A Survey of Top-Level Ontologies

Ontological commitment overview

Our overview of the framework for ontological commitments is divided into three parts:

1. Section 4.1 looks at the general choices TLOs make on whether and what kind of overall ontological commitment to make;
2. Section 4.2 looks at the overall formal structure; and
3. Section 4.3 considers the individual core commitments that lead to that structure.

More detailed technical notes are given in Appendix J.

4.1.1  Ontologically committed: ontological or generic

The top-level ontologies longlist was compiled to include any data models that might have content useful for the construction of a top-level ontology. Hence, one of the key conditions for inclusion is that the model must be sufficiently general to include content that might be useful.

There are cases where the TLO specifies a data structure with no intended ontological commitment; to deliberately leave open how the data is modelled. A classic indication of this is where the modeller can validly choose which data type to use in a model (whether something is modelled as an entity or attribute) based upon, typically, performance requirements. These TLOs are classified as generic; Topic Maps and Schema.org are examples of this. One consequence of this choice is that these top-level ‘ontologies’ are not able to harness the interoperability benefits of adopting ontological commitments mapping to the real world (discussed above).

4.1.2  High or low ontological commitment

Where TLOs are ontologically committed, the analysis reveals that some have explicitly committed to most, if not all, of the choices whereas others have only committed to a few. This gives us a good basis for distinguishing between the heavyweight TLOs that are highly committed and the lightweight TLOs that are only committed to a few.

4.1.3  Subject: appearance or reality: natural language or foundational ontology

One can broadly classify top-level ontologies into two kinds by their subject matter. The subject matter can be what a community implicitly accepts when using a language – a natural language ontology. This will take the surface structure of the language, for example the distinction between nouns and verbs (or the words it uses), as a window on the ontology. Or it can be an ontology of what ‘really’ exists according to science (and philosophy) – a foundational ontology. This is suspicious of the surface structure of the language as it has often turned out to be a false friend. For example, the English language classes tomatoes as a vegetable, but this has not persuaded botanists to stop classifying them as ‘really’ a fruit.

The natural language ontology may include merely conceived objects as well as those that happen to be actual – whereas the foundational ontology should only include actual ones, as well as some infrastructure to help assure that they are actual. The natural language ontology may focus on the linguistic structure of the language or on the concepts implied by the language. See Appendix J for a more detailed background.

Some TLOs on our longlist have explicitly stated their aspirations to one or other kind of subject matter – and provided the appropriate infrastructure. Clear examples are DOLCE as a natural language ontology; BFO and BORO as foundational ontologies. Some TLOs with no stated aspirations are clearly focussed on language and its linguistic infrastructure (nouns, verbs, etc.) and thereby categorised natural language ontologies: Wordnet and FrameNet are good examples.

Sometimes it is difficult to make the case for a classification; where there is neither a clear statement of intent nor clear infrastructure for one or other approach. These have not been classified.

Where one’s focus is on the language used in a community, then, other things being equal, a natural language ontology makes a better fit. If the focus is on reality, then a model of what really exists makes more sense. However, both kinds of ontology should be considered as useful sources for components for a TLO.

4.1.4 Categorical

There is a long tradition of categorical ontologies, where the types of the ontology are meant to be comprehensive, covering all types of thing that can exist – or, at the very least, a broad swathe; Aristotle and Kant’s Categories are historic examples of this. In principle, one would expect a TLO to be categorical. However, in practice, the comprehensiveness is often limited. In some cases, the scope is limited to a broad family of domains – such as MIMOSA’s focus on asset information for machinery and systems. In other cases, the TLO adopts a cautious position and its ontology is explicitly left open-ended allowing for extensions that involve new top-level categories, so making the TLO technically non-categorical – BFO is an example of this.

4.1.5 General classifications

In summary, the general level has the following classifications

Figure 1 provides a visual summary of this.

Figure 1 – General classification of the TLOs

4.2      Formal structure – horizontal and vertical

Many, if not most, of the ontological choices leave their mark on the formal structure, the ontological architecture, of the TLOs in characteristic ways; this section is about two ways we use these marks to classify them – which we tag vertical and horizontal aspects.

Three core hierarchical relations – each usually visualised upwards – provide a backbone to the TLOs. The ontological choices shape these upwards (vertical) structures in various ways – and we use these ways to characterise the impact of the choices on the TLOs on the ontological architecture.

If one looks in more detail at one of these hierarchies – the super-sub-type hierarchy – then one can see a repeating pattern of stratification across the hierarchy (horizontal) that mark particular choices. We use these to determine whether the TLO has made a particular choice.

These two ways of looking at the formal structure (the ontological architecture) – tagged vertical and horizontal aspects – map neatly onto the simplicity basis introduced above. There we divided simplicity broadly into structural and ontological – roughly the shape of the organising structure and the number of objects. The vertical aspect deals with the structure, and so structural simplicity, of the various hierarchies; roughly their shape up and down. The horizontal aspect deals with the broad ontological choices that can introduce a division across the hierarchy (horizontal stratification) – which impacts the ontological simplicity – as they increase the number of objects. Taking a broad-brush view, this section of the framework separates the vertical and horizontal aspects of the formal hierarchies.

In practical terms, these characterise the formal structures that arise in the ontological architecture from the various ontological choices. Together these form the backbone of the ontological architecture upon which the flesh of the ontology is built. Here we identify the broad structures and outline how their component ontological commitments fit into this structure. In the next section, we look inwards into the specific details of the commitments – rather than outwards at their impact of the structure.

4.2.1  Vertical aspect – varieties of hierarchies

There is a core of basic ontological hierarchical relations that are typically found in top-level ontologies; whole-part, type-instance and super-sub-type (they go by various names, these are the ones we adopt in this paper – Table 1 lists some alternatives with examples).

Table 1 – Hierarchal relations – terms

There is debate about whether some of these are fundamental (for example, super-sub-type can be defined in terms of type-instance). There is also debate whether these all belong to the same family of relations or are distinct types. Whatever the outcome of these debates, as noted earlier, in practice these hierarchies are a key part of the backbone of the ontological architecture. One powerful way they do this is through their formal structure. Here we look at the formal properties of hierarchies and how these apply to the three relations – to see how they, together, help shape the ontological architecture. We outline the properties below and consider their relevance to the three relations.

These three relations normally manifest as hierarchies; in other words, they have the structure of a partially ordered set (or in the case of type-instance, it’s cover relation, as it is not transitive). They are standardly represented in an obvious way in Hasse diagrams (sometimes known as upward diagrams) as a directed acyclic graph – nodes connected by arrows that have no cycles – see Figures 1 to 6 below. We use these diagrams to show the formal structures we are examining. The relations have a conventional direction, given in Table 2.

Table 2 – Conventional directions 

There are some TLOs – such as Entity-Attribute-Relation (the original Chen version) – where there are no super-sub-type relations. This is often found in the physical implementation – SQL being a clear example. Further, it is often the case that whole-part relations are not explicitly marked, in other words, separated out from other relations.

Typically, TLOs will have a range of choices on how they constrain the three hierarchies – 4.2.1.1 to 4.2.1.8 identify the relevant choices which we use below to analyse the TLOs. Often, as noted earlier, the underlying question is whether these constraints breach an explanatory sufficiency (plenitude) principle and so unnecessarily limit expressiveness. As always, there is often various factors in play, so the decision is not clear cut.

4.2.1.1 Parent-child-arity

In hierarchies, the number of parents a node can have is the parent-arity, the number of children the child-arity (note that the number of parents may differ from the number of ancestors). In some TLOs some of the relations have their parent-arity or child-arity limited to one. This changes the structure from lattice-like to tree-like (see Figure 2).

Figure 2 – Parent-child-arity structures in Hasse diagram format

The way these constraints are typically applied to the three relations is outlined in Table 3; which shows that the relevant choices are for type-instance and super-sub-type. In the object-oriented modelling community, these are known respectively as single or multiple classification and single or multiple inheritance.

Table 3 – General parent-child-arity

Constraining the hierarchy to a single parent is prima facie parsimonious. However, it also seems prima facie explanatorily insufficient. Why should a type such as mare not have female and horse as its supertypes? Why should an individual such as Donald Trump not be an instance of the types ‘human being’ and ‘biologically male’? These choices for single parent structures look likely to be less than optimal unless there are other factors counting in their favour.

4.2.1.2 Super-sub-type – transitivity

We focus here on the transitivity of the super-sub-type relation. Type-instance is generally considered not to be transitive and whole-part to be transitive.

The super-sub-type relation can be found in the early logic, in, for example, Aristotle’s syllogisms – in the assertion that ‘Every S is P’ (Every Human is an Animal). This can be translated into ‘S is a sub-type of P’ (Human is a sub-type of Animal). Its explicit recognition as a relation came with the nineteenth century mathematization of logic by Boole and others. Implicit visualisations of it as containment appear in Euler and Venn circles. However, it is more commonly visualised now as a hierarchy diagram – where the links represent instances of the sub-type relation. The majority of the graphic representations of the TLOs (in Appendix F) are super-sub-type hierarchy diagrams.

However, some care needs to be taken when interpreting these diagrams – as they only show the cover relation (parents and children with no ancestors or descendants). The traditional semantics of super-sub-type is transitive: if every B is A and every C is B, then it seems clear that every C is A. So, ancestors or descendants are automatically included (though not shown in the diagrams).

In some TLOs, their version of super-sub-type is not transitive – ancestors or descendants are not automatically included. Typically, only the links shown in the hierarchy are deemed to exist. The UML TLO is an example of this, which is most likely driven by implementation rather than semantic concerns. This choice should be made explicit.

Figure 3 – Intervening subtypes 

A similar kind of interpretation situation occurs when the super-sub-type hierarchy diagram only shows the relevant types. This is commonplace where the TLO supports extensional types. In this case, where a super-sub-type hierarchy diagram shows B as a sub-type of A, one cannot automatically infer that B is a child sub-type of A – as there may be intervening sub-types. An extensional TLO allows any collection of objects to be a type. If there is more than one instance of A that is not an instance of B – for example c and d in Figure 3, then there is a type C which has the members of B plus c as its members. C is not identical to either A or B as it has c but does not have d as a member. C is however a super-type of B and a sub-type of A This hopefully illustrates how ontological commitments impact upon the interpretation of these diagrams. This choice is dealt with under the formal generation section.

4.2.1.3 Boundedness

Hierarchies as ordered relations might or might not have a top or bottom. As shown in Figure 2, the hierarchy is bounded if all of the maximal paths terminate, and unbounded if any maximal path does not terminate, though, as the diagram also shows, some may. The hierarchy is upwards bounded if all the maximal paths terminate upwards, and the set of terminating nodes are the top elements of the hierarchy. The hierarchy is downwards bounded if all the maximal paths terminate downwards, and the set of terminating nodes are the bottom elements of the hierarchy.

These four options permute into four possible configurations. One of them, upwards and downwards bounded, opens up the possibility of further constraining the hierarchy to a finite number of levels.

The interesting hierarchical relation for us, in the top-level ontologies we have reviewed, is type-instances. The first interesting case for us is firstly, whether type-instances is downwards bounded – the left-most case in Figure 4.

Figure 4 – Possible boundedness options in Hasse diagram format 

Type-instance downwards boundedness is associated with the universals-particulars division that goes back to the Ancient Greek Aristotle, and beyond; where universals have instances, but particulars do not (another way of defining bottom). All seriously ontologically committed top-level ontologies make this division. Some of the generic ontologies have meta-models that place no constraints on the hierarchy. An example would be OWL’s use of punning; it does not identify a bottom level, so it is always possible to extend downwards. The Topic Map Reference Model is similarly unconstrained.

A pragmatic argument for this lack of constraint is that it is too onerous to build the bound into the model at design time, and that it is more useful to let the users at runtime decide on whether or not to extend the hierarchy down a level. This then places the onus on the users to ensure the quality of the boundary, to ensure, for example, that something that is clearly an individual, such as Donald Trump, has no instances.

Figure 5 – Fixed level boundedness

Then if type-instance is also, upwards bounded – the left-most case in Figure 5; there is a choice as to whether it is finitely bounded to a fixed number of levels – and if so, to how many levels. If TLOs are so constrained, they are often fixed to either three or two levels. Figure 5 has examples of two and three levels. OMG’s Meta Object Facility (MOF) is a case whether there are four.

The way these constraints are typically applied to the type-instance relations is outlined in Table 4; the boundedness choices for the other two relations (whole-part and super-sub-type) are not sufficiently interesting to make it to the framework.

Table 4 – Type-instance boundedness options 

4.2.1.4 Intransitive vertical stratification

Type-instance is intransitive – for example, if a is an instance of type b and b is an instance of type c – it does not follow that a is an instance of type c. This allows us to distinguish between cases where a node’s descendants could have its ancestors as parents – and where it does not (for transitive relations, it is always the case). This affects the structure and is visible in the hierarchy’s Hasse diagram as illustrated by Figure 6. Also, stratified hierarchies can be ranked – also illustrated in Figure 6.

Another way of characterising this is as a distinction between hierarchies where each new rank can only be constructed, or based upon, the components of the previous rank (stratified) – and ones that can be constructed from all earlier ranks (unstratified). Of course, in cases of two levels, the previous rank is all earlier ranks, so it is a limit case of stratified. The standard technical terms for these are stratified and unstratified respectively – so we use them. This vertical stratification is a different sense of stratified from the one used in horizontal stratification; it is worth paying attention to the different senses.

Figure 6 – Ranks: vertically stratified and unstratified 

Ontologies that are defined using meta-models and meta-meta-models, such as UML and MOF, are typically stratified. Extensional ontologies, such as those based upon BORO and IDEAS, are usually unstratified. This distinction is much discussed in the mathematics of set and type theory, where sets are unstratified and types stratified.

The stratified approach, by some measures, is less structurally simple as it involves more restrictions. Also, as one can see from the Figure 6, the stratified approach is ontologically parsimonious and the unstratified approach plenitudinous. The key question is which provides more relevant expressiveness. This naturally leads to questions about what motivates the stratification restriction – there does not seem to be a good ontological answer for this.

4.2.1.5 Formal generation

Ontology models are typically built through the careful manual addition of references to objects in the model. However, this is not the only way the structure in the model is created. Some top-level ontologies include algorithms for automatically adding new objects to the model. This is known as formal generation, as there are formal (algorithmic) rules for the generation. If we want a rounded picture of the structure, we need to consider this formal generation as well.

There are a variety of types of algorithm that can be adopted. For our broad-brush picture, we just consider two core cases here: fusion and complement, the first an upwards (parent) generation the second a downwards (child) generation. This is enough to give a measure of the generative approach. Fusion is where one is given two objects of the right kind and then one can infer the existence of their parent fusion. Classic cases are mereological fusion and the pairing axiom in set theory – a whole that consists exactly of two or more particulars. Complement is where, when one is given a parent and one of its children, one can infer the existence of another child that is the rest of the parent. As Figure 7 shows, the formal generation produces both the object and its hierarchical relation(s).

Figure 7 – Two kinds of formal generation 

As Table 5 – formally generative options shows, there are choices for both these modes of generation for all three relations except for type-instance and complement. To see why type-instance is an exception, consider a singleton type A = {a}. It has the single instance a, but there is no complement of a. 

Table 5 – formally generative options 

Adopting formal generation for each of the three relations can be seen as examples of plenitude; all possible applications of the rule are automatically allowed. But this raises questions of whether there is overgeneration (see discussion on Basis in 3.2.1 above).  Could these be examples of profligacy and promiscuity? Given the inter-related nature of TLOs, this assessment needs to be done in the context of all the choices made by the TLO. However, a prima facie case for them can be made on the basis of their close association with the two standard examples of ontological economy, classical mereology and set theory.

4.2.1.6 Relation class-ness

The concept of first- and second-class objects was introduced by Christopher Strachey in the 1960s (Strachey, 2000). A second-class object is one that is not given the same ‘rights’ as other objects, a first-class object has the same rights as other objects. The particular right we are considering here is whether an object can be an instance of a type. If the three core relations are first-class objects, then they can be. Though the details differ slightly for the three relations, in each case, this allows for a (type-instance) link in our Hasse diagrams that starts with a link – as shown in Figure 8. The resultant graph structure is known as a hyper-graph.

Figure 8 – First-class relations Hasse diagram 

Whole-part relations are usually first-class. Type-instance and super-sub-type are often second-class but can be first-class. 

Table 6 – Relation class 

Imposing second-class-ness on these relations is a restriction on plenitude – as it introduces a block on the existence of possible objects. Hence, recognising all three relations as first-class would be an example of plenitude; all possible applications of the type-building rule are automatically allowed. The question then arises whether this plenitude veers into profligacy and promiscuity. It turns out that the standard pattern for classification, as used by Linnaeus in his taxonomy, needs these first-class objects (see Formalization of the classification pattern (Partridge, 2016) and Business Objects (Partridge, 1996).

4.2.1.7 Vertical structures

These vertical classifications are shown below.

Figure 9 provides a visual summary of this.

Figure 9 – Visual summary of the vertical aspects

4.2.1.8 Other vertical structures

There are a number of other vertical structures that have not been included as they are less relevant. These include:

• connectedness
• restricted single type-instance parent-arity – single classification.

Connectiveness

It is not necessarily the case that any two nodes in the graph are connected. If some nodes are not connected, then the graph is disconnected. In this case, the disconnected graph can be divided into connected graphs. See the section below on possibilia for an application. While the connectedness of the structure is important, there is no overall pattern in these core relations that allows us to broadly characterise the owning TLO.

Single classification

There are some groups of types where one would expect the instances to belong to only one type – in other words, the types partition their instances. Quantities are an example. We would not expect something to have two masses, to both weigh 5 kg and 10 kg – it weighs one or the other. Similarly, for qualities, we would not expect an object to be both coloured and transparent at the same time, it has to be one or the other. This kind of restriction is common in TLOs, but again there is no overall pattern that allows us to broadly characterise the owning TLO.

4.2.2  Horizontal aspects: stratification versus unification

There is a group of fundamental choices that impact the ontological architecture which involves whether or not to make a distinction. If one chooses not to make the distinction, one only introduces a single type. If one chooses to make the distinction, one introduces two types; one for each alternative. The choice boils down to whether to horizontally stratify or unify. One can describe choosing to make the distinction as ‘separating one potentially unified type into two’, creating a horizontal stratification in the hierarchy – and not making the distinction, ‘unifying the potentially separated two types into one’.

These choices are perhaps best explained by looking at the specific cases (see 4.2.2.1 to 4.2.2.8). We only consider the major cases relevant to our review of the TLO candidates. We focused on identifying the formal choice – whether to horizontally stratify or unify – and leave the other aspects driving the decision to the more detailed description later in the report (see 4.3). We have mostly described the choices from a unifying perspective, they could equally well have been described from a stratifying perspective.

4.2.2.1 Spacetime

We start with one familiar from 20th century physics. Prior to then, it was assumed that the spatial geometry of the universe was independent of one-dimensional time. There were two related but independent types, spatial regions (regions of space) and temporal regions (regions of time). The work of Einstein and Minkowski introduced the idea – which became accepted – that space and time could be fused into spacetime. Ontologically, this can be seen as unifying spatial regions and temporal regions into spatio-temporal regions whose instances are regions of spacetime. Figure 10 provides some examples from the TLOs. BFO is an interesting case as it hyper-separates, it separates but keeps the unifying type. This raises interesting ontological accounting questions about whether this is overgeneration (as so profligate) or interesting plenitude.

Figure 10 – Separating spacetime – TLO examples 

While space, time and spacetime may appear to be familiar notions for interpreting data, it turns out to be a tricky area to tie down formally. It takes some study to develop a clear idea of what the spacetime stratification choice here implies. 

We can illustrate the choice simply as between a 1D time plus 3D space or a 4D spacetime – as shown in Figure 11 (based upon Figure 1 in (Gilmore, 2016)) 

Figure 11 – Separation and unity of instances 

n many cases, as here, the stratification (or unification) of the types also implies a separation or unity of their instances. To appreciate the consequences of the choices, Figure 11 shows how three (simple) instances of locations end up under the two regimes – this is recapitulated in Table 7.

Table 7 – Three locations

An under-appreciated consequence of the separation is that 3D space is multiply located – it is located as a whole at each instant of 1D time.

Typically, a TLO will choose to stratify or unify the types and so separate or unify the instances. However, it can attempt to do both. As noted earlier, the TLO BFO provides us with an example. It opts to include both spacetime as well as space and time. This raises interesting semantic redundancies analogous to data redundancy. And so, a requirement that the spaces and times need to be coordinated with spacetimes – one can regard this as a kind of semantic or ontological denormalization analogous to database denormalization.

4.2.2.2 Locations

People often talk of physical objects and their locations, where physical objects occupy their locations, suggesting two related types; objects and locations (let’s leave the decision whether the location is spatial, temporal or spatiotemporal to the previous choice). For example, “today your car is parked in the same place as mine was yesterday” could be regarded as a location which was occupied by my car (a physical object) yesterday and your car today. There is a debate going back to Newton and Leibnitz in the 17th century as to whether location is absolute or relative. If it is relative, then location is clearly fundamentally different from physical objects – which aren’t. However, if it is absolute, a kind of substance, then this opens the possibility that one could unify objects and their locations as fundamentally the same, technically known as supersubstantivalism. If one does not have cases of interpenetration (see 4.3.3) then this resolves the oddity where physical objects exactly occupy a single location throughout their life – unifying eliminates this double-counting. If there is interpenetration, then two objects may collapse to the same location – which may have unintended consequences. After the unification, the physical object and its location, two kinds of substance, are replaced by a single supersubstantival object. One has a broad choice between separating or unifying physical objects and locations.

4.2.2.3 Properties

In language, there is a distinction between nouns and adjectives; between rose and red. This has been taken as an indication of a more fundamental distinction, between what are known as substances and the properties or qualities they bear, for example, where a red rose would have a rose substance that bears a red property/quality. However, in other contexts, such as a Venn or Euler diagrams, we would be happy to have overlapping circles for roses and red objects – with a single icon for each red rose in the overlap. This implies there are instances of the type object that belonged to both the lower level types rose and red. So, here is a choice between stratifying to substances as the bearers of properties or unifying to objects.

4.2.2.4 Endurants

Philosophers have noted that people say some types of object, such as stones and chairs, exist; whereas other types, events, occur or happen or take place. It is suggested that this marks a fundamental distinction between continuants and occurrents – where occurrents (that occur) are the events that happen to continuants (that exist). There is a competing view that there is no fundamental difference between the two, rather a different perspective on the same object – this has been labelled perdurantist. A classic example (for perdurantists) is glaciers.  From a day to day perspective they are solid, unmoving material objects – they exist and so could be classified as continuants. From a geological perspective, glaciers flow – they are events like the flowing of a river – so could be classified as occurrents. A common continuant/occurrent stance, is that there are two glaciers; the existing continuant and the flowing occurrent. A perdurantist stance would be there is a single perdurants object which can be looked at from two perspectives.

4.2.2.5 Immaterial

Philosophers have suggested that the hole inside a doughnut is different from the doughnut. The doughnut is composed of stuff whereas the hole is not composed anything – it is defined by the doughnut. They suggest making a stratification where the doughnut is a material object and its hole is an immaterial object dependent upon the material doughnut. A unifying stance would not regard this distinction as fundamental and not recognise material and immaterial are fundamental types in its ontology. The hole has a spatial extent that contains matter, though this matter may well change over time. In a sense it is ‘immaterial’ what matter is in the hole, but this does not, by itself, make it either immaterial or a fundamentally different kind of object.

4.2.2.6 Summary

Table 8 lists these specific cases, and the stratifying relations that typically relate the separated objects. All of these choices are present in some of the TLOs we have surveyed. The list is not intended to be complete but gives an indicative picture of the range of stratifications. For example, there is a further major choice, whether to make a distinction between form and matter (often known as hylomorphism – for more details see “Form vs. Matter” (Ainsworth, 2020)). Even though this is currently an active area of research, we have found no examples of this among the candidate TLOs. So, we merely note the choice here and omit it from the list.

Table 8 – Summary of the horizontal stratification choices introduced 

4.2.2.7 Stratification journey
There is limited inter-dependence between the choices meaning that a range of permutations are possible. For a top-level ontology, one can visualise the architectural stratification choices being adopted in a sequence, starting with no stratifications and introducing the choices one or two at a time – as illustrated in the figures below. This sequence or journey is a rational reconstruction – the original development of the top-level ontology is most likely ad hoc and bottom up. However, this reconstruction gives us a good picture of the underlying architecture.

Figure 12 and Figure 13 show a four stage example top-level ontology stratification journey (or sequence) for BFO, which includes multiple stratifications– where five choices result in six strata. Figure 14, shows a journey with no choices resulting a single stratum based upon the IDEAS TLO. Finally, Figure 15 is the legend for these stratification journey diagrams.

Figure 12 – An example top-level ontology stratification journey – BFO stages 1 to 3 

Figure 13 – An example top-level ontology stratification journey – BFO stage 4 

Figure 14 – An example top-level ontology stratification journey with no stratification - IDEAS 

Figure 15 – Legend for stratification journey diagrams 

As these examples show, choosing to make the distinction stratifies the architecture – choosing to not make it, correspondingly, unifies it. From the perspective of fundamental parsimony, making the distinction is always multiplicative, simpliciter – in the sense that it results in two fundamental types rather than one. It is also, in many cases, even more multiplicative in that it introduces a new type of fundamental relation between the separated types. There can be a variety of reasons for making the distinction. The interesting question for us is whether the cost accounting shows this worthwhile. It is often difficult to do this for the individual stratifications as useful derived objects – including fruitfulness ones – often emerge from the way the choices interact.

4.2.2.8 Other divisions

A common division, often mentioned, is the division into universals and particulars. However, unlike the stratification choices we have looked at above, this is not really a stratification. As we noted when looking at boundedness above, this is better seen as a choice as to whether the type-instance relation is downwards bounded.

4.3 Universal commitments

The section focuses on the details of the commitments themselves. It focuses on universal commitments; ones that one would expect to be exercised in all (or almost all) domains. Some of these commitments have appeared in the previous section – as they impact directly upon the ontological architecture of the hierarchies. We deal with the details of these first (see 4.3.1 and 4.3.2).

4.3.1 Type-instance

It is relatively easy to find examples of this relation. The cat called Holly is an instance of the type cat. My hand is an instance of the type hand. However, it has a variety of potential ontological explanations depending upon the details of the ontological commitment. The vertical and horizontal aspects help to characterise what has been chosen, but heavyweight TLOs will typically fill in more detail. This can vary substantially – as the following simplified examples show. One form of explanation is that types are the collection of their instances – often labelled extensional. In this case, the type-instance relation boils down to being a member of that collection.  Another, form of explanation is that the instance exemplifies the type and so is in a way partially identical to it. So, Holly exemplifies cat-ness, in the sense that she is partially identical to it. Similarly, my arm exemplifies arm-ness. This topic is subsumed under the more general topic criteria of identity and dealt with in 4.3.6.

4.3.2 Whole-part – mereology

Mereology (from the Greek μερος, ‘part’) is the theory of the whole-part relation. This relation is typically transitive, where if A is a part of B and B is a part of C then A is a part of C. This relation has been extensively formalised where a number of decomposition principles have been identified of various strengths from which one can build the overall theory. These start with the weakest, core mereology (CM) though minimal mereology (MM) and extensional mereology (EM) to general extensional mereology (GEM) (The logical formulation of these can be found in (Varzi, 2019)). If a TLO makes its mereology explicit, one would expect it to adopt a selection of the identified principles, typically one of these variants above. Indeed, a number of the TLOs adopt GEM.Mereology is closely related to topology, in the sense of the ways in which objects overlap and connect. This is why mereology is often extended to mereotopology. This has also been extensively formalised giving rise to a range of theories, with the strongest theory being General Extensional Mereotopology with Closure conditions (GEMTC). A detailed description of this can be found in (for example) Chapter 4 of Casati and Varzi’s Parts and places: the structures of spatial representation (Casati, 1999). Again, if a TLO makes its mereotopology explicit, one would expect it to adopt a selection of the identified principles – or be able to provide its own.

4.3.3  Interpenetration: location and mereology (supersubstantivalism+)

The separation of location and objects provides a simpler background for explaining how mereology and interpenetration interact. Consider the standard example of a statue and the clay it is made of. Under one view, the statue and the clay are different objects and they share no parts. However, they do share a location. We typically introduce a direct relation to capture this, saying the statue is composed of clay. We also assume that the statue and the clay have separate parts and parthood relations, but that the parts of the statue align with the parts of the clay. So, if an arm (a part of the statue) breaks off, the corresponding part of the clay does too. There is some kind of mereological divorce and associated harmony or coordination. There are other kinds of similar cases. Consider a road that marks an administrative boundary. We could say the road and boundary share a location, but do not overlap – they share no common parts. In general, we say that two objects interpenetrate when they do not share parts, but their locations do – and the two examples above are cases of interpenetration.

We are faced with here a choice about how we want to deal with these cases. We can adopt a position, known as supersubstantivalism+, which does not allow the mereological divorce and coordination needed for interpenetration. Instead, it assumes there is no divorce, the objects share parts. At the times when the clay composes the statue, that part of the clay is part of the statue. At the times when the road marks the administrative boundary, they overlap, sharing common parts.

At a general level, supersubstantivalism+ is prima facie more qualitatively parsimonious as there is no need for the occupies relations. It is more quantitively parsimonious as there is no need for the separate parts – and their parthood relation. However, to make this position work it helps if one also has a unifying view of spacetime together with objects and their locations.

4.3.4  Materialism: abstract particulars and non-materialism

In modern thought, there is an attachment to the idea that the world is composed of only material objects that exist in space and time – and so one’s ontology is built from these material objects – (roughly) materialism. The idea behind this is that it is difficult to see how objects that exist outside space and time could affect the world and, in particular, could affect our minds such that we could know them. An alternative view is that there are also abstract particulars – individuals that have no existence or dependence on space or time. Numbers are often given as an example of these abstract objects. TLOs often explicitly commit to one or other view.

It is difficult to see how these abstract particulars could have an extension in the normal sense. As we discuss later in 4.3.6, extension can be used as a basis for a view of identity. If one adopted this position, then one will probably favour the materialism choice and avoid the difficulty of developing an extensional criterion of identity for abstract particulars.

4.3.5  Possibilia: actual or possible worlds

Most information processing systems seem to involve possible objects that sometimes are not actual. When we arrange a meeting in the future that eventually does not take place, this is possible but not actual. When we draw up plans for a building that is not built, this is possible but not actual. The TLO needs to provide an account of such objects. In this regard, there is traditionally one major choice to be made. This is whether to limit existence to the actual world or allow it to range over (all) possible worlds.

If one adopts a possible worlds approach, then talk of possible objects becomes talk about objects in possible worlds. The possible meeting that did not happen in this world happened in some other possible world. The planned building that was not built in this actual world was built in some other possible world. If one restricts oneself to the actual world, one needs to develop alternative explanations for these objects. One example, called encoding, suggests talk about possible non-actual objects encodes the object – and that encoding works with a different logic that does not imply actual existence. There are a range of these alternatives in the literature, but none of these are as comprehensive or simple as possible worlds, which is why it almost universally adopted in the TLOs.

4.3.6  Criterion of identity: extensional or intensional

One of the key architectural choices for a top-level ontology is the basis or strategy for its criteria of identity. This establishes a key part of the infrastructure. These criteria determine for the various types of objects whether, in principle, so not necessarily in practice, selected objects are identical or different. There are two broad choices; extensional and intensional (with an ‘s’, not a ‘t’).

Extensional criteria of identity are compositional (constructional); where objects are identical if they are ‘constructed’ from some external criteria – often involving its components. A classic example of an extensional object is sets, where sets composed (constructed) from the same members/components are identical. Another example is material objects’ identity defined in terms of spatiotemporal extension – making their identity dependent upon spatio-temporal regions. These regions then, typically, have identity defined in terms of equivalent (spatio-temporal) parts – assuming some kind of extensional mereology. So, two spatio-temporal regions will differ if one has a part that is not a part of the other.

Intensional criteria of identity aim to capture the meaning or essence of the entity; in practice this is typically represented as a definition. We can construct a classic example of an intensional object using the Euclidean equilateral triangle. Given Euclid’s Elements – Book I – Definition 14: “A figure is that which is contained by any boundary or boundaries” and Definition 20: “Of trilateral figures, an equilateral triangle is that which has its three sides equal.” An equilateral triangle is then defined as any figure with three sides, where these three sides are equal. This equilateral triangle object referred to by the definition has an extension, the set of figures it applies to – but it is, in principle, possible that other definitions will refer to different objects with the same extension.

One can get to the heart of the distinction as follows. Under an extensional strategy, any object with this set as its extension is equivalent – defining identical objects. However, this is not the case under the intensional strategy; two different intensional objects can have exactly the same extension without being identical. The subject has some key detailed technical aspects which are briefly summarised in Appendix B.

There are clear links here to other choices. Consider the choice between spacetime and space and time. Spatial extension (at a time) is insufficient for identity. There are lots of examples of objects that occupy exactly the same space at a time – at the time of writing, Donald Trump and the President of the United States is an example. However, spacetime is sufficient for identity in these cases – Donald Trump and the President of the United States have different spatio-temporal extents. This makes it natural to choose spacetime over space and time to open up the possibility for extensional identity based upon spacetime. There is a similar situation for types and their extension. In this actual world, there may not be enough verity to capture differences in meaning in the actual extensions. For example, the types renate (having a kidney) and cordate (having a heart) could have exactly the same extension. When we extend extension over possible worlds, then this becomes impossible. If it is possible to have animals with a heart but no kidney, then they will exist on some possible world. Making a choice for possible worlds over the single actual world creates the space for types to have extensional identity.

From an ontological engineering perspective, one can summarise the choice between the two as follows. An extensional strategy allows one to have, in principle, a clear, accurate criteria of identity – the extension. However, these are thin criteria, they do not attempt to capture the characteristics that one might use to identify the object. This is done elsewhere.

An intensional strategy cannot provide clear, accurate principles as there is a difficulty giving these definitions to most common notions (person being an example). However, the definitions given are thick and typically contain the characteristics that enable easy identification.

Prima facie, an extensional strategy is useful when one needs to clearly and unambiguously identify objects. However, this choice comes entangled with other choices, so a case also needs to be made in the context of an integrated set of choices.

4.3.7 Time: presentist versus eternalist (including change)

Natural language is often tensed. We say “Jane was in Glasgow yesterday, she is in London today and she will be in Dover tomorrow” – using past, present and future tenses. We use the tenses in ways that imply existence. So, we say “there are no more dinosaurs” implying they no longer exist. Presentists believes that these tenses in ordinary language have an ontological significance. What is going on now really exists, what happens in the past has existed and what might happen in the future has yet to exist. The eternalists do not, they assume tenses have no real ontological significance.

One way to understand this position is to look at a problem it raises. Presentism prima facie imposes restrictions on cross-time relations; relations where the relata are in different times – so never present at the same time. Being a great-great-grandfather (for example) will typically involve people from different non-overlapping times. Presentism would seem to deny the existence of any of these kinds of relations. There are, as always, ways around this, but this helps to illustrate the effect this choice has on the architecture.

We mention this choice here, as it is a well-recognised choice in philosophy textbooks and also in the computer/applied ontology design. However, all the candidate top-level ontologies that make an explicit choice, choose eternalism. This is understandable from a data perspective. There would be a large processing overhead in having to switch tenses as objects ‘move’ from future to present to past.

4.3.8 Indexicals: here and now

If the previous choice is eternalism (which it is for all the candidate TLOs that make the choice) then this raises a new issue. How does one recapture the present? This is a key requirement. If one does not know when now is, then one loses track of all sorts of things. One can know the balance of an account at every point in time, but not be able to work out what the current balance is. Being able to represent the present is an obvious requirement for a system. One solution, if one is eternalist, is that one needs to include non-ontological epistemological (or agentological) aspects into the model for the system. For further discussion see Appendix J.

4.3.9 Relations – arity

We often think of relations as being between two objects. Examples are father-of or earlier-than. However, there are relations of higher-order arity (greater than two) – an example of a three-place relation is: X is between Y and Z. This is an example of plenitude, where it is possible to have relations of higher order – where there is no, in principle, bound. Hence, it is worth noting whether TLOs support higher-order arity, and where they restrict themselves to two objects, what the motivation is. Pragmatically, higher-order relations are more difficult to implement, especially if there is not a low finite bound. In practice, one tends not to find relations with orders of more than a single digit – so a pragmatic finite bound may be acceptable when implementing.

The formal nature of relations is an active area of research. So, when doing the more detailed analysis within the framework and when looking in more detail at the TLOs, it may be worth looking at what position is taken on this. In particular, for extensional TLOs it may be worth considering their criterion of identity for relations. We do this in Appendix F.

4.3.10 Choices

These cash out into seven choices in the assessment framework.

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