The background to this paper is the now widespread recognition that many existing biological and medical ontologies (or 'controlled vocabularies') can be improved by adopting tools and methods that bring a greater degree of logical and ontological rigor. We describe one endeavor along these lines, which is part of the current reform efforts of the Open Biomedical Ontologies (OBO) consortium 12 and which has implications for ontology construction in the life sciences generally.

The OBO ontology library 1 is a repository of controlled vocabularies developed for shared use across different biological and medical domains. Thus the Gene Ontology (GO) 34 consists of three controlled vocabularies (for cellular components, molecular functions, and biological processes) designed to be used in annotations of genes or gene products. Some ontologies in the library - for example the Cell and Sequence Ontologies, as well as the GO itself - contain terms which can be used in annotations applying to all organisms. Others, especially OBO's range of anatomy ontologies, contain terms applying to specific taxonomic groups such as fly, fungus, yeast, or zebrafish.

Controlled vocabularies can be conceived as graph-theoretical structures consisting on the one hand of terms (which form the nodes of each corresponding graph) linked together by means of edges called relations. The ontologies in the OBO library are organized in this way by means of different types of relations. OBO's Mouse Anatomy ontology, for example, uses just one type of edge, labeled part_of. The GO currently uses two, labeled is_a and part_of. The Drosophila Anatomy ontology includes also a develops_from link. Other OBO ontologies include further links, for example (in the Sequence Ontology) position_of and disjoint_from. The National Cancer Institute (NCI) Thesaurus adds many additional links, including has_location for anatomical structures and different part_of relations for structures and for processes.

The problem is that when OBO and similar ontologies incorporate such relations they typically do so in informal ways, often providing no definitions at all, so that the logical interconnections between the various relations employed are unclear, and even the relations is_a and part_of are not always used in consistent fashion both within and between ontologies. Our task in what follows is to rectify these defects, drawing on the requirements analysis presented in 5.

Of the criteria that ontologies must currently satisfy if they are to be included in the OBO library, the most important for our purposes are: first, inclusion of textual definitions or descriptions designed to ensure that the precise meanings of terms as used within particular ontologies will be clear to a human reader; second, employment of a standard syntax, such as the OWL or OBO flatfile syntax; third, orthogonality to the other ontologies already included in the library. These criteria are designed to support the integration of OBO ontologies, above all by ensuring the compatibility of ontologies pertaining to an identical subject matter. OBO has now added a fourth criterion to assist in achieving such compatibility, namely that the relations (edges) used to connect terms in OBO ontologies should be applied in ways consistent with their definitions as set forth in this paper.

The Relation Ontology offered here is designed to put flesh on this criterion. How, exactly, should part_of or located_in be defined in order to ensure maximally reliable curation of each single ontology while at the same time guaranteeing maximal leverage in building a solid base for life-science knowledge integration in general? We describe a rigorous methodology for providing an answer to this question and illustrate its use in the construction of an easily extendible list of ten relations of a type familiar to those working in the bio-ontological field. This list forms the core of the new OBO Relation Ontology. What is distinctive about our methodology is that, while the relations are each provided with rigorous formal definitions, these definitions can at the same time be formulated in such a way that the underlying technical details remain invisible to ontology authors and curators.

While considerable effort has been invested in the formulation and definition of terms in biomedical ontologies, too little attention has been paid in the ontological literature to the associated relations. A number of characteristic types of shortcomings of controlled vocabularies can be traced back especially to the neglect of issues of formal structure in the treatment of relations 5678910. To take just one example, the pre-2004 versions of GO allowed at least three different readings of the expression 'part of' as representing simultaneously: inclusion relations between vocabularies; a relation of possible parthood between biological entities; a relation of necessary parthood between biological entities. As was shown in 6, this coexistence of conflicting readings meant that three of the four rules given in the then effective documentation for reasoning with GO's hierarchies were logically incorrect.

Another characteristic family of problems turns on the paucity of resources for expressing relations in ontologies like GO. For example, because GO has no direct means of asserting location relations, it must capture such relations indirectly by constructing new terms involving syntactic operators such as 'site of', 'within', 'extrinsic to', 'space', 'region', and so on. It then simulates assertions of location by means of 'is_a' and 'part_of' statements involving such composites, for example in:

extracellular region is_a cellular component

extrinsic to membrane part_of membrane

both of which are erroneous. Additional problems arise from the fact that GO's extracellular region and extracellular space are both specified in their definitions as referring to the space (how large a space?) external to the outermost structure of a cell.

Another type of problem turns on the failure to distinguish relational expressions which, though closely related in meaning, are revealed to be crucially distinct when explicated in the formally precise way that is demanded by computer implementations. An example is provided by the simultaneous use in OBO's Cell Ontology of both derives_from and develops_from while no clear distinction is drawn between the two 11. This problem is resolved in the treatment of derivation and transformation below, and has been correspondingly corrected in versions 1.14 and later of the Cell Ontology.

Efforts to improve GO from the standpoint of increased formal rigor have thus far been concentrated on re-expressing the existing GO schema in a description logic (DL) framework. This has allowed the use of a DL-reasoner that can identify certain kinds of errors and omissions, which have been corrected in later versions of GO 12. DLs, however, can do no more than guarantee consistent reasoning according to the definitions provided to them. If the latter are themselves problematic, then a DL can do very little to identify or resolve the problems which result. Here, accordingly, we take a more radical approach, which consists in re-examining the basic definitions of the relations used in GO and in related ontologies in an attempt to arrive at a methodology which will lead to the construction of ontologies which are more fundamentally sound and thus more secure against errors and more amenable to the use of powerful reasoning tools. This approach is designed also to be maximally helpful to biologists by avoiding the problems which arise by virtue of the fact that the syntax favored in the DL-community is of a type which can normally be understood only by DL-specialists.

The relations in biological ontologies connect classes as their relata. The term 'class' here is used to refer to what is general in reality, or in other words to what, in the knowledge-representation literature, is typically (and often somewhat confusingly 13) referred to under the heading 'concept' and in the literature of philosophical ontology under the headings 'universal', 'type' or 'kind'. Biological classes are in first approximation those classes which have been implicitly sanctioned through usage of the corresponding general terms in the biological literature, for example cell or fat body development.

Our task is to develop a suite of coherently defined bio-ontological relations that is sufficiently compact to be easily learned and applied, yet sufficiently broad in scope to capture a wide range of the relations currently coded in standard biomedical ontologies. Unfortunately the realization of this task is not a trivial matter. This is because, while the terms in biomedical ontologies refer exclusively to classes - to what is general in reality - we cannot define what it means for one class to stand to another, for example in the part_of relation, without taking the corresponding instances into account 6. Here the term 'instance' refers to what is particular in reality, to what are otherwise called 'tokens' or 'individuals' - entities (including processes) which exist in space and time and stand to each other in a variety of instance-level relations. Thus we cannot make sense of what it means to say cell nucleus part_of cell unless we realize that this is a statement to the effect that each instance of the class cell nucleus stands in an instance-level part relation to some corresponding instance of the class cell.

This dependence of class-relations on relations among corresponding instances has long been recognized by logicians, including those working in the field of description logics, where the (all - some) form of definition we utilize below has been basic to the formalism from the start 14. Definitions of this type were incorporated also into the DL-based GALEN medical ontology 15, though the significance of such definitions, and more generally of the role of instances in defining class relations, has still not been appreciated in many user communities.

It is also characteristically not realized that talk of classes involves in every case a more-or-less explicit reference to corresponding instances. When we assert that one class stands in an is_a relation to another (that is, that the first is a subtype of the second), for example, that glucose metabolism is_a carbohydrate metabolism, then we are stating that instances of the first class are ipso facto instances of the second. When we are dealing exclusively with is_a relations there is little reason to take explicit notice of this two-sided nature of ontological relations. When, however, we move to ontological relations of other types, then it becomes indispensable, if many characteristic families of errors are to be avoided, that the implicit reference to instances be taken carefully into account.

We focus here exclusively on genuinely ontological relations, which we take to mean relations that obtain between entities in reality, independently of our ways of gaining knowledge about such entities (and thus of our experimental methods) and independently of our ways of representing or processing such knowledge in computers. A relation like annotates is not ontological in this sense, as it links classes not to other classes in nature but rather to terms in a vocabulary that we ourselves have constructed. We focus also on general-purpose relations - relations which can be employed, in principle, in all biological ontologies - rather than on those specific relations (such as genome_of or sequence_of employed by OBO's Sequence Ontology) which apply only to biological entities of certain kinds. The latter will, however, need to be defined in due course in accordance with the methodology advanced here.

The ontologies in OBO are designed to serve as controlled vocabularies for expressing the results of biological science. Sentences of the form 'A relation B' (where 'A' and 'B' are terms in a biological ontology and 'relation' stands in for 'part_of' or some similar expression) can thus be conceived as expressing general statements about the corresponding biological classes or types. Assertions about corresponding instances or tokens (for example about the mass of this particular specimen in this particular Petri dish), while indispensable to biological research, do not belong to the general statements of biological science and thus they fall outside the scope of OBO and similar ontologies as these are presented to the user as finished products.

Yet such assertions are still relevant to ontologies. For it turns out that it is only by means of a detour through instances that the definitions and rules for coding relations between classes can be formulated in an intuitive and unambiguous - and thus reliably applicable - way.

We can distinguish, in fact, the following three kinds of binary relations:

<class, class>: for example, the is_a relation obtaining between the class SWR1 complex and the class chromatin remodeling complex, or between the class exocytosis and the class secretion;

<instance, class>: for example, the relation instance_of obtaining between this particular vesicle membrane and the class vesicle membrane, or between this particular instance of mitosis and the class mitosis;

<instance, instance>: for example, the relation of instance-level parthood (called part_of in what follows), obtaining between this particular vesicle membrane and the endomembrane system in the corresponding cell, or between this particular M phase of some mitotic cell cycle and the entire cell cycle of the particular cell involved.

Here classes and the relations between them are represented in italic; all other relations are picked out in bold.

The terms 'continuant' and 'process' are generalizations of GO's 'cellular component' and 'biological process' but applied to entities at all levels of granularity, from molecule to whole organism. Continuants are those entities which endure, or continue to exist, through time while undergoing different sorts of changes, including changes of place. Processes are entities that unfold themselves in successive temporal phases 16. The terms 'continuant' and 'process' thus correspond to what, in the literature of philosophical ontology, are known respectively as 'things' (objects, endurants) and 'occurrents' (activities, events, perdurants) respectively. A continuant is what changes; a process is the change itself. The continuant classes relevant to biological ontologies include molecule, cell, membrane, organ; the process classes include ion transport, cell division, fat body development, breathing.

To formulate precise definitions of the <class, class> relations which form the target of ontology construction in biology we will need to employ a vocabulary that allows reference both to classes and to instances. For this we take advantage of the machinery of logic, and more specifically of the standard device of variables and quantifiers 17, using different sorts of variables to range across the classes and instances of continuants and processes, spatial regions and temporal instants, respectively. For the sake of intelligibility we use a semi-formal syntax, which can, however, be translated in a simple way into standard logical notation.

We use variables of the following sorts:

C, C₁, ... to range over continuant classes;

P, P₁, ... to range over process classes;

c, c₁, ... to range over continuant instances;

p, p₁, ... to range over process instances;

r, r₁, ... to range over three-dimensional spatial regions;

t, t₁, ... to range over instants of time.

In an expanded version of our formal machinery we will need also to incorporate further variables, ranging for example over temporal intervals, biological functions, attributes and values.

Note that continuants and processes form non-overlapping categories. This means in particular that no subtype or parthood relations cross the continuant-process divide. The tripartite structure of the GO recognizes this categorical exclusivity and extends it to functions also.

Continuants can be material (a mitochondrion, a cell, a membrane), or immaterial (a cavity, a conduit, an orifice), and this, too, is an exclusive divide. Immaterial continuants have much in common with spatial regions 18. They are distinguished therefrom, however, in that they are parts of organisms, which means that, like material continuants, they move from one spatial region to another with the movements of their hosts.

The three-dimensional continuants that are our primary focus here typically have a top and a bottom, an anterior and a posterior, an interior and an exterior. Processes, in contrast, have a beginning, a middle and an end. Processes, but not continuants, can thus be partitioned along the time axis, so that, for example, your youth and your adulthood are temporal parts of that biological process which is your life.

As child and adult are continuants, so youth and adulthood are processes. We are thus clearly dealing here with two complementary - space-focused and time-focused - views of the same underlying subject matter, with determinate logical and ontological connections between them 16. The framework advanced below allows us to capture these connections by incorporating reference to spatial regions and to temporal instants, both of which can be thought of as special kinds of instances.

We shall also need to distinguish two kinds of instance-level relations: those (applying to continuants) whose representations must involve a temporal index, and those (applying to processes) which do not. Note that the drawing of this distinction is still perfectly consistent with the fact that processes themselves occur in time, and that processes may be built out of successive subprocesses instantiating distinct classes.

We cannot, on pain of infinite regress, define all relations, and this means that some relations must be accepted as primitive. The relations selected for this purpose should be self-explanatory and they should as far as possible be domain-neutral, which means that they should apply to entities in all regions of being and not just to those in the domain of biology.

Our choice of primitive relations is as follows:

c instance_of C at t - a primitive relation between a continuant instance and a class which it instantiates at a specific time

p instance_of P - a primitive relation between a process instance and a class which it instantiates holding independently of time

c part_of c₁ at t - a primitive relation between two continuant instances and a time at which the one is part of the other

p part_of p₁, r part_of r₁ - a primitive relation of parthood, holding independently of time, either between process instances (one a subprocess of the other), or between spatial regions (one a subregion of the other)

c located_in r at t - a primitive relation between a continuant instance, a spatial region which it occupies, and a time

r adjacent_to r₁ - a primitive relation of proximity between two disjoint continuants

t earlier t₁ - a primitive relation between two times

c derives_from c₁ - a primitive relation involving two distinct material continuants c and c₁

p has_participant c at t - a primitive relation between a process, a continuant, and a time

p has_agent c at t - a primitive relation between a process, a continuant and a time at which the continuant is causally active in the process

This list includes only those <instance-instance> relations, together with one <instance-class> relation, which are needed for defining the <class, class> relations which are our principal target in this paper. The items on the list have been selected because they enjoy a high degree of intelligibility to the human authors and curators of biological ontologies. For purposes of supporting computer applications, however, the meanings of the corresponding relational expressions must be specified formally via axioms, for example in the case of 'part_of' by axioms of mereology (the theory of part and whole: see below), and in the case of 'earlier' by axioms governing a linear order 17. The relation located_in will satisfy axioms to the effect that for every continuant there is some region in which it is located; instance_of will satisfy axioms to the effect that all classes have (at some stage in their existence) instances, and that all instances are instances of some class.

The formal machinery for reasoning with such axioms is in place, and a comprehensive set of axioms is being compiled. For the typical human user of biological ontologies, however, the listed primitive relations and associated axioms are designed to work invisibly behind the scenes. That is, they serve as part of the background framework that guides the construction and maintenance of such ontologies.

We employed a multi-stage methodology for the selection of the relations to be included in this ontology and for the formulation of corresponding definitions. First, a sample of researchers involved in ontology construction in the life sciences, representing different groups and including the co-authors of this paper, was asked to prepare lists of principal relations in light of their own specific experience but focusing on relations which would be: 'ontological' in the sense introduced above; 'general-purpose' in the sense that they apply across all biological domains; and also such as to manifest a high degree of universality (in the sense explained in the section 'Types of relational assertions' below). The submitted lists manifested a significant degree of overlap, which allowed us to prepare a core list in whose terms a large number of the remaining relations on the list could be simply defined.

A further constraint on the process was the goal of providing a simple formal definition for each included <class-class> relation. Those relations for which an appropriate simple definition could not be agreed upon were not included in this interim list. This includes most conspicuously relations involving analogs of the GO notion of molecular function. The relation has_agent was, however, included in light of a common understanding that the notion of agency would be involved in whatever candidate definition of function in biology is eventually accepted for use in OBO. This further constraint was chosen in light of the fact that our capacity to provide simple formal definitions - definitions which will at one and the same time be intelligible to ontology authors and curators and also able to support logic-based tools for automatic reasoning and consistency-checking - is the primary rationale for the methodology here advanced.

The two relations is_a and part_of were unproblematic candidates for inclusion in the resulting list (though providing simple definitions even for these relations was not, as we shall see, a simple matter). Is_a and part_of have established themselves as foundational to current ontologies. They have a central role in almost all domain ontologies, including the Foundational Model of Anatomy (FMA) 1920, GO and other ontologies in OBO, as well as in influential top-level ontologies such as DOLCE 21 and in digitalized lexical resources such as WordNet 22.

In preparing our sample lists we drew on representatives not only of the OBO consortium but also of GALEN and the FMA (itself a candidate for inclusion in OBO). Our temporal relations draw on existing OBO practice (where transformation_of is a generalization of the develops_from relation used in OBO's cell and anatomy ontologies) and our participation relations draw on current work addressing the need to provide relations that link entities in different ontologies (for example entities in GO's process, function and component ontologies) and on an evolving Physiology Reference Ontology that is being developed in conjunction with the FMA 23, from which our spatial relations were extracted.

The first proposed version of the OBO Relation Ontology is shown in Table 1. We shall deal here with each of the ten relations listed in Table 1 in turn, providing rigorous yet easily understandable definitions.

In light of the above, we can now observe certain differences in what we might call the relative universality of class-level relational assertions. There are many cases, above all involving is_a relations, where relational assertions hold with a maximal degree of universality, which means that they hold for every instance of the classes in question because they are a matter of analytic connections, that is, connections resting on the compositional nature of the class terms involved 10, as, for example, in: eukaryotic cell is_a cell, or adult walking behavior has_participant adult. (Contrast, adult participates_in adult walking behavior.)

There are also other kinds of statements enjoying a high degree of universality, for example: penetration of ovum has_participant sperm. The first of our two corresponding reciprocal statements - sperm participates_in penetration of ovum - is in contrast true only in relation to certain isolated instances of sperm, and the second of our reciprocal statements - sperm always_participates_in penetration of ovum - is true in relation to no instances at all.

It then seems reasonable to insist that biomedical ontologies should reflect those sorts of biological assertions that enjoy a high degree of universality (typically assertions involving just one of each pair of reciprocal relations).

We hope that, by providing clear and unambiguous specifications of what the class-level relational expressions used in biological ontologies mean, our formal definitions will assist curators engaged in ontology creation and maintenance. The corresponding definitions are summarized in Table 2, which also contains representative examples for each of the relations distinguished.

Our definitions are designed to ensure that the corresponding general-purpose relational expressions are used in a uniform way in all biological ontologies. In this way we shall be in a position to contribute to the realization of the goal of bringing about a high degree of interoperability even where ontologies are produced by different groups and for different purposes. These definitions are designed also to enable the automatic detection of errors in biomedical ontologies, for example by allowing the construction of extensions of OBO-Edit and similar tools with the facility to test whether given relations are employed in an ontology in such a way as to involve relata of the appropriate types 31 or in such a way as to have the formal characteristics, such as transitivity or reflexivity, dictated by the definitions (Table 3). The framework can also support reasoning applications designed to enable the automated derivation of information from existing bodies of knowledge - for example to infer the parts of a given cell continuant via the traversal of a part_of hierarchy - including instance-based knowledge derived from the clinical record.