The Basic Formal Ontology (BFO) version 1.1 has, compared to v1.0, the additions SpecificallyDependentContinuant (SDC) and GenericallyDependentContinuant (GDC); at least on 30 June when I downloaded it. They are defined as follows (emphasis added):
SDC = “A continuant [snap:Continuant] that inheres in or is borne by other entities. Every instance of A requires some specific instance of B which must always be the same”. To note: it subsumes Quality and RealizableEntity.
GDC = “A continuant [snap:Continuant] that is dependent on one or other independent continuant [snap:IndependentContinuant] bearers. For every instance of A requires some instance of (an independent continuant [snap:IndependentContinuant] type) B but which instance of B serves can change from time to time”.
Setting aside the lack of similarity in the formulation of the definitions, difference in constraints on the participating entities, awkward English, and absence of full formal definitions (neither in the text nor in the OWL file), the interesting bit I will zoom in on now is the mandatoryness with “same” [at all times] and “some…from time to time”. This sounds just like our work on essential versus plain mandatory parts and wholes, but then counting for an arbitrary relation that relates [in]dependent continuants as opposed to limiting it to part-whole relations. For more details, see also the previous post on essential and mandatory parts or the DL’08 paper with technical details, and the extension that specifically deals with specific and generic dependence , constrained to part-whole relations due to the scope of the paper.
Put differently, one needs to represent the life cycle semantics of the participating entities to be able to distinguish between “some instance—be it x1, or …, or xn—of type X must participate in a relational instance of relation of type R” and “the same instance y of type Y must participate in a relational instance of relation of type S”. More practically, and pattern-wise, given some object z that is an instance of Z (a continuant) and t0, t1, … , tn point in time, then we have for GDC
r1 : < x1, z> at t0 (at the start of active z)
r2 : < x2, z> at t1, where t1>t0, and (x1 = x2 or < x1, z> or not < x1, z> )
r3 : < x3, z> at t2, where t2 >t1 , etc… until z cease to exist as instance of Z at tn
whereas for SDC
s1 : < y1, z1> at t0 (at the start of active z)
s1 : < y1, z1> at t1, where t1>t0
s1 : < y1, z1> at t2, where t2 >t1 until z cease to exist as instance of Z at tn.
s2 : < y2, z2> at t0 (at the start of active z)
s2 : < y2, z2> at t1, where t1>t0
s2 : < y2, z2> at t2, where t2 >t1 until z cease to exist as instance of Z at tn, and where it may be that z1 = z2 or y1 = y2 or both.
Taking the GDC example from the OWL file “a certain PDF file that exists in different and in several hard drives”, then we have an example where x…xi are the distinct hard drives and z the PDF file (well, the elusive ‘contents’ of the file—clearly, there are different bits involved in the different hard drives).
The provided SDC examples, however, are somewhat more complicated: “the mass of a cloud, the smell of mozzarella, the liquidity of blood, the color of a tomato, the disposition of fish to decay, the role of being a doctor, the function of the heart in the body: to pump blood, to receive de-oxygenated and oxygenated blood”. Obviously, each cloud must have a mass, but generally not the same mass, and some mass, say, 10kg, is not necessarily related always to the same cloud as clouds can grow and decrease in volume and, thus, in amount of mass. Given the example, we only can have the specific dependence if a ‘grown’ cloud (>10kg) counts as a different cloud (which is counterintuitive). Likewise, a certain liquidity of blood can change in value (due to drinking alcoholic beverages, for instance), although blood must have some value for liquidity (which may or may not be measures and which reaches 0 if it is dried up blood in a healing wound). Vice versa, a certain liquidity value does not have to be related to the same blood for the duration of its existence. If, however, we consider instead, say, that the doctor takes a blood sample and measures the liquidity and the result of that measurement is stored in a database or written on a paper-based health record, then that measured value ‘123’ is permanent for the duration of its existence related to ‘blood sample from patient p1 taken at time hh:mm at date dd-mm-yyyy’. But the latter reading is certainly a different case from just blood & liquidity. So, overall, this seems to contradict the SDC definition—or the examples don’t quite fit the definition.
In addition, we can have variations in the life cycles of the SDC and its bearer, which I don’t think are covered. Take the following figure, where there are two principal options: we fix the lifetime of the [independent]continuant and vary the SDC’s lifetime in (A), or fix the lifetime of the SDC and vary the lifetime of the [independent]continuant in (B).
In the case of the SDC definition, one would have to focus on (B): the [independent]continuant bearer might have one or more SDCs, but given an SDC, it must always be related to the Cx, which has the same or a longer lifetime than the SDC but never a shorter lifetime. In the case of our blood sample as bearer, then we have either C2 (if the sample continues after the record of the measurement is destroyed) or C4 (if the sample is destroyed together with the recording of the taken measurement).
So, it is either me who doesn’t get it, or there is room for improvement in the SDC/GDC definitions and/or examples. Anyone has some clarifying thoughts on this?
 Artale, A., Guarino, N., and Keet, C.M. Formalising temporal constraints on part-whole relations. 11th International Conference on Principles of Knowledge Representation and Reasoning (KR’08). Gerhard Brewka, Jerome Lang (Eds.) AAAI Press. Sydney, Australia, September 16-19, 2008.