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Overview

the semantics of OWL can be a little tricksy at times. Having a firm hold of the semantics of axioms, the implications of those axioms and how the descriptions logics underlying OWL work should help in understanding the behaviur of one’s ontology when it’s given to a reasoner. This quiz presents some axioms and then asks some questions that allows one’s knowledge to be tested and possiblely enhanced once the answers are shown. …you are cordially invited to make up your own example, and your own modifications/enforcements! And to drink beer while doing this quiz.

The Authors

Uli Sattler and Robert Stevens
Information Management and BioHealth Informatics Groups
School of Computer Science
University of Manchester
Oxford Road
Manchester
United Kingdom
M13 9PL
sattler@cs.man.ac.uk and robert.stevens@Manchester.ac.uk

Introduction

There are quite a lot of facts about OWL ontologies to know that may affect our modelling, and these are rarely spelled out completely. Rather than making our “Top 16 things you need to know about OWL ontologies, but were too scared to ask”, we have made a quiz for you to test your understanding of them, together with explanations and examples. While we try to figure out a way to make this quiz interactive, you can try it out as it is, and we hope you enjoy the experience.

Preliminaries

Our example ontology is:

A EquivalentTo P some B
B SubClassOf C
C SubClassOf Q only D
C DisjointFrom D
Dom(Q) = C

b:A

All questions are “True or False” questions.

Questions about models

1) For an axiom to be entailed by an ontology, it has to be true in one of the ontology’s models [1] ?

False: An entailed axiom has to be true in all models of an ontology – and there may be many of these.

2) A model has some minimum size?

True: Sort of – it has to have at least one element in it. In fact, our example ontology has a model of size 1, where b is P-related to itself, and an instance of A, B, and C.

If we want larger models, we need to say so….see below.

3) Different individual names mean different things?

False: If we add c:B to our example ontology, we can still have a model with only 1 element that is both b and c, and P-related to itself, and an instance of A, B, and C.

If we want a form of unique name assumption, we need to say so: b DifferentIndividualFrom c.

4) Different class names denote different sets?

False: Unless we force this to be the case, we can always have a model where two classes have exactly the same instances. In our example ontology, B and C can have exactly the same instances.

An extreme way of forcing classes to be different is a disjointness axiom.

5) A class always has an instance?

False: In our example, we can have models where, e.g., D has no instances at all, like the one sketched under (1).

If we want a class to always have an instance, we need to introduce it: we need to coin a name for an individual and say its type is that class.

6) (We assume that we now all know the answer to “Does a property always have a pair of elements in it?”) If Dom(Q) = C is in our ontology, then each instance of C has a Q-successor?

False: We can still have a model where not even a single pair of elements is related by Q! The domain axiom only says that if two elements are related by Q, then the first element is an instance of C.

7) If we write C SubClassOf Q only D, this means that all instance of C have a Q-successor, and all its Q-successors are in D?

False: We can have models where instances of C don’t have a single Q-successor. All we know is that, if they have Q-successors, then they are instances of D.

If we want to force that C+s do have indeed one or more +Q-successors, then we need to add something like C SubClassOf Q some Thing.

8) A property P can relate an element to itself, say P(b,b)?

True: It can – unless we prevent it explicitly, e.g., by making P‘s domain and range disjoint, or by saying that P is irreflexive.

9) The following ontology has a model: A SubClass (P some (B and not B)), b:A?

False: It doesn’t have one: A now has an instance, b, which needs a P-successor, which would need to be both a B and not a B. Since the latter is impossible, our model is impossible.

10) The following ontology has a model: A SubClass (B and not B), b:B?

True: It has one – just not one with an instance of A.

11) There is an upper bound on the size of a model?

False: Models can be of any size we want – as long as they have at least 1 element.

12) Can a model be infinite in size?

True: It can be. And in it, we can have some classes with no instances, some with finitely many instances, and others with infinitely many.

13) Can an ontology have infinitely many models?

True: It can – our example ontology from the beginning has!

14) Given class names A, B, and C, I can build only finitely many class expressions?

False: Even with a single name A, I can build A, A and A, A and A and A, …. so infinitely many class expressions. Of course these are all equivalent, but they are still syntactically different. Similarly, I could consider A, A and B, A and (B or A), A and (B or (not A)), A and (B or (not (A and B))), A and (B or (not (A and (B or A)))), …. a slightly more diverse infinite sequence of class expressions.

15) Given a class name A and a property P, I can build only finitely many class expressions that are not equivalent?

False: Consider A, P some A, P some (P some A), P some (P some (P some A)),…and we have an infinite sequence of (increasingly long) class expressions, no two of which are equivalent. If you read P as hasChild and A as happy, then this sequence describes happy (people), parents of happy (people), grandparents of happy (people), great grandparents of happy (people), etc., and of course these are all different/non-equivalent concepts.

16) Given an ontology O that has class names A, B, and C, it can entail infinitely many axioms?

True: In fact, every ontology entails infinitely many axioms – but most of them are boring. For example, every ontology entails A SubClassOf A, A SubClassOf (A and A), A SubClassOf (A and A and A), …, so we already have infinitely many entailments (these boring entailments are called tautologies). Now assume our ontology entails A SubClassOf B, then it also entails A SubClassOf (B and B), … and it also entails (A and B) SubClassOf B, so there are many boring variants of originally interesting axioms.

Finally, there are ontologies that have infinitely many interesting entailments: we can easily build an ontology that entails A SubClassOf (P some B), A SubClassOf (P some (P some B)), A SubClassOf (P some (P some (P some B))), and none of these axioms is redundant, for example the following 2-axiom ontology:

A SubClassOf P some B
B SubClassOf P some B

So, when an ontology editor like Protege shows us the inferred class hierarchy or selected entailments, it only shows us a tiny fraction of entailments: there are always many more, and it depends on your ontology and your application how many of these are interesting or boring.

References

1. U. Sattler, "OWL, an ontology language", Ontogenesis, 2010. http://ontogenesis.knowledgeblog.org/55

Overview

We are going to discuss various options for modelling properties or qualities of objects, using colour as an example. We try to compare the different options with respect to what they allow us to distinguish and query.

The Authors

Uli Sattler and Robert Stevens
Information Management and BioHealth Informatics Groups
School of Computer Science
University of Manchester
Oxford Road
Manchester
United Kingdom
M13 9PL
sattler@cs.man.ac.uk and robert.stevens@Manchester.ac.uk

Characterising classes

Assume we want to model some concepts, like toys, ideas, or plants, in an OWL ontology, e.g., Ball, Plan, or Rose. Of course we will fix, in this ontology, a vocabulary (a set of terms) for these concepts, and arrange it in a subclass hierarchy using SubClassOf axioms. But we also want to describe their relevant characteristics, i.e., the things for which we use adjectives, as in “red Ball”, “cunning Plan”, or “thorny Rose”.

OWL affords several modelling options for this very common situation. Some work better than others and the various options can be useful in describing various things about OWL. In particular, options will differ with respect to the questions we can ask in our ontology – and get answered via a reasoner. This modelling situation and what OWL can offer is also a useful place to discuss those modelling options.

isGreen as an object property

Following a pattern we see frequently, we could use an object property isGreen, restrict its range to true and false: we introduce a Class TruthValues and make true and false its only instances. Furthermore, we can restrict its domain to Physical objects, and state that isGreen is functional. Thus, a physical object can hold only one isGreen object property which is filled by either true or false and this would appear to capture all the situations we need for saying whether or not an object is green.

While we may not find this style of modelling pretty, it allows us to retrieve all green things by asking for instances of isGreen value True. Or we can introduce a class GreenObjects as equivalent to PhysicalObject and (isGreen value True).

Why would we consider this first approach to be not well modelled?

Firstly, we use abstract objects for the Boolean values true and false. As a consequence, we need to state explicitly that they are different, to ensure, for example, that (isGreen value True) and (isGreen value False), when appearing on the same object, is indeed inconsistent. We would usually do this by making the individuals true and false different, using DifferentFrom.

We would also need to decide where these abstract objects true and false “live”, i.e., do we have a suitable superclass of TruthValues? And should we introduce other ways of writing them, like “0” and “1”?

Of course not: for cases like this, OWL has data properties and XML Schema datatypes: if we really like this modelling style, at least we should use a (functional) data property isGreen whose range is Boolean.

Now is there anything else wrong with this style? Yes: assume we want to introduce another colour (i.e., data property), isLightGreen, and another class LightGreenObjects, following the same scheme. Then we would expect the reasoner to infer that LightGreenObjects is a subclass of GreenObjects, i.e., that everything that is light green is also green – but of course this is not entailed by our ontology! To fix this, we could try to make isLightGreen a sub (data)property of isGreen – but this will not have the desired effect: it will work fine in the case that, say, MyBall isLightGreen true because then our ontology entails that MyBall isGreen true. Unfortunately, an analogous yet unwanted behaviour will take place if MyBall isLightGreen false, i.e., our ontology would then entail that MyBall isGreen false which would lead to a contradiction in the case that MyBall is dark green!

So, I think we can safely consider this modelling approach to be unsuitable.

Class: Green as the class of green things

Next, let us consider another very simple approach: let’s introduce a class Green and make MyBall an instance of it, i.e., the class Green really stands for “the green things”. We can then introduce a subclass LightGreen of Green, and entailments work in the right way: light green things will be entailed to be green, whereas green things are simply green (i.e., we don’t know whether they are light green as well).

So, we can clearly say that this approach is superior – but we will soon see its limitations if we consider another colour, say Red. Of course, red isn’t green, and so we should make Red and Green disjoint. But what if MyBall is green with red dots? If I make MyBall an instance of both Red and Green, my ontology will be inconsistent! Similarly, we could not write a definition for things with more than one colour – other than by enumerating all possible colour choices, which clearly is not evolvable at all, since it requires major reworkings each time we add a new colour or change the name of a colour.

Green as a subclass of colour

What the previous approach has shown us is that we should distinguish between a colour and things that have this colour. That is, let’s introduce a class Colour with subclasses Red and Green, with the latter having a subclass LightGreen. We can again state that Red and Green are disjoint. And let’s introduce a property hasColour with domain PhysicalObject and range Colour. Of course we won’t make this property functional so that MyBall can be an instance of hasColour some Red and hasColour some LightGreen.

Things work much better in this modelling approach than they did before:

• the ontology is consistent,
• MyBall is now also an instance of hasColour some Green – because LightGreen is a subclass of Green, and
• MyBall is an instance of multi-coloured things, i.e., of (atleast 2 hasColour Colour)$ – because Red and Green are disjoint, and
• we don’t need to change the definition of multi-coloured things when we add a new colour.

So, is this the best we can do?

Green as an instance vs a class

You may wonder whether we shouldn’t make LightGreen an instance of the class Colour? After all, isn’t light green is a colour?! We may think so today – but tomorrow we may want to distinguish different kinds of light green, like lime green: if we want that limet green things are also light green things, then we should better make both classes and the latter a subclass of the former – so that we could also consider lime green as a subclass of light green (we have written a blog on the question “instances versus classes” earlier).

Defining Colour

As an alternative or extension to the above naive model of colour, we can use well-established models of colour such as RGB or CMYK or such like. Choosing RGB as an example, we can define a colour as a (visual perceptual) property that has three numerical values associated with it, adapting one of the standard coding schemes, e.g.,

Class: Colour
        EquivalentTo:
(hasRValue some nonNegativeInteger) and
(hasGValue some nonNegativeInteger) and
(hasBValue some nonNegativeInteger)

DataProperty:  hasRValue
Domain: Colour
Range: xsd:nonNegativeInteger[<= "255"^^nonNegativeInteger]

DataProperty:  hasGValue
...

In this way, we can specify specific colour instances, e.g.,

Individual: limegreen
Facts:
        hasRValue "50"^^nonNegativeInteger,
        hasGValue "205"^^nonNegativeInteger,
        hasBValue "50"^^nonNegativeInteger

and we can try to (!) define colour classes, e.g.,

Class: Green
        EquivalentTo  :
(hasRValue some nonNegativeInteger[<= "100"^^nonNegativeInteger]) and
(hasGValue some nonNegativeInteger[>= "150"^^nonNegativeInteger]) and
(hasBValue some nonNegativeInteger[<= "100"^^nonNegativeInteger])

although the above is not really a good definition of Green in this way: we would need to compare the values of hasRvalue, hasGvalue, and hasBvalue, which requires data range extensions. So, while this approach would allow us to hold, in our ontology, the exact colour(s) of things – which we could then use to, say, render their graphical representation – it has its limitations w.r.t. how we can define classes. We could consider a hybrid approach whereby we keep the RGB values of our objects, but also add suitable symbolic names for their colours; the latter could be done automatically.

Is Colour different from other characteristics

For this blog, we chose the example of colour. Of course, you may need to model, in your ontology, other characteristics such as texture, shape, taste, etc. While these characteristics differ, the general approach of modelling these, and of evaluating the fitness of a model are similar: can I refine my model easily? Do I get the expected entailments? Can I define interesting classes or query for instances that share the same property?

Summary

We hope we have (a) shown you various ways in which a property of an entity (a quality) can be modelled, and (b) the effects they have on what we can define or query in these different approaches, and how robust they are wrt future extensions. The penultimate option (having a Colour class with an object property hasColour with objects that have that colour at the left-hand-side) is the one usually followed for describing qualities in an OWL ontology; here the dependant thing (the adjective or modifier) is separated from the independant thing (the object to which the characteristic, adjective, quality, …) is applied. This is a typical separation of concerns type approach. Most top ontologies will make this separation in some form Whilst we’ve not explicitly used a top ontology in the Entity hasColour some Colour pattern above, we have implicitly done so [1]. It should also be pointed out that modelling colour is a tricky one [2], but it is a good example to bring up this common modelling situation and some options for doing so in OWL that highlights some aspects of how OWL works.

References

1. M. Egaña, A. Rector, R. Stevens, and E. Antezana, "Applying Ontology Design Patterns in Bio-ontologies", Knowledge Engineering: Practice and Patterns, pp. 7-16, . http://dx.doi.org/10.1007/978-3-540-87696-0_4
2. P. Lord, and R. Stevens, "Adding a Little Reality to Building Ontologies for Biology", PLoS ONE, vol. 5, pp. e12258, 2010. http://dx.doi.org/10.1371/journal.pone.0012258

Summary

Reasoners should play a vital role in developing and using an ontology written in OWL. Automated reasoners such as Pellet, FaCT++, HerMiT, ELK and so on take a collection of axioms written in OWL and offer a set of operations on the ontology’s axioms – the most noticeable of which from a developer’s perspective is the inference of a subsumption hierarchy for the classes described in the ontology. A reasoner does a whole lot more and in this kblog we will examine what actually goes on inside a DL reasoner, what is offered by the OWL API and then what is offered in an environment like Protégé.

authors

Uli Sattler and Robert Stevens
Information Management BioHealth Informatics Groups
School of Computer Science
University of Manchester
Oxford Road
Manchester
United Kingdom
M13 9PL
Ulrike.Sattler@Manchester.ac.uk and robert.stevens@Manchester.ac.uk

Phillip Lord
School of Computing Science
Newcastle University+ Newcastle
United Kingdom
NE3 7RU
phillip.lord@newcastle.ac.uk

What a reasoner does

One of the most widely known usages of the reasoner is classification – we will first explain what this is, and then sketch other things a reasoner does. There are other (reasoning) services that a reasoner can carry out, such as query answering, but classification is the service that is invoked, for example, when you click “Start Reasoner” in the Protégé 4 ontology editor.

So, assume you have loaded an ontology O (which includes resolving its imports statements and parsing the contents of all relevant OWL files) and determined the axioms in O – then you also know all the class names that occur in axioms in O: let’s call this set N (for names). When asked to classify O, a reasoner does the following three tasks:

First, it checks whether there exists a model [1] of O, that is, whether there exists a (relational) structure that satisfies [2] all axioms in O. For example, the following ontology would fail this test since Bob cannot be an instance of two classes that are said to be disjoint, i.e., each structure would have to violate at least one of these three axioms:

 Class: Human
 Class: Sponge
 Individual: Bob types: Sponge
 Individual: Bob types: Human
 DisjointClasses: Human, Sponge

In case this test is failed, the reasoner returns a warning “this ontology is inconsistent [2] ” which is handled differently in different tools. In case this test is passed, the classification process continues to the next step.

Second, for each class name that occurs in O – i.e., for each element A in N, the reasoner tests whether there exists a model of O in which we find an instance x of A, i.e., whether there exists a (relational) structure that satisfies all the axioms in O and in which A has an instance, say x. For example, the following ontology would pass the first “consistency” test, but still would fail this “satisfiability” [2] test for A (while passing it for the other class names, namely Human and Sponge):

 Class: Human
 Class: Sponge
 DisjointClasses: Human, Sponge
 Class: A SubClassOf: (likes some (Human and Sponge))

The picture above shows a model of this ontology with x and z being instances of Sponge, y being an instance of Human, and x and y liking each other. Classes that fail this satisfiability test are marked by Protégé in red in the inferred class hierarchy, and the OWL API has them as subclasses of owl:Nothing.

Thirdly, for any two class names, say A and B, that occur in O, the reasoner tests whether A is subsumed by B, i.e., whether in each model of O, each instance of A is also an instance of B. In other words, whether in each (relational) structure that satisfies all axioms in O, every instance of SBL is also one of SL. For example, in the ontology below (where Sponge and Human are no longer disjoint), DL is subsumed by SBL which, in turn, is subsumed by AL.

 Class: Animal
 Class: Human SubClassOf: Animal
 Class: Sponge SubClassOf: Animal
 Class: SBL EquivalentTo: (likes some (Human and Sponge))
 Class: AL  EquivalentTo: (likes some Animal)
 Class: DL SubClassOf: (likes some Human) and (likes only Sponge)

The picture above shows a model of this ontology with, for example, x being an insance of Sponge, Human, and Animal, and z being an instance of SBL and AL.

The results of these subsumption tests are shown in the Protégé OWL editor in the form of the inferred class hierarchy, where classes can appear deeper than in the (told) class hierarchy.

Alternatively, we can describe the classification service also in terms of entailments: a reasoner determines all entailments of the form

A SubClassOf B

of a given ontology, where

• A is owl:Thing and B is owl:Nothing – this is the consistency test, or
• A is a name and B is owl:Nothing – these are the satisfiability tests, or
• A and B are either class names in the ontology – these are the subsumption tests.

When we talk about a “reasoner”, we understand that it is sound, complete, and terminating: i.e., all entailments it finds do indeed hold, it finds all entailments that hold, and it always stops eventually. If a “inference engine” relies on an algorithm that is not sound or complete or terminating, we would not usually call it a reasoner.

Other things we can ask a reasoner to do is to retrieve instances, subclasses, or superclasses of a given, anonymous class expression, or to answer a conjunctive query.

How a reasoner works

These days, we usually distinguish between consequence-driven reasoning and tableau-based approaches to reasoning, and both are available in highly optimised implementations, i.e., reasoners.

Consequence-driven approaches have been shown to be very efficient for so-called Horn fragments of OWL
[A Horn fragment is one that excludes any form of disjunction, i.e., we cannot use “or” in class expressions, or (not (A and B)), or other constructs that require some form of reasoning by case.]
. In a nutshell, given an ontology O, they apply deduction rules (not to be confused with those in rule-based systems or logic programs) to infer entailments from O and other axioms that have already been inferred. For example, one of these deduction rules would infer

M SubClassOf (p some B)

from

A SubClassOf: B
M SubClassOf (p some A)

For example, ELK employs such a consequence-driven approach for the OWL 2 EL profile.

Tableau-based reasoners have been developed for more expressive logics, e.g., Fact++, Pellet, Racer, Konclude. As you can see, the first 2 tests (consistency and satisfiability) ask for a (!) model of the ontology – where a given class name has an instance, for the satisfiability test. And a tableau-based reasoner tries to construct such a model using so-called completion rules that work on (an abstraction of) such a model, trying to extend it so that it satisfies all the axioms. For example, assume it is started with the following ontology and asked whether DL is satisfiable in it:

 Class: Animal SubClassOf: (hasParent some Animal)
 Class: Human SubClassOf: Animal
 Class: Sponge SubClassOf: Animal
 Class: SBL EquivalentTo: Animal and (likes some (Human and Sponge))
 Class: AL  EquivalentTo: Animal and  (likes some Animal)
 Class: DL SubClassOf: Animal and  (likes some Human) and (likes only Sponge)

The reasoner will try to generate a model with an instance x of DL. Because of the last axiom, a completion rule will determine that x also needs to be an instance of

 Animal and  (likes some Human) and (likes only Sponge)

A so-called “and” completion rule will take this class expression apart and will explicate that x has to be an instance of DL (from the start), Animal, (likes some Human), and (likes only Sponge). Yet another rule, the “some” rule, will generate another individual, say y, as a likes-filler of x and makes y an instance of Human. Now various other rules are applicable: the “only” rule can add the fact that y is an instance of Sponge because y is likes-related to x and x is an instance of (likes only Sponge). The “is-a” rule can spot that y is an instance of Animal (because it is an instance of Human and the second axiom). And we can also have the “some” rule add a hasParent-filler of x, say z, and make z an Animal to satisfy the first axiom. We would also need to do a similar thing to y since y also is an Animal.

In this way, completion rule “spot” constraints imposed by axioms on a model, and thereby build a model that satisfies our ontology. Two things make this a rather complex task: firstly, we can’t continue creating hasParent-fillers of Animal because then we wouldn’t terminate. That is, we have to stop this process while making sure that the result is still a model. This is done by a cycle-detection mechanism called “blocking” (see Baader and Sattler paper at the end of this kblog). Secondly, our ontology didn’t involve a disjunction: if we were to add the following axiom

Class: Human SubClassOf: Child or Adult

then we would need to guess whether y is a Child or an Adult. In our example, both guesses are ok – but in a more general setting our first guess may fail (i.e., lead to an obvious contradiction like y is an instance of 2 disjoint classes) and we would have to backtrack.

So, in summary, our tableau algorithm tries to build a model of the ontology by applying completion rules to the individuals in that model – possibly generating new ones – to ensure that all of them (and their relations) satisfy all axioms in the ontology. For an inconsistent ontology [2] (or a consistent one where we try to create an instance of an unsatisfiable class), this attempt will fail with an obvious “clash”, i.e., an obvious contradiction like an individual being an instance of 2 disjoint classes. And it will succeed otherwise with (an abstraction of) a model. For a subsumption test to decide whether A is subsumed by B, we try to build a model with an instance of A and not (B): if this fails, then A and not(B) cannot have an instance in any model of the ontology, hence A is subsumed by B!

Last words

We have tried to describe what reasoners do, and how they do this. Of course, this explanation had to be high-level and leave out a lot of detail, and we had to concentrate on the classification reasoning service and thus didn’t really mention other ones such as query answering. Moreover, a lot of interaction with a reasoner is currently being realised via the OWL API, and we haven’t mentioned this at all.

To be at least complete in some aspect, we would like to leave you with the following links:

• List of OWL reasoners
• List of reasoners (curated at Manchester)

Some helpful web sites:

• OWL-2 primer
• OWL Reasoning Examples

The paper by Franz Baader and Ulrike Sattler [3] will be useful.

References

1. U. Sattler, "OWL, an ontology language", Ontogenesis, 2010. http://ontogenesis.knowledgeblog.org/55
2. U. Sattler, R. Stevens, and P. Lord, "(I can’t get no) satisfiability", Ontogenesis, 2013. http://ontogenesis.knowledgeblog.org/1329
3. F. Baader, and U. Sattler, "Array", Studia Logica, vol. 69, pp. 5-40, 2001. http://dx.doi.org/10.1023/A:1013882326814

Summary

To paraphrase Davis, Shrobe & Szolovits [1], an ontological commitment is an answer to the question of “how should I think about the world?”. An ontology is a model or knowledge representation of a field of interest [2]. By using an ontology, you are committing to its world view; if you borrow from an ontology, you should also be borrowing its commitment. That is, an ontology says “there are these objects and this is how they are related”; the ontology has made that commitment and, by dint of using that ontology, so are you. This has consequences for how ontologies are used and re-used. This kblog gives an introduction to ontological commitment and illustrates how it is worth bearing in mind as you use and re-use ontologies.

Author

Robert Stevens
Bio-health Informatics Group
School of Computer Science
University of Manchester
Oxford Road
Manchester
United Kingdom
M13 9PL
robert.stevens@Manchester.ac.uk

Phillip Lord
School of Computing Science
Newcastle University+ Newcastle
United Kingdom
NE3 7RU
phillip.lord@newcastle.ac.uk

What is it?

wikipedia’s summary of ontological commitment [3] goes like this:

[… an] ontology refers to a specific vocabulary and a set of explicit assumptions about the meaning and usage of these words, then an ontological commitment is an agreement to use the shared vocabulary in a coherent and consistent manner within a specific context.

That is, when using an ontology there should be a commitment to its view on the field of interest it describes. This is the sharing or shared view that is often refered to in an information systems version of an ontology. To keep it succinct, when using terms (classes) and axioms from an ontology, one is buying into the world view of that ontology. An ontology is a theory of a field of interest [2]; that theory uses objects in its explanation of that field – those objects are its ontological commitment.

This is not only true when using an ontology for annotation, but when an ontology is authored – either de novo or when re-using another ontology.

The way knowledge is modelled makes a commitment to a world view. When modelling de novo the modelling style makes a statement about how the entities in the field of interest are arranged. When an existing domain neutral or top ontology [4] is used, a modeller is making a commitment to that upper ontology’s understanding of how entities are arranged. By, for example, using BFO, an ontologist is commiting to a view where continuants can have qualities, but processes may not; if DOLCE is used as a domain neutral ontology, a commitment is made, for example, to dividing qualities into qualia and qualities. It has to be added, that the user need not believe it in the slightest, but the bottom line is that in re-using another ontology or ontology fragment, that ontology’s interpretation of a field of interest should also be re-used.

These views provided by another’s ontology are not a la carte; they are more like the menu – you take the whole view or you leave it altogether. One shouldn’t pick and choose pieces of viewpoint from a variety of ontological commitments, especially radically different upper level, domain neutral, ontologies. One can’t just take the partial viewpoint (though one can take part of an ontology and not break ontological commitment) of an ontology to which one agrees; it’s the whole commitment or nothing – just as one cannot be a bit pregnant one cannot be a bit ontology x.

Another way of achieving an ontological commitment is by re-using parts of another ontology. For instance, by re-using relationships from the Relationships Ontology [5] an commitment is made to the ontological view taken on by that ontology fragment. When using those relationships, for instance, a modeler should commit to re-using them in the way intended. For example, part_of should be used for describing the relationships between an entity and its parts, not for describing the relationship between an entity and that in which it is contained. Similarly, taking a class from another’s ontology and changing its definition and assuming it’s the same class doesn’t work; one commits to the donor ontology’s definition or one needs a new class.

By using an ontology I’m committing to its “world view”. When using, for instance, the Gene Ontology [6] to describe the major attributes of a gene product, the annotator should be committing to adopting the GO’s view of the world – making arbitrary decisions like “GO says x means blah,b but I’ll interpret x as meaning yadda yadda” leads to confusion and the world will collapse into a maelstrom of sin and corruption. Possible sins include:

• Answers to queries are different in different uses of the ontology as interpretations change
• One should be able to re-combine re-used parts of an ontology from gvarious re-using ontologies back into the original and everything work fine. if interpretations have changed in the re-using ontologies, then bad things will happen.

In re-using a concept, one should look not only at the label of that concept, but its definition and its context to be sure the ontological commitments being made are the ones you want.

Practicalities

When we say that in using an ontology, you should effectively commit to it, this does not, of course, mean that you should use all of the ontology, in the sense of referring to all the terms in that ontology. In fact, many ontologies, refer to very few of the terms in the domain neutral ontologies that they import.

There are also important practical considerations; reasons why you might not wish to commit to all of an ontology. Consider, for example, an OWL ontology [7]. If we import another ontology into ours, we get all of the axioms from the imported ontology whether we like it or not. This can be extremely problematic if, for instance, the other ontology is very large and we wish to use a single term. An obvious use case, is refering to Homo sapiens from the NCBI taxonomy. There are a number of ways to address this problem; tools associated with MIREOT[8] for example, will extract just the terms you need. This is a relatively safe thing to do, but there are still some potential pitfalls. For example, if you just import ViridiPlantae (green plants) and Homo sapiens, and then make one a subclass of the other, your ontology will be consistant. But if anyone else imports both your ontology and the NCBI taxonomy, these statements will be see to contradict. In this case you’re also breaking the ontological commitment to the NCBI taxonomy, where plants and humans do not have this relationship.

There are also reasons why you might wish to add new axioms describing terms from an ontology that you import. For example, say you import the Pizza Ontology [9], and discover the lack of labels in Italian is problematic; you could add these annotations in a second ontology. Another common reason for adding more axioms to an existing ontology is to switch OWL profile. For example, versions of DOLCE can be found in the EL, QL and DL, all refering to the same terms. The DL version contains axioms which will disallow statements that would be valid against the EL version.

In each of these cases, the practical considerations must be weighed up against the potential consequences. Ignoring axioms will mean that you are also ignoring potential inconsistencies; adding multi-lingual labels may be safe, but equally make break software which is expecting only English; adding axioms to terms from another ontology may cause undesired consequences in a third.

In general, the rule should be that if you ignore part of, or add to another ontology you should be careful to retain as much ontological commitment as you can by not contradicting the original.

Layers of commitment

Davis, Shrobe & Szolovits [1] talk of layers of commitment; what’s gone above is towards a “top” layer. Down at the bottom layer, we have the ontological commitment of the representation language itself. An knowledge representation language makes it possible to say some things about a field of interest and not others. Thus an ontology’s language is itself making an ontological commitment; it takes a view upon what things are important in the world and it is these that can be represented.

Moving up a layer, the modelling choices made in the ontology are making a commitment about the field of interest; by classifying aalong one primary axis as opposed to another, an ontologist is saying what he or she believes to be important about that aspect of the domain. By using, re-using or extending that ontology a modeller should “buy-in” to that commitment and is implicitly doing so by taking on the task.

Final words

An ontology makes commitments about the world it is representing. When using an ontology one is taking on that ontological commitment – there should be no “ontology x makes interpretation y, but I’ll make interpretation z”. Similarly, an ontology’s commitments are not a la carte, one cannot just leave out the bits of a point of view one doesn’t like and re-use the bits of a viewpoint one does like – by committing to a bit one is committing to the whole (though one, of course, doesn’t have to commit to the whole thing in a mechanical sense – that is, import the whole thing). In summary, an ontology is about shared, common understanding and ontological commitment is one of its central aspects. As ontologies are used and re-used, especially when re-using fragments of an ontology, ontological commitment should be born in mind.

References

1. R. Davis, H. Shrobe, and P. Szolovits, "What is a Knowledge representation?", AI Magazine, 1993.
2. R. Stevens, A. Rector, and D. Hull, "What is an ontology?", Ontogenesis, 2010. http://ontogenesis.knowledgeblog.org/66
3. "Ontological commitment - Wikipedia", Wikipedia, 2016. http://en.wikipedia.org/wiki/Ontological_commitment
4. F. Gibson, "Upper Level Ontologies", Ontogenesis, 2010. http://ontogenesis.knowledgeblog.org/343
5. B. Smith, W. Ceusters, B. Klagges, J. Köhler, A. Kumar, J. Lomax, C. Mungall, F. Neuhaus, A.L. Rector, and C. Rosse, "Array", Genome Biology, vol. 6, pp. R46, 2005. http://dx.doi.org/10.1186/gb-2005-6-5-r46
6. M. Ashburner, C.A. Ball, J.A. Blake, D. Botstein, H. Butler, J.M. Cherry, A.P. Davis, K. Dolinski, S.S. Dwight, J.T. Eppig, M.A. Harris, D.P. Hill, L. Issel-Tarver, A. Kasarskis, S. Lewis, J.C. Matese, J.E. Richardson, M. Ringwald, G.M. Rubin, and G. Sherlock, "Gene Ontology: tool for the unification of biology", Nature Genetics, vol. 25, pp. 25-29, 2000. http://dx.doi.org/10.1038/75556
7. U. Sattler, "OWL, an ontology language", Ontogenesis, 2010. http://ontogenesis.knowledgeblog.org/55
8. . Melanie Courtot, Frank Gibson, Allyson L. Lister, James Malone, Daniel Schober, Ryan R. Brinkman, Alan Ruttenberg, "MIREOT: the Minimum Information to Reference an External Ontology Term ", Nature Precedings, 2009. http://precedings.nature.com/documents/3574/version/1
9. R. Stevens, "Why the Pizza Ontology Tutorial?", Robert Stevens' Blog, 2010. http://robertdavidstevens.wordpress.com/2010/01/22/why-the-pizza-ontology-tutorial/

Summary

OWL has a tree model property. This property is (one of the) reasons why the reasoning problems underlying, say, the computation of the inferred class hierarchy, are decidable [1]. As a modeller in OWL, we notice this property because it restricts what can be said in an ontology. Very roughly speaking, in OWL, we describe tree-shaped structures: we illustrate what this means using pictures and videos of two fingers walking along the trees. Some things one would like to say in OWL require using three fingers to do the tracing between the objects in our axioms – making triangles between the objects being related. However, some form of triangles can be described in OWL, and we illustrate these as well.

Authors

Robert Stevens and Uli Sattler

Bio-Health and Information Management Groups
School of Computer Science
University of Manchester
Oxford Road
Manchester
M13 9PL

Robert.Stevens@Manchester.ac.uk and sattler@cs.man.ac.uk

The tree model Property of OWL

The description logic upon which OWL is based uses a form of the tree-model property: the expressive power of OWL is such that the axioms in an ontology can only enforce the (anonymous) objects in a model [2]. We use the core of an ontology about family history to illustrate how OWL restricts ontologies to descriptions of trees. Take the ontology:

Class: Man SubClassOf Person
Class: Woman SubClassOf Person
Class: Person SubClassOf (hasMother some Woman) and (hasFather some Man)
ObjectProperty: hasMother Characteristics: Functional SubPropertyOf hasParent
ObjectProperty: hasFather Characteristics: Functional SubPropertyOf hasParent

Here we have a simple ontology that introduces two classes, Man and Woman, that are each a subclass of Person. A person hasFather some Man and hasMother some Woman; hasFather and hasMother are functional and are sub-properties of hasParent. We have illustrated the restriction that OWL places on how instances of the classes introduced can be related via a video.  In the video you can see how the axioms enforce a world where persons and their parents are related via the properties hasMother and hasFather in a tree-shaped structure.

Now assume we add another axiom that describes happy grandchildren (HGC) as those who have a mother who has a mother who is Nice (a nice grandmother):

Class: HGC EquivalentTo: Person and (hasMother some (hasMother some Nice)

An explanation of how we can figure out the meaning of HGC by walking our (family) tree with 2 fingers is given in the next video. Again, you can see that it is possible to use just the two fingers to talk about how the objects in these axioms are related to each other.

Making triangles of properties and objects is (mostly) not allowed

So far, what we have seen is what we can say in OWL. If we, however, wished to define a class of happy children as those children whose mother loves their father, we are facing some difficulties, as explained in our third video. In a nutshell, this idea of happy children would involve the description of a “triangle” between the child, their mother, and their father – and thus it would involve “3 fingers” to keep hold of the relationships between those elements. This breaks the tree shaped structure of the axioms – the triangle forms a non-tree shaped graph. In fact, we cannot define such a concept in OWL, since OWL class descriptions are mostly of the kind that is traceable with two fingers – that is, the tree.

When triangles of things can be done in OWL

Next, we will discuss exceptions to this rule of thumb (or fingers!).

First, we can describe triangles – or any form of structure – on named individuals. For example, see the following assertions:

Individual: Peter
Facts: hasMother Sue,
hasFather Bob

Individual: Sue
Facts: loves Bob

Here the facts asserted about Bob, Sue and Peter form a triangle with the hasMother, hasFather and loves properties. This happens all the time with individuals and it is fine to do lots of this sort of non-tree like thing.

Second, we can describe triangular forms of relations via transitive properties or via sub-property chains, as in the following property axioms:

ObjectProperty: hasGrandParent
SubPropertyChain: hasParent o hasParent

ObjectProperty: hasUncle
SubPropertyChain: hasParent o hasBrother

With the hasGrandParent property, where we see objects linked along the hasParent property, we’re forming triangles: a person’s grandparent is also linked to them via their parent. A similar observation holds true for a person’s uncle. Also, transitive properties such as has Ancestor lead to the formation of whole series of triangles between a person and all their ancestors via the direct has Parent relationships.

Last words

So, while OWL is great at describing trees, we face some difficulties when we want to describe classes via some features that involve triangular shapes – but triangular structures are ok in other parts of OWL, such as in facts about named individuals and as general characteristics of properties. The tree model property keeps the description logic underlying OWL decidable. Sometimes the things we’d like to say as a modeller break this tree-shaped aspect of OWL’s axioms – you can check what’s going on in your axioms and explain the constraint to yourself and others by walking along a set of objects in a model of your ontology with your fingers; when you need more than two to walk along the objects involved in your description, then you’re often going to be in problems, apart from the exceptions outlined above.

References

1. Q.Y.E. Grädel, "Why Are Modal Logics So Robustly Decidable?"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.5238