical Informatics, Freiburg University Hospital, Stefan-Meier-Strasse 26,79104 Freiburg, Germanyb Jena University Language and Information Engineering (JULIE) Lab, Friedrich-Schiller-Universitat Jena,Germany

Received 22 December 2004; received in revised form 5 December 2006; accepted 6 December 2006

KEYWORDSBiomedical ontologies;Biomedical knowledgerepresentation

Summary

Objective: Support for the symbolic representation of the physical structure of livingorganisms by an ontologically solid and logically sound foundation as a basis for formalreasoning.Methods: A set of canonical relations and attributes necessary for empiricallyadequate descriptions of biological entities is proposed.Results: It is shown how a broad range of biological organisms and their parts can berepresented by cascading theories which are ordered by the dimensions of granularity,development, species, and canonicity.Conclusion: The proposed representation of biological objects is non-redundant andcompatible with inter- and intra-species similarities, developmental stages andpathological deviations.# 2006 Elsevier B.V. All rights reserved.

1. Introduction

Biological and medical knowledge is rapidly growing,becoming mutually dependent from each other, andthus is increasingly getting more and more complex.This trend is evidenced by the growth rates of majorbibliographical resources suchasMEDLINE [1], aswell asbiological fact databases [2]. Hence, there is an often

* Corresponding author. Tel.: +49 761 203 3252;fax: +49 761 203 6711.

E-mail address: [email protected] (S. Schulz).

0933-3657/$ — see front matter # 2006 Elsevier B.V. All rights resedoi:10.1016/j.artmed.2006.12.001

stated need for structuring the vast amount of con-ceptual knowledge in these fields in order to easemore effective access to biomedical data. As far asmedicine is concerned, controlled vocabularies, ter-minologies, thesauri, and clinical classification sys-tems have a long tradition to supply semantic metadata for bibliographic searches, coding, and accoun-tancy issues,while biology is embarking on increasingefforts in both species-dependent and species-inde-pendent, carefully crafted ontologies mainly forenriching biological fact databases such as evidencedby theOpenBiomedicalOntologies (OBO)project [3].

rved.

mailto:[email protected]

http://dx.doi.org/10.1016/j.artmed.2006.12.001

238 S. Schulz, U. Hahn

A cursory review of these systems reveals thatmost upper-level descriptions of living systems dis-tinguish between continuants, i.e., entities whichare present in their entirety at any moment of time(such as molecules, tissues, cells, cell components)and occurrents, i.e., time-dependent entities (pro-cesses, actions, states). This distinction has directlybeen incorporated into top-level ontologies such asDOLCE [4], BFO [5], and GOL [6]. It is a well-knownfact that occurrents are dependant entities,whereas continuants are independent ones. In orderto talk about an occurrent, e.g., mitosis, we have totalk about continuants such as the cell nucleus,chromosomes, etc. If we want to describe the struc-ture of a specific cell or biomolecule, however, wedo not need to refer to any occurrent. A closerexamination of continuants and occurrents in thelight of biomedical terminology systems reveals thatthe latter are considered by a large number ofvocabularies supporting clinical encodings, whereasbiology increasingly focuses on continuant entitiesdue to the surge of descriptive data about genes andgene products. Principled descriptions of the phy-sical composition of biological continuants havetherefore attracted growing attention due to theirpivotal role in biomedical ontologies [7—13].

In order to achieve a comprehensive formalrepresentation of living systems, we, first, mightconstruct a multi-purpose reference ontology ofbiological structure, i.e., the physical basis oforganisms. Such an approach should ideally crossthe borders between species, because even organ-isms with largely different phenotypes share inter-esting similarities with regard to tissues, cells,molecules and genes. Hence, knowledge aboutone organism should be re-usable in order to under-stand other organisms as well [14].

Any biological domain ontology should begrounded in an ontological upper level. These toplevel ontologies account for the description of verygeneral categories like space, time, matter, pro-cesses, which are then inherited by the subsumedclasses of the respective domain ontology. The con-straints encoded at the top level can then be used inorder to avoid modeling errors on the domain level.For instance, a top-level constraint such as thedisjointness between continuants and occurrentsis helpful to detect common errors such as the classTumor being both a subclass of Disease and Patho-logical Structure [15].

In terms of domain coverage, a large amount ofterms for biological structure are already repre-sented by vocabularies and ontologies such as theFoundational Model of (Human) Anatomy [16,11],Open Galen [17], the species-independent GeneOntology [18], SNOMED CT [19], and a continuously

increasing number of so-called ‘‘anatomies’’, devel-oped within the OBO framework [3]. However, all ofthese systems are bound to a highly selective view ofbiological structure in terms of developmentalstages, granularity, and species-specific (human,mouse, drosophila, etc.) structure. The anatomy ofeach species is usually built from scratch, althoughthe rough architecture of organisms exhibits consid-erable similarities between species and developmen-tal stages [20]. This creates unnecessary redundancyand hampers semantic interoperability.

An analysis of several OBO ontologies revealsmany commonalities between diverse organisms.Fig. 1 shows a synopsis of several OBO models,together with the Foundational Model of Anatomy(FMA) [8,16,11]. For example, a heart is always apart of some circulatory system. Except in thecase of flies and in the early developmental stagesof the mouse, hearts have chamber(s) and valves.The distinction between heart atriums andventricles exists in fish as well as in mice andhumans.

With the exception of the FMA, which is based onstrict principles and is undergoing a formally rigidredesign, the anatomies of the other species as wellas the (theoretically) species-independent GeneOntology were initially designed as controlled voca-bularies. They were not grounded upon a commonupper ontology, but rather used thesaurus-like rela-tions which lacked a rigid semantics [21]. Clear-cutdistinctions of themeaning of classes and relations —as it is the casewith theFMA—are anecessary but notsufficient requirement for proper ontology design.For example, the decision as to whether an assertionsuch as Has PartðCell;NucleolusÞ holds — given addi-tional assertions such as Has PartðCell;NucleusÞ andHas PartðNucleus;NucleolusÞ — cannot be made,simply because there is no ontological commitmentto either the algebraic properties of Has Part (e.g.,transitivity), or to the dependency status of Nucleuswith regard toCell and vice versa. Only recently,withtheOBO relation ontology [12] a formal foundation ofthe relations to be used in OBO ontologies has beenproposed.

Wherever biological terms and their underlyingmeanings are to be handled not only by humans butalso by machines, domain descriptions should beprovided as sets of formal axioms and theories inorder to allow the computation of inferences. Build-ing such descriptions from a set of formally foundedconceptual relations may be a good starting pointfor a formally adequate treatment of biologicalstructures, a claim which was already raised inthe early 20th Century [22]. In the following sec-tions, we focus on various aspects of conceptualmodeling of biological structure in its broadest

Towards the ontological foundations of symbolic biological theories 239

Figure 1 Comparative heart anatomy (only part-whole links) from OBO biological ontologies and the foundationalmodel of anatomy.

sense, aiming at a foundational ontology for a for-mal theory of biomedical entities.

2. Fundamental relations for biology

In this article, we introduce a canon of foundationalrelations and attributes which are useful to repre-sent temporally invariant regularities between(classes of) biological continuants.1 In mathematicsand philosophical logics, a relation is a subset of aCartesian product of sets. In ontologies, relationsare mostly binary ones. Whereas the term ‘‘founda-tional relation’’ has increasingly been used by

1 We use the following naming conventions: names of classesare formulated in Upper Case initials while names of instances arewritten in lower case letters. Relations in which one or moreinstances are involved are expressed by means of bold faceexpressions and lower case initials. Relations involving classesonly come with Upper Case Initials and Italic Fonts.

different authors in the field of formal and domainontologies, a clear definition is still missing. We heretry to clarify this notion by introducing the followingcriteria:� Foundational relations should be ‘‘primitive’’, in

the sense that they cannot be inferred fromother relations. As an example, the instantiationrelation relates an instance to a class (or a parti-cular to a universal), e.g., inst_ofðmyCat;CatÞ,and cannot be expressed in terms of otherrelations. A counterexample is the relationshared_partðmyDia phragm;myAbdomenÞ, be-cause it can be derived from the assertion thatmyDiaphragm is also part of another structure,viz.myThorax, which overlaps withmyAbdomen.

� F
oundational relations should be self-explanatoryand domain-neutral [12].
� F
oundational relations describe the associations ofentities in reality as they are immediately percei-vable. We here do not consider relations whichare cognitive abstractions of our perception of


Table 1 UMLS semantic network: class-level relations between biological continuants

Relation Inverse relation Relation Inverse relation

isa inverse_isa part_of has_partconceptual_part_of has_conceptual_part contains contained_inlocation_of has_location branch_of has_branchtributary_of has_tributary consists_of constitutesadjacent_to adjacent_to connected_to connected_tointerconnects interconnected_by surrounds surrounded_bydevelopmental_form_of has_developmental_form traverses traversed_by

Table 2 Open biomedical ontologies: class-level relations between biological continuants

Relation Inverse relation Relation Inverse relation

isa has_subclass part_of has_partcontains contained_in adjacent_to adjacent_tolocated_in (location_of) transformation_of (has_transformation)derives_from (has_derivate)

2

be

nature (e.g., Ad jacentðLung; LiverÞ), or probabil-istic assertions, e.g., CausesðSmoking;Cancer;HighlyProbableÞ.

� O
nce the characteristics of the entities the argu-ments of the relation refer to are properly iden-tified, the assertion of a foundational relation isindependent from human cognition. As an exam-ple, the relation has_locationðrhine; euro peÞ candirectly be inferred from their spatial extensions,once their properties (e.g., their exact geogra-phical coordinates) are fixed. A counterexample isan assertion like adjacent_toð france; englandÞ.The truth value of this statement is a matter ofdiscretion even when we do not include the inter-vening sea into the extension of the countries.
We are aware that these criteria reflect a com-mitment to a certain type of ontologies, viz. foun-dational ontologies, which represent those factsabout entities in the world which are generallyassumed to be true. We contend that this approachsuits the necessity of representing biological con-tinuants as they are subject to inquiry in the lifesciences, as well as diagnostic observations andtherapeutic manipulations in clinical practice.

Several attempts have already been made toidentify themost important relations as a backbonefor the construction of biomedical terminologiesand ontologies. We here juxtapose one of the clas-sical approaches, viz. the UMLS semantic network(cf. Table 1), with the most recent proposal, theOBO relations (cf. Table 2).2 In both cases weobserve a phenomenon which is characteristic ofbiomedical ontologies, viz. the relations used

In both cases we restrict ourselves to relations which holdtween biological continuants.

exclusively range over classes of individuals insteadof individuals. This characteristic has far-reachingconsequences which will be repeatedly addressedin this article.

The UMLS relations are more closely relatedto natural language, and they are defined interms of natural language statements, e.g.,has develo pmental formðC;DÞ means ‘‘D is an ear-lier stage in the individual maturation of C’’, orconce ptual part ofðC;DÞmeans ‘‘C is conceptuallya portion, division, or component of some largerwhole D’’. In contradistinction, OBO defines itsclass-level relations referring to the correspondinginstance-level relations. Here the expressiontrans formation ofðC;DÞ is used as an abbreviationfor ‘‘every C at any time is identical with some D atsome earlier time’’.

In the next section we will discuss those relationswhich we consider important for the description ofbiomedical structure. We depart from the sets ofrelations such as introduced in Tables 1 and 2. Forthepurposeofthisarticle,wefocusonanon-temporalview on biological continuants. So we refrain from adiscussion of relations such as transformation_ofand derives_from, which are sufficiently treatedelsewhere [23,12]. The ontological framework wepropose has two axes. One axis describes the assign-ment of entities to classes, as well as relationsbetween classes. The second axis analyzes the spa-tial arrangement of individual entities and proposes,on this basis, inter-class relations which expressmer-eotopological regularities between their instances.

2.1. Instantiation and subclassing

Two relations doubtlessly fulfill the criteria forfoundational relations, viz. subclassing and


instantiation. The instantiation relation relates anindividual with its corresponding class such asinstance_ofðmyCat;CatÞ. This relation is irreflex-ive, intransitive and asymmetric. It is the basis fordefining the subclass (also called taxonomic or Is A)relation which relates classes in terms of increasingspecificity or generality, e.g., Is AðCat;MammalÞ orIs AðAlanin;AminoAcidÞ. In biological and medicalontologies, Is A generally stands for proper subclas-sing, i.e., no class is a subclass of itself. Accordingly,we consider Is A as an asymmetric relation. Itstransitivity follows from the definition (cf. Defini-tion (1)), just as the acyclicity.

Since all instances of a subclass are instances ofthe corresponding superclass(es), all propertiescommon to the instances of the superclass are alsoproperties of the instances of the subclass, corre-sponding to what is called inheritance in the field ofobject-oriented structured knowledge representa-tion.Is AðA;BÞ¼def

8 x : instance ofðx;AÞ! instance ofðx;BÞ (1)

The definition of a class illuminates its distinctivecharacteristics in relation to already defined (moregeneral) classes, following the Aristotelian principleof genus and differentiae [24]. Ideally, propertiesshould not only be necessary but also sufficient.Thus, it is sufficient for an instance of the classHand to have the laterality attribute left, to bereclassified into the class LeftHand. With regard tobiological structures, it is not always easy to finddefining properties: whereas it is straightforward tostate that an index finger is a finger (and everyinstance of index finger inherits all properties ofthe class finger), the differentiae between fingerand index finger can only be expressed by complextopological descriptions.

Taxonomies can either have a monohierarchical(single parent) or a polyhierarchical (multiple par-ent) internal structure. The Foundational Model ofAnatomy (FMA) [8,16,11] adheres to the principlethat huge taxonomies can be represented as strictmonohierarchies. This constitutes, compared toother biomedical taxonomies (e.g., SNOMED CT),an exception rather than a rule.

Union and intersection between classes caneasily be expressed by the Is A relation. FromIs AðA;CÞ and Is AðB;CÞ, it follows that C is the union(disjunction) of A and B, whereas D is the intersec-tion (conjunction) of A with B, given Is AðD;AÞ andIs AðD;BÞ. As an example, the class Extremity is asuperclass (union) of the classes UpperExtremityand LowerExtremity. The class LeftThumb isthe conjunction (intersection) of LeftFinger withThumb.

The relation Dis joint From relates two classeswhich do not have any instance in common:Dis joint FromðA;BÞ¼def

8 x : ðinstance ofðx;AÞ! : instance ofðx;BÞÞ(2)

This is the default assumption for siblings in strictmonohierarchies, in which all classes which do notsubsume each other are, as a consequence,mutually disjoint. But even in taxonomies wheremultiple hierarchies are allowed, most pairs ofclasses are disjoint: an Organ cannot be a Cell, aLeaf cannot be a Fruit, and a Nucleotide cannot be aLipid. The lack of explicit disjointness assertionsgives rise to numerous unintended models whenrepresentation formalisms with an open worldassumption [25] are chosen.

When formalizing classes and instances, the simi-larity to set theory is evident, and, indeed, set theoryis often used as the theoretical basis for the formalmodeling of taxonomies. This equivalence, however,is far less evidentwhenwe take thedimensionof timeinto account. Here, we adhere to the following dis-tinction between sets and classes: whereas sets areidentified by their extension, this is not the case withclasses which may remain the same even if theirinstances change. For example, the class HomoSapiens has preserved its identity across a largeperiod of time, even though almost all of its instancesare completely exchanged every 100 years.

There is an ongoing controversy about whetherclasses are the extension of cognition-independenttypes or universals, or whether they are extensionsof mind-dependent concepts [26]. We do not take anexplicit standpoint on this issue in this paperbecause we argue that our framework is neutralwith regard to this discussion. However, we conjec-ture that ontologies of biological structure shoulddescribe biological objects as they are in reality or,equivalently, in practice, as they are univocallyconceived and conceptualized by biomedicalresearchers.

2.2. Mereotopological relations

2.2.1. Upper levelBesides taxonomies, mereotopological relations,i.e., relations which describe the spatial arrange-ment of physical objects and spaces are of equalimportance for describing tangible objects in biol-ogy. Fig. 2 depicts the graph of relations to beintroduced. It is based upon the basic relationsproposed by the OBO consortium [12], includesthe relations which constitute the framework ofthe RCC theory [27], and builds upon the work onparthood, connection and location by [28]. The


Figure 2 Mereotopological relation hierarchy for biological continuants (relation properties are indicated by shortcutsfor S(ymmetric), T(ransitive), A(symmetric)).

relations are, unless otherwise stated, mutuallyexclusive and exhaustive, at each level (as indicatedby the ‘? ’ symbol in Fig. 2).

The root of the relation hierarchy, the symmetricand transitive relation spatially_related holdsbetween any two different3 continuant entities.First of all, we introduce, according to [29] theregion function r which maps an instance a to theunique spatial region rðaÞ at which a is exactlylocated. Regions are point sets in the Euclideanthree-dimensional space. Two entities a and b areconnected, if their regions rðaÞ and rðbÞ share atleast one common point, otherwise they are spa-tially disconnected.

8 a; b : connectedða; bÞ¼def

9 x; y; z2 E3 : rðx; aÞ ^ rðy; bÞ ^ z2 x \ y (3)

As a general principle, we here extend thedomain and range of relations which are originallymeant to hold between regions only to all kinds ofspatially relevant entities. In this case, two spatial

3 We exclude the identity relation from our dicussion, since wedeny any relevance for it in biomedical ontologies.

entities are connected, iff the regions they occupyare connected.

The relation located inða; bÞ corresponds to atrue subset relation between the two point setsrðaÞ and rðbÞ. The symmetric relationadjacent toða; bÞ means that the two related pointsets have a (two-dimensional or less-dimensional)boundary in common, whereas for the equally sym-metric relation overlapsða; bÞ, the intersectionbetween the two point sets yields a non-empty pointset in a three-dimensional space.

2.2.2. The mereological branchAccording to its point-set-theoretic axiomatizationand to its isomorphism with the proper subset rela-tion, located_in is asymmetric and transitive. loca-ted_in can further be specialized either by part_ofor contained_in, as discussed in [30,31]. Accord-ingly, its inverse, location_of, can be specialized interms of has_part and contains. An object a iscontained_in another one, b, iff a is located inthe region occupied by b without being part of b.Using these mereotopological relations for describ-ing biological reality requires a strict separationbetween mereological and topological notions in


Figure 3 Secretion (top) and phagocytosis (bottom), as examples of where a crisp delimitation between parthood andlocation is problematic.

order to prevent discretionary modeling decisions.This requirement, however, is not easy to fulfill. It isquite difficult to decide whether substances pro-duced, stored, and excreted by exocrine or endo-crine cells are to be considered parts of these cellsas long as they are inside the cell (cf. Fig. 3, top).The same boundary problem applies to a situation inwhich an alien particle or organism (e.g., a virus) isingested by a killer cell. Here the question ariseswhether and when its components (e.g., molecules)become parts of the ingesting cell after decomposi-tion (cf. Fig. 3, bottom). These examples drawattention to the fact that, when dealing with naturalkinds, it can be difficult to decide whether parthoodor containment actually holds. Ontological criteriawhich can be used to draw this line were recentlysuggested by Schulz et al. [32,31]. But even thesecriteria exhibit some epistemological problem,mainly related to the concept of biological function,

so that the common view of part_of as a founda-tional relation is challenged. Refraining from part-hood and using only location as a foundationalrelation in bio-ontologies as suggested in [33] maybe considered another possible solution.

The relation pair located_in/location_of can alsobe specified along another dimension in which thecriterion is, again, a topological one. The relationtangentially_located_in is to be asserted whereverthe interior entity touches the space external to theentity it is located in. It holds between a proteinlocated in the cellmembrane and the containing cell,as well as between a metastasis at the surface of theliver and the liver itself. The relation non_tangen-tially_located_in holds when the located objecthas no contact to the surface, e.g., my stomachin my body, or a mitochondrium in a cell. Subrela-tions such as non_tangentially_contained_in ortangential_part_of are possible. For example,


Figure 4 Left: Trunk (a) with ramifications (b) and (c).Right: Trunk (a0) with a branch (c).

non_tangentially_contained_in holds between thevirus in Fig. 3 and the cell.

In addition, the relation tangentially_located_incan further be specialized by the relation bounds[34]. Subscribing to this view leaves open whether aboundary is part of the spatial entity it bounds oronly of the region the latter occupies.

2.2.3. The topological branchThe refinement of the adjacency relation leads to aset of symmetric relations which are important forthe description of anatomical struture. Our conceptof adjacency is the same as that underlying therelation adjacent_to in the OBO relations [12]. Allsubrelations of the relation adjacent_to relate spa-tial objects, not regions. The criterion of differen-tiation between the relation contiguous_with andtouches is the physical connection between the twoobjects under scrutiny. If the two objects are con-nected by a chemical bond, then we want to assertthe relation contiguous_with, otherwise we assertthe relation touches. An example for touching is thecontact between two serous membranes, orbetween a liquid and its container. The relationcontiguous_with can further be specified accordingto whether there is an intervening (self-connected)object which shares parts with the two objects inquestion. If this is the case we specialize conti-guous_with by attached_to, otherwise we assertthe relation continuous_with. The first one is thenormal case with biological solid entities, becausethere are always macromolecules which bridge twoconnected entities. This is true regardless ofwhether the two entities are separated by a (struc-turally relevant) bona fide boundary [35], such asbetween two layers of a mucosa or an arbitrary fiatboundary (e.g., as between regions of the brain).The relation continuous_with is rather common formolecules in a liquid. For instance, it holds betweentwo neighbor amino acids in a protein molecule.

The relation continuous_with can be further spe-cified by the relation pair ramifies/ramification_ofon the one hand, and branch_of/has_branch on theother hand. These relations are fundamental fordescribing biological structures. Tree-shaped path-ways enable the flow of matter or information inhigher organisms such as blood, lymphatic vesselsand nerves, but may also constitute the buildingprinciple of organisms such as plants or corals. Fortrees, subtrees, and branches we introduce the classbranching structure (BS). A tree consists of a trunkandmanygenerations of branches.A ramification canbe considered a trunk of a higher-order tree. Thedifference between tree and branch (subtree) is thatthey are attached, whereas the two branches onlytouch.More exactly, thismeans that thebranches are

delimited in a way that regions they occupy abut, butwithout any physical connection, according to thedefinition of the relation touches. Ramification canbe formalized as follows:

8 a; b : ramifiesða; bÞ) instance ofða;BSÞ^ instance ofðb;BSÞ ^ attached toða; bÞ^ 9 c : instance ofðc;BSÞ ^ attached toða; cÞ^ touchesðb; cÞ (4)

According to this definition, a tree ends at everybifurcation, cf. Fig. 4 (left) such as with the abdom-inal aorta which bifurcates into the left and rightcommon iliac artery. A different case is where thetrunk does not end with the branch, such as theabdominal aorta related to the renal arteries.Although this is, topologically, not different fromthe first case (compare the two pictures in Fig. 4), itneeds to be distinguished because the commonconceptualization of a tree in biological branchingsystems is that the same trunk contains severalbranching points. We may describe this situationtaking our above axiomatization as a basis and con-sider the ‘‘persisting’’ trunks as mereological sums,in Fig. 4, a0 would then be constituted by the sum ofa and b.

Finally, the relation part_of can be assertedbetween subtrees and trees. A tree can be gener-ated by recursively applying the relations ramifiesand has_branch and adding up the traversed seg-ments.

2.3. Inter-class relations

All themereotopological relations introduced in Sec-tion 2.2.3 exclusively relate individuals. As is com-mon practice in biomedical ontologies, the samerelations are asserted between classes in a ratherintuitive way. Only lately, several ontologists haveanalyzed in detail the class-level relations comparedto instance-level relations [36,37,31,13]. We defineclass-level relations on the basis of instance-level


relations in the following way. The symbol rel standsfor an arbitrary relation between individuals, rel�1

for its inverse relation. We then define the class-to-class relations Rel and Relinv. Note that we can showthat Relinv is not the inverse of Rel, cf. [37].

RelðA;BÞ¼def 8 x : instance ofðx;AÞ)9 y : instance ofðy;BÞ ^ relðx; yÞ (5)

RelinvðA;BÞ¼def 8 x : instance ofðx;AÞ)
9 y : instance ofðy;BÞ ^ rel�1ðx; yÞ
(6)

As an example, Part OfðA;BÞ means that everyinstance of A is part of some instance of B. So isevery cell nucleus part of some cell. Has PartðA;BÞmeans that every instance of A has some instance ofB as its part.

Therefore, analogous class-to-class relationshave to be introduced (e.g., Continuous With),wherever they occur in class definitions, accordingto the definitional scheme (5). It can be shownthat the algebraic properties of class-to-class rela-tions differ from the ones which hold for theirindividual-level counterparts. For instance, con-tinuous_with is symmetric, but Continuous Withis not. Using definition (5), in an individual neuron,the cell body is connected to its axon and viceversa. This contrasts with what we observe at thelevel of classes–—although each axon is connectedto some cell body, not every cell body is connectedto an axon.

3. A sketch of biological theories

(Foundational) relations such as those introducedin the previous section provide a vocabulary bywhich basic biological entities can be related interms of predicates or assertions. Biologicalknowledge, however, is not focused on a singlespecies but rather investigates structures acrossvarious species (or model organisms, from ahuman perspective). It also deals with differentstages of developmental processes related tothese species rather than a single one (e.g., adult-hood). Additionally, a layer of canonical (ideal)descriptions usually has to be supplementedby distinct levels of deviation from this idealdescriptions (e.g., in terms of pathologies).Finally, the level of granularity may vary greatly,e.g., from a macroscopic to a molecular view on aparticular species. The latter aspect, in particular,leads us to a decomposition of biological descrip-tions into groups of local theories, both withregards to scope [38] and in terms of granularity[39,40].

We define a theory as a set of formal axiomswhich describe a restricted (local) domain. Further-more, we design a lattice of theories which takesthree ontological parameters into account, viz.species (S), development (D), and canonicity (C).We discuss, separately, granularity as a fourth para-meter which includes epistemological aspects, butis, nevertheless, a fundamental characteristic ofevery ontology–—not only for the life sciences.

3.1. Species

Given the myriad of biological species, the domainof human anatomy is an extremely restricted andspecialized one. Mediating domains are those ofvertebrates or mammals, for instance. Accordingto the Linnaean classification of organisms, whichis the prototype of a taxonomic order, propertiescan be introduced at any level of the classificatorytree and can be propagated across that tree. Apply-ing a more simplified point of view, Heart denotesthe class of muscular organs which have a cavity andare part of some Circulatory System. These proper-ties hold true for Chordates, Arthropods, and someother phyla. As far as the hearts of more specificorganisms are concerned, additional properties arerequired, e.g., a certain number of ventricles andvalves, the presence of blood or hemolymph, dif-ferent locations of pacemaker cells. Additionally,we have to consider intra-species variations such asgender or race, or the morphological distinctions inbees, ants and other social insects. No surprise thenthat there are several ways of carving out theoriesout of the universe of species.

3.2. Development

Organisms pass through a life cycle from birth todeath. When we understand developmental stagesas snapshot views of reality, each stage has its owncharacteristics. Even distantly related organisms,such as humans and flies, exhibit a high degree ofsimilarity in the first embryonic stages. The exis-tence of many parts of an organism is restricted tocertain stages. For example, in mouse embryos,an ectoderm exists only in the so-called Tannerstages TS9—TS19, and there is no heart beforeTanner stage TS11. Other body parts, e.g., theheart (cf. Fig. 1) appear in a certain embryonicstage and perdure all subsequent steps of the lifecycle.

3.3. Canonicity

Here we introduce the notion of canonicity asthe well-formedness of biological structure, and


Table 3 Ordinal scale of canonicity

Level

1 2 3 4 5

Theory Any amount of matter,if of biological origin

Any living ordead organism

Any livingorganism

Living organism withoutpathologic modifications

Ideal organism

Set of axioms n1 n2 n3 n4 n5n1� n2 n2� n3 n3� n4 n4� n5

define it as the degree by which a biological objectcorresponds to its canonical, i.e., idealized form.We suggest an ordinal scale with five levels ofcanonicity (cf. Table 3). The higher the canonicitylevel themore axioms have to be applied. All axiomsintroduced at a lower level are propagated to allhigher levels. Axioms describing structural modifi-cations specific to a concrete disorder, e.g.,Has PartðStomach;UlcerÞ, are not considered inthis framework.

� L
evel 1 introduces those axioms which holdeven with lethal structural modifications orpost-mortem degeneration, such as Has Partð Erythrocytes; Hemoglobin Þ, Has PartðBone;CalciumÞ, Part Of ðHeartVentricle;HeartÞ,Has PartðLeather; CollagenÞ.
� L
evel 2 introduces all those axioms which hold forthe description of biological structures organizedin an organism, irrespective of whether it is livingor dead, e.g., the axiom Part OfðHeartValve;HeartÞ is introduced at this level, as well asPart OfðCellNucleus;CellÞ.
� In
Level 3 all those axioms are added whichare consistent with living organisms in additionto dead organisms, e.g., Location OfðAorta;BloodÞ, or Has PartðVertebrateBody;HeadÞ.
� L
evel 4 introduces, additionally, all thoseaxioms which characterize a healthy organism,e.g., Has Part ðHand; Thumb Þ and Has PartðGastrointestinalTract; StomachÞ. However, itstill allows anatomical variations when they haveno impact on the proper working of the organism.
� L
evel 5, finally, completes the set of axiomsneeded for the description of the ‘‘ideal’’ organ-ism. At this level, many cardinality constraints(e.g., in human: 32 Teeth, one Spleen, three Lobesof the Right Lung) are entered into the canonicalstructure.
3.4. Granularity

The conceptualization of biology is coined by ourcognition. Macroscopic anatomy is restricted tothe naked eye’s view, histology requires a lightmicroscope, our notions of cell biology are formed

by the electron microscope, and knowledge ofmolecular biology and genetics is gathered usingchemical and physical techniques. Here, granular-ity refers to the level of detail at which organismsare described. Granularity is, therefore, not pri-marily an ontological notion. It is tightly attachedto the way humans observe and conceptualize theworld. We then distinguish three axes of granu-larity:1. Classification. Here, the granularity is conceived

as the degree of subclassing. A fine-grainedontology of cells would, for example, specializecell populations, e.g., Leukocytes, by theclasses Lymphocytes, Granulocytes, and others.A distinction of Lymphocytes into B- and T-Lym-phocytes, and the latter into T4- and T8-lym-phocytes may be required only in fine-grainedtheories, e.g., as needed for the description ofthe pathology of immunodeficiency. It is likelythat a cell ontology with a sophisticated taxon-omy of classes of cells, would not exhibit thesame degree of classification granularity for,e.g., proteins.

2. D
issection. Here, the focus is on the biologicalcontinuants, i.e., the class members themselves.Are they on a macroscopic, on a microscopic, or amolecular level? For example, the Gene Ontology[18] focuses exclusively on biological continuantson a subcellular level, whereas the scope of theFoundational Model of Anatomy is macroscopicanatomy.
3. R
elations. A high level of granularity correspondsto the sophistication of the relation hierarchy,e.g., in terms of the relations introduced above.Even more fine-grained distinctions mayhold between subtle semantic variations of,e.g., the part-of relation (e.g., segment o f;functional part o f; layer o f; shared part o f).
We observe, e.g., a low level of relation gran-ularity in most of the OBO ontologies [3], as theyuse only taxonomic subsumption and parthoodrelations between their classes.

Along these lines, granularity issues may have amajor impact on high-level properties. In a verycoarse-grained view (in terms of dissection granu-larity), one may be apt to abstract a microscopically


thin membrane, such as a basement membrane, to atwo-dimensional boundary, thus completelyneglecting its spatial extent. This has an impactnot only on the sortal differences (degrees of dimen-sionality are mutually disjoint), but also on theconnection of neighboring structures. What maybe defined as externally connected to the nakedeye will appear disconnected under the microscope.

Note that these distinctions are not really onto-logical ones. It is a piece of undisputed evidencethat a biological membrane in reality, extends intothree spatial dimensions. However, we have toacknowledge that many practical purposes (e.g.,the spatial reasoning about macroscopic body parts,for instance in radiology) require drastic abstrac-tions. Here, reasoning about maps of reality maysubstitute reasoning about the real stuff, andobviously it does make sense to talk about a biolo-gical membrane (or better a map of a biologicalmembrane) in terms of a two-dimensional boundary.

3.5. A case study in biological inferencing

A theory can be expressed by a node in the latticeof the three axes viz. S, D, and C (cf. Fig. 5).Hereby, the values development (D), and canoni-city (C) are located on an ordinal scale, whereasthe values of species (S) are given by the nodes ofthe classification of organisms. Each node of thisclassificatory tree introduces properties whichare inherited by its subsequent nodes, e.g.,Is AðFishHeart;VertebrateHeartÞ or Is AðDrosophilaEye;Arthro podEyeÞ. This means that FishHeart inherits all properties from VertebrateHeart and Drosophila Eye inherits all propertiesfrom Arthropod Eye. The same mechanism can beobserved with regard to canonicity. All propertiesthat structures of low canonicity have in common

Figure 5 Schema of canonicity (C), development (D) and spgraph is a magnification of some nodes of the left hand grap

(e.g., Tissue consisting of Cells) are inherited bythe more canonical structures. No such inheri-tance rules apply to the parameters development(D) and granularity (G).

Taking Heart as a prototypical example, we willnow demonstrate practical inferences which aresupposed to be drawn from a biological ontologycapturing formal biological theories, all based onour assumptions:� A heart with four chambers is not compatible,

ech.

e.g., with any theory characterized by S ¼ fish orby S ¼ human and D ¼ 4-week-embryo.

� L
et us assume the relation Ad jacent To which ismaintained between the right and the left ven-tricles. We may then exclude most non-mammals(since they have no right and left ventricle), butwe may also exclude anatomical hearts of adultmammals (because they have a septum betweenthe two ventricles). This scenario is compatiblewith the theories D ¼ embryo and S ¼ mammal aswell as with S ¼ mammal and C ¼ 3.
� T
he assertion Contiguuous withðHeart;Aortic-ArchÞ holds true for all vertebrates beginning witha certain embryonic stage within a given range ofcanonicity. It is compatible with the situation inwhich there is only one aortic arch, as well withsituations where there are two or more aorticarches, e.g., in fish or in early embryonic stages.For these cases, the above assertion can then benarrowed to Rami fiesðHeart;AorticArchÞ.
� G
iven the theory D ¼ adult and S ¼ vertebrateand C ¼ 5, every instance of heart implies thelocation of blood and every instance of blood hasan instance of erythrocytes as part. Assuming thatHas Part implies Location O f and thatLocation O f is transitive, we are able to inferthat, in this theory, every instance of Heart is thelocation of an instance of Erythrocytes, as well.
ies (S) related anatomic theories. The right part of the


Figure 6 Framework of theories for the classification ofbiomedical ontologies.

The above framework can also be used to bettercharacterize and classify biomedical ontologies,such as depicted in Fig. 6.

4. Conclusions

In this paper, we defined requirements for ontolo-gies of biological structure. We introduced a set ofcanonical relations required for the description ofbiological structure and discussed their semanticsand algebraic properties. Finally, we sketched anarchitecture by which terminological knowledge ofthe anatomy of a broad range of organisms, devel-opmental stages, malformations, and pathologicalmodifications can be expressed. A central element isthe decomposition into theories, which help orga-nize the hierarchies and the axioms in terms ofgranularity, developmental stage, species, andcanonicity.

We claim that by using this approach the follow-ing improvements can be achieved:� Redundancies are avoided. Most axioms that

describe the species mice, humans, and dogsare identical and therefore can reasonably beencoded into a more general theory (such asthe one of vertebrates). In turn, the more generaltheory propagates the shared properties to morespecific theories, e.g., the ones pertaining tomice, humans, or dogs. In a similar way, attributesthat healthy and pathologically modified organ-isms have in common are described in the non-canonical theory from which the canonical theoryinherits the shared properties.

� A
dequate theories for a specific application canbe selected. It is neither computationally tract-able nor useful to export the whole knowledge ofbiology into a formalism in which logical opera-tions can be performed, e.g., by a terminologicalreasoner. For example, if we need to reason abouta TS12 mouse embryo, we select the adequateintersection of theories to access the axioms wereally need. Some of these axioms are inheritedfrom the mammal theory, others from the theoryof the vertebrates, and still others come from thetheory of the chordates. Some axioms areencoded in the subtheory of a developmentalstage of the vertebrates, and, last but not theleast, there are some axioms which are onlyspecific to the TS12 mouse embryo.
� T
he intersection of arbitrary theories have vari-able extensions. Nonetheless there are manycases without extensions. The compatibility oftheories can be checked by formal reasoningdevices. For example, a heart with one ventriclein a theory restricted by S ¼ human and D ¼ adultis not compatible with C ¼ canonical.
Whereas the three axes species, development,and canonicity are used to carve out segments ofreality according to the ontology users and providers(e.g., embryologists, geneticists, molecular biolo-gists, surgeons, pathologists), the granularity axisdescribes the ontology artifact itself, not in terms ofits scope for reality, but concerning its fine- orcoarse-grainedness of description, equally in termsof classes, mereotopological dissections, and rela-tions.

We expect that the presented framework pro-vides contextual coordinates for each truth state-ment in a bioontology. As a result, mapping betweenontologies is facilitated, especially with regard tothe avoidance of unintended models which com-monly arise when ontology mapping is based onterm and taxonomy mapping as commonly done inbiomedical informatics.


Acknowledgments

This work was supported by the EU Network ofExcellence ‘Semantic Interoperability and DataMining in Biomedicine’ (NoE 507505), as well asthe EC STREP project ‘‘BOOTStrep’’ (FP6 - 028099).

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