on April 5, 2011 by Phillip Lord in Under Review, Comments (1)

# Do Cyclists pay tax? An investigation of roles and number.

## Abstract

Most long term cyclists in the UK face the accusation from other road users that, as they “don’t pay tax anyway”, then they should not be accorded with full rights as road users. In this article, we consider this claim along ontological grounds, as it demonstrates nicely the use of roles and the importance of number on properties when building ontologies. As a result, we show that claim does not really make sense.

## Author

Phillip Lord,
School of Computing Science,
Newcastle University

## Introduction

There are many standard elements and patterns that appear in most ontologies, or ontology languages. Two of the most common are roles and number. A good understanding of both is critical for an ontologist. Although neither concept is complex they are often misunderstood. Roles are mechanism for expressing optionality, things which may be true for a set of otherwise unrelated classes, but are not necessarily true for all individuals in these classes. Number, in this context, describes how a relation holds between individuals in two classes. For ontology languages which are built on a formal logic, the ability to express number is normally a feature of the language.

This article uses an example to demonstrate the application of role and number in building an ontology. It also shows how we can use the process of ontology building to ask questions about whether arguments are reasonable or not.

## Example and Disclaimer

In the UK, cyclists have the most of the same legal rights and responsibilities as other road-users. One significant difference, however, between cyclists and car drivers is that the latter pay a specific tax, strictly called Vehicle Excise Duty, although most commonly known as road tax. This tax varies between different classes of vehicle. Most car drivers pay between £100 and £200 per vehicle, per year; lorries, buses or coaches cost far more, while a few cars (very old “classic”, or very low emission cars) pay nothing at all.

Most roads, including motorways (the equivalent of autobahns, autostrada or interstates in other countries) in the UK are free at the point of use, and do not attract tolls. Although, in reality, road building is funded from general taxation such as income tax, many believe it is or should be funded specifically from road tax. As cyclists do not pay road tax, goes the argument, they should have lesser rights to the use of the roads.

As a disclaimer, while the author (PL) is both a cyclist and car driver, in practice he identifies himself far more as a cyclist and is, in practice, fairly militant about this. In this context, the article is entirely biased, as it was written partly as a catharsis, partly as self-justification.

## Do cyclists pay tax?

Ontologies describe objects in terms of their properties. Bicycles, for example, have two wheels, are capable of movement and operate as to transport the user. Some of these properties are intrinsic or necessary to the entities in question, while others are not. For instance, it seems reasonable to claim that a bicycle must, by its nature, have two wheels; if it has three, then it is a tricycle; if you take the wheels off a bicycle, then while you will still have all the parts necessary to make a bike, you no longer have a complete bike.

Some properties are, however, not intrinsic or essential. My own bike, for instance, has inner tubes, a pannier rack and is light grey in colour. Other bicycles may share none of these characteristics and, yet, can still reasonably be considered to be a bicycle. In short, while a bike can have a pannier rack, it is optional.

When it comes to a person, many of the things that we use to define or to categorise people fall into this optional category. We would be surprised, when asking someone what they do, if they replied that they breath, eat and, well, do all the other things that every person does. As well as being surprising, it would not be very useful — all people eat, so knowing that a specific person eats, says very little. On the other hand, knowing that a person is a cyclist or an ontologist is more useful.

Ontologically, modelling this is difficult. Ontological relationships are either present or not: so we can say that a person eats

 Class: Person SubClassOf: involved_in some Eating

which is a reasonable ontological statement, expressed in Manchester syntax. However, we cannot say

 Class: Person SubClassOf: involved_in some Cycling

unless we wish to assert that all people necessarily cycle. Unfortunately, most Ontology languages, including OWL cannot express the idea of conditionality, or “some people cycle”. The solution to this is a layer of indirection. We define a role which is an independent class from a person, but which is realized in a cycling process. For an individual, we can then state that while they are necessarily a person (and so must be involved in eating), they just happen to be a cyclist.

 Class: Person Class: Cyclist SubClassOf: Role, realized_in some Cycling Individual: phil Types: Person Facts: has_role Cyclist

I (Phil) do not cycle as a result of being a person, rather it is just (one of the many) roles that I can play. The same pattern can be used to describe taxation as, again, it is optional (even if it often does not feel this way). So, we might say:

 Class: TaxPayer SubClassOf: Role, realized_in some Taxing Individual: phil Types: Human Facts: has_role Cyclist has_role TaxPayer

Which leaves us to the conclusion, that cyclists do not in fact pay tax, but then neither do car drivers. Being either CarDriver or a Cyclist is a Role, and roles do not pay tax; people do. An individual person might just happen to be a tax payer and they might be a car driver. So, the argument that cyclists should have less rights as they do not pay tax does not really make sense.

## But Car Drivers have to pay tax?

There is surely a difference, however; even if car driving is just a role, individuals who are car drivers have to pay tax, while those who are just cyclists do not. So, we could say:

 Class: TaxPayer SubClassOf: Role, realized_in some Taxing Class: CarDriver SubClassOf: TaxPayer, realized_in some Driving

The critical point in this definition is the use of the some keyword, which indicates existential quantification; this says that for every individual CarDriver there must be at least one individual Driving process, and that additionally there must be at least one individual Taxing process because of inheritance from TaxPayer.

However, if we complete the ontology, it becomes clear that there is a problem. There are two classes of vehicle, and therefore classes of driver who do not pay road tax.

 Class: ClassicCarDriver SubClassOf: CarDriver, realized_in only (not Taxing) Class: GreenCarDriver SubClassOf: CarDriver realized_in only (not Taxing)

In this case, we have used universal quantification, through the use of the only keyword. It has quite different semantics to some. only does not imply, as some does that a GreenCarDriver is realized_in any process at all. It does, however, state that if it is realized_in any process, that process must be not Taxing.

If we create this ontology in a tool such as Protege and reason over it, we will quickly discover an inconsistency; we have said that individual CarDrivers must pay tax, while accepting that some do not.

So, it appears that it is not true that car drivers pay tax, even if it maybe true that some car drivers pay tax as a result of their choice of vehicle.

## Anyway, everybody pays taxes

The final stage of the argument often given to cyclists is that, accepted that not all car drivers pay tax, most do. Does this make sense, as a mechanism for differentiating them from cyclists? Again, we can consider this by extending our ontology. At this point, however, we reach the limit of the expressivity of most ontology languages. We cannot express concepts such as “most” or “more than half” or “a few”. Instead, we will have to look at one individual, and extrapolate.

Earlier, we asserted that I (Phil) am a cyclist.

 Individual: phil Types: Person Facts: has_role Cyclist

As well as all the other things that people do, there is one great certainty in life, and that is taxation. Considering only adults, we can model this as:

 Class Person: SubClassOf: has_role some TaxPayer Class NotTaxed: SubClassOf: has_role only (not TaxPayer)

At the same time, we can try to assert that I (phil) am not a TaxPayer as I am Cyclist. Creating this ontology in Protege results and reasoning again shows an inconsistent ontology. I (phil) am a Person and therefore must play the role of a TaxPayer whether I wish to or not. In this case, the universal and existential quantification operates between the role and its bearer, not between the role and the process it is realized in. We can use similar logic to counter the argument that I do not pay the more specific road tax because I am a cyclist; like most cyclists I am also a car driver and so do pay road tax.

## Conclusion

While the example is this article may seem somewhat flippant, at least when fulfilling my role as an ontologist, it does demonstrate neatly the use of roles as well as the difference between universal and existential quantification. It also shows how, by building an ontology iteratively, and adding complexity, we can test whether the statements that we have made early make sense, by looking for contradictions.

## 1 Comment

1. Why multiple authors? | The Knowledgeblog Process

August 22, 2012 @ 10:43 am

[...] We can however make a split between two authorship roles (http://ontogenesis.knowledgeblog.org/1062); first as a person who contributes to the writing of an article, and second as a person who [...]

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