Many of the entities most commonly studied and investigated by biologists are processes, that is, they involve change over time, such as cell development and blood circulation. Most bio-ontologies such as the Gene Ontology distinguish processes from the entities that participate in them (cells, blood). As bio-ontologies of processes become more sophisticated, however, we need to accurately describe their properties, such as rates and speeds. Unlike the properties of material entities, there is as yet little consensus within the bio-ontology community on how such properties should be represented. Upper-level ontologies such as BFO and DOLCE are divided on whether to allow properties of processes as foundational entities. We discuss the properties of processes in formal ontology and specifically whether they can be said to have qualities, that is to say categorical properties that are separate from those of their participants. We will concentrate on heart rate.
Colin Batchelor,1* Janna Hastings2 and Christoph Steinbeck2
1 Royal Society of Chemistry, Thomas Graham House, Cambridge, UK CB4 0WF.
2 European Bioinformatics Institute, Hinxton, Cambridge, UK CB10 1SD.
Jones drove along the road. How did he drive? He drove without a licence, without insurance, without lights after dark, under the influence of alcohol and above the speed limit. Naughty Jones. But how many of those properties were truly properties of his driving process, and how many of them were “really” properties of something else, such as Jones himself? One test is whether the property goes away when the process finishes. In this simple case we can see that nearly everything is uncontroversially a property of one of the participants, be it Jones or his vehicle, except for perhaps the speed.
But what happens when Jones sees the inevitable flashing blue light in his rear-view mirror? In the following paper we look at Jones’s heartrate, a difficult case for ontology. The rest of the paper is structured as follows. In section 2 we briefly review existing ontological frameworks for processes. In section 3 we consider ontological dependence, a vital part of the formal-ontological approach to bio-ontologies, and in section 4 we look at how an is_a hierarchy of process properties compares to the typically discrete hierarchies of objects and the typically continuous hierarchies of qualities. We present our conclusions in section 5.
We follow Davidson (1967) and latterly BFO: Smith (2005), DOLCE: Masolo et al. (2003) and GFO: Herre et al. (2007) in identifying processes as first-class citizens in our ontological framework. It goes without question that we can write genus–differentia definitions for processes. The question we address is what sort of differentia is most suitable for representing the sorts of processes that biomedical scientists are interested in.
Taking BFO, DOLCE and GFO together, BFO stands out as not explicitly providing for properties of processes beyond their boundaries and durations. GFO admits process roles, but only DOLCE explicitly identifies temporal qualities as being properties of processes, as applied by Devaraju and Kauppinen (2010) in their account of a blizzard. But all of these are quite vague. The shared framework is that processes/perdurants have proper temporal parts, are never wholly present at a given time, and are clearly distinct from continuants/endurants. Of the three, BFO deals most explicitly with ontological dependence as an organizing principle and has the fewest classes in it.
Outwith bio-ontologies, Seibt (2004) takes a monocategorial approach to ontology where all things are processes, but we do not know of any practical implementations of her work. Aitken and Curtis (2002) have an approach taking three perspectives, those of ordering, participants and conditions. Conditions here are preconditions for a process taking place and postconditions are consequences of a process. There are no obvious slots here for process properties as such. Galton (2008) defines processes as things that are ongoing; once a process is complete and becomes history, he calls it an event. His approach admits process attributes such as speed and throughput.
Johansson (2006) provides a useful structure for thinking about processes. He identifies four kinds of is_a relation, those of genus-subsumption, determinable-subsumption, specialization and specification. Most familiar to us in the bio-ontology community is genus-subsumption, which proceeds by way of class intersection. Less familiar is determinable-subsumption, which applies to certain sorts of quality. Here red, let us say, is the gerrymandered portion of colour that consists of scarlets, vermilions, crimsons and so forth. Another way of expressing this contrast is that genus-subsumption hierarchies are discrete rather than continuous; there is no way of smoothly moving between a benzene molecule and a water molecule, just as there is no way of moving smoothly between a portion of cytoplasm and an ion channel. In contrast, with a determinable-subsumption hierarchy, one can move smoothly across a colour volume, say, without encountering discontinuities. This is exactly like DOLCE’s quality–quale distinction. A quality is a determinable and a quale is a determinate.
Specialization and specification are directly relevant to our discussion of processes. Specifications of processes involve definitions in terms of the participants, so Jones’s driving of a milkfloat, a tractor, a dodgem, a golf cart, a combine harvester, are all specifications of driving a vehicle. These can be written as class intersections in the normal way. Johansson, however, leaves specialization somewhat vague, giving as examples careful painting, careless painting, fast painting and slow painting, and pointing out that carefulness, carelessness, fastness and slowness in the context of painting derive from painting and aren’t universals that are somehow transferable to other activities.
We will investigate heart rate in the following sections in the light of this framework.
At least on first glance, heart rate appears to be intrinsically bound up with a heart beating process. Furthermore, it allows comparison between different heart beating processes: we would like to have some sort of way of getting at the idea that person A’s heart rate is faster than person B’s heart rate. This is similar to person A’s height, at least in some frameworks a determinable quality of person A, being greater than person B’s.
Previous work on heart rate includes Lord and Stevens (2010) who argue for using mathematical modelling as the ontological model for this sort of scenario, which has much to recommend it from a computer programming point of view, but reasoning with combined mathematical and ontological models is not yet well developed, and thus, exposing the implications of the mathematical part of the model for standard reasoning tasks such as data integration will be difficult. Temal et al. (2009) model heart rate beneath both BFO and DOLCE and conclude that DOLCE is better since it allows heart rate to be a property of the heart beating process. In the Gene Ontology (GOC 2000), ‘regulation of heart rate’ is a class (GO:0002027) with definition ‘Any process that modulates the frequency or rate of heart contraction.’ and synonyms “regulation of heart contraction rate”, “cardiac chronotropy”, and “regulation of rate of heart contraction”, however, heart rate is only referred to in the text name as the target of the regulation, not explicitly included in the ontology as a separate entity. Lastly Nunes et al. (2007), using an approach based on DOLCE, explicitly describe the different steps in a single heartbeat but don’t consider the heart rate itself.
There is an important way in which heart rate differs from speed. Since Newton we have been happy with taking the limit of a speed as the length over which we evaluate the speed goes to zero, there is a minimal length of time over which we can think about a heart rate—a single cycle. The key point is that heart rate is only ever an average, in contrast to Jones driving along a residential street at 31 mph. This means that if the heart rate is a property of anything, it is a property of some proper part, specifically a proper temporal part, of the heart beating process, and different temporal parts have different heart rates. We need to modify proposition (1) to say:
This is similar to how hair colour might be different for different spatial parts of your hair, but more complex because hair colour, like speed, is wholly defined for each (arbitrarily small) part. A more fruitful analogy is with length in geographic science. While most people are comfortable with length being a property (however defined), some lengths, famously that of the coastline of Scotland, vary with scale, getting longer the smaller the ruler you use until we reach the atomic scale and edges become difficult to identify. Similarly, Jones’s heart rate at time t differs according to the length of time T, the precise processual part p, over which we consider it. For length, BFO prefers to talk about projections, so that each object has a projection onto a particular portion of space, and that space has a length. But the same thing applies to, for example, the circumference of the projection of Scotland into space, and it is not clear that using this strategy gets around the underlying problem, since the projection process preserves the ambiguity.
What does this mean for dependence relations? We contrast DOLCE, which allows chains of (presumably) transitive dependence relations, so that qualities can have qualities and those qualities too can have qualities, with BFO, where any property y must first depend directly on some independent continuant x and second all y must depend on instances x of some universal X, as opposed to some “defined class”. BFO’s approach is stronger in that it is more useful in constraining ontology developers, but is weak because it lacks a clear definition of ontological dependence. Lowe (2010) discusses ontological dependence at length and it is clear that the sort of dependence intended by BFO in the sense of “independent continuant” as opposed to “dependent continuant” is not unlike Lowe’s substance dependence. Lowe defines it in terms of identity dependence: x depends for its identity upon y iff there is a function f such that it is part of the essence of x that x is f(y) and then says that x is a substance iff x is a particular and there is no particular y such that y is not identical with x and x depends for its identity upon y.
The DOLCE approach would be to say something like:
but if we follow BFO and disallow dependence chains then we get:
and regularly beating heart is not a universal. If a given heart stops beating, or starts to beat irregularly, then it has not changed into a different kind of thing, it has merely changed its behavior. Hence there are two universals here: the heart and the beating process. Is there a way out that allows us to define heart rate in terms of formal relations in the sense of Smith and Grenon (2004)? The first thing to observe is that there are hidden dependence relations in the BFO framework. For example, every disposition depends on some underlying quality. Every process depends on some disposition. Likewise, just as the life of a frog substance-depends on the frog, so conversely the frog depends on its own life. But these dependence relations are weaker than Lowe’s substance dependence, and are examples of Lowe’s essential existential dependence, the case where it is part of the essence of x that x exists only if y exists. So our dependence relations at the class level, according to the pattern all x related_to some y, for heart rate are as follows:
Without all three parts of the triad (5)–(7) we cannot have a heart rate.
BFO and DOLCE concur in dividing most of the furniture of the universe into things wholly present at a given time, which BFO calls “continuants” and DOLCE calls “endurants”, and things not wholly present at a given time, which BFO calls “occurrents” and DOLCE calls “processes”. They do, however, give us different answers to whether a quality is a continuant/endurant or an occurrent/perdurant. BFO says a continuant, DOLCE says neither. Since our own work, see for example Batchelor et al. (2010), relies on dispositional properties, on which DOLCE is silent, we will attempt to build on the BFO framework.
One argument against process qualities per se, voiced by a participant at an OBO Foundry meeting, is that a quality, a dependent continuant, is wholly present at one point in time, and can change over time (for example, your height changes as you grow up), whereas a process quality depends on the process as a whole, thus would have to extend over time (the time of the process) and cannot be wholly present at a given time nor change over time. Hence it would have to be an occurrent rather than a continuant. We have already dealt with that last point and identify a process quality as being an occurrent in the general case, see proposition (2), but there are further difficulties with that counterargument.
The possibly naïve straw man that it counters is that instead of defining a 90 bpm heartbeat as
then that BFO approach would instead say
(9) heartbeat at 90 bpm
In other words, the BFO approach is to use the subsumption hierarchy for heart beating processes to model attributes of processes. How do we decide between the two? (9) is simpler but it fails the basic test of proposition (1). There is nothing in the structure of (9) that enables us to say that heartbeat at 90 bpm is quantitatively different from heartbeat at 100 bpm. There is also nothing to contrast these classes with other heartbeat subclasses such as feeble heartbeat or pounding heartbeat, which cannot be straightforwardly quantitatively compared. Proposition (8) achieves this since it includes ’90 bpm’ as a first-class entity in its own right.
A further argument for process qualities comes from considering Johansson’s (2006) kinds of is_a relation. We can see straight away that if we have heart rates as a kind of process quality then they fit into a clean determinable-subsumption hierarchy and proposition (8) becomes a sort of specification that we can handle with an OWL reasoner in the usual way. Conversely, we see that while
is_a cyclical physiological process
is an example of genus subsumption, any tree that contains both (9) and (10) will mix subsumption relations, since (9) is really a determinable subsumption relation where the processes stand in relation to each other as determinable and determinates.
Therefore we reject (9) and choose (8). There are process qualities, and they are occurrents because they are not wholly present at any one point of time, in contrast to BFO qualities. We can now go further and suggest that this sheds light on Johansson’s mysterious specialization relation between properties. Just as in a specification hierarchy each specification is a genus–differentia definition of a process where the differentia fits into a genus-subsumption hierarchy, so is a specialization hierarchy one where each definition is a genus–differentia definition where the differentia fits into a determinable-subsumption hierarchy.
We have argued that upper-level ontologies should accept process qualities in order to handle things like heart rate, on the basis of its ontological dependence relations and from a consideration of Johansson’s four kinds of is_a relation. Process qualities themselves are occurrents. They existentially-depend on the processes that they are process qualities of and substance-depend on the participants of those processes. They fit into a determinable-subsumption hierarchy. Not all things that might be considered to be process qualities, however, should be. In our view, speed and acceleration, for example, being wholly present at a single point in time, are conventional continuant qualities. In future work we will consider the rates of chemical reactions and whether they are qualities or process qualities.
JH thanks Werner Ceusters and Barry Smith for useful discussions. This work was partially supported by the BBSRC, grant agreement number BB/G022747/1 within the “Bioinformatics and biological resources” fund.
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