# A Means-End Account of Explainable Artificial Intelligence

Oliver Buchholz  University of Tübingen, Cluster of Excellence “Machine
Learning: New Perspectives for Science”, Tübingen, Germany. E-mail:
<EMAIL_ADDRESS>
I would like to thank audiences in Tübingen and Frankfurt a. M., in particular
Kate Vredenburgh and David Danks, for helpful comments on a talk based on this
article. I would also like to thank Sara Blanco, Karoline Reinhardt as well as
Thomas Grote for helpful feedback and Wolfgang Spohn for very valuable
comments on an earlier draft. Finally, I would like to thank Eric Raidl for
his guidance and continuing support during the entire process that led up to
this article.
My research was funded by the Baden-Württemberg Foundation (program
“Verantwortliche Künstliche Intelligenz”) as part of the project AITE
(Artificial Intelligence, Trustworthiness and Explainability).

Explainable artificial intelligence (XAI) seeks to produce explanations for
those machine learning methods which are deemed opaque. However, there is
considerable disagreement about what this means and how to achieve it. Authors
disagree on _what_ should be explained (topic), _to whom_ something should be
explained (stakeholder), _how_ something should be explained (instrument), and
_why_ something should be explained (goal). In this paper, I employ insights
from means-end epistemology to structure the field. According to _means-end
epistemology_ , different means ought to be rationally adopted to achieve
different epistemic ends. Applied to XAI, different topics, stakeholders, and
goals thus require different instruments. I call this the _means-end account_
of XAI. The means-end account has a descriptive and a normative component: on
the one hand, I show how the specific means-end relations give rise to a
taxonomy of existing contributions to the field of XAI; on the other hand, I
argue that the suitability of XAI methods can be assessed by analyzing whether
they are prescribed by a given topic, stakeholder, and goal.

## 1 Introduction

Methods of machine learning (ML) are gaining relevance in a variety of
domains. They are employed to navigate self-driving vehicles (Bojarski et al.,
2016), support medical diagnosis (Esteva et al., 2017), and to detect objects
ranging from particles at the subatomic level (Baldi et al., 2014) to
exoplanets (Foreman-Mackey et al., 2015).111I use the term ‘ML method’ to
refer to some general methodology, e.g., deep learning, and distinguish it
from the term ‘ML model’ by which I refer to a specific model, e.g., a deep
neural network for which the weights have already been determined. Thus, the
term ‘ML method’ explicitly includes the learning process, while the term ‘ML
model’ only refers to the learned function.

At the same time, it is widely acknowledged that their very nature makes ML
methods essentially ‘black boxes’ to human agents. Both their specific
functioning and their complexity, especially in the field of deep learning,
are inherently opaque or beyond human grasp (Burrell, 2016, Creel, 2020).
Thus, frequently, laymen and experts alike do not know how these methods work,
why they are successful, or why they fail. This observation led to the widely
shared belief that ML methods should be made explainable and sparked research
in the field of explainable artificial intelligence (XAI). Since the ‘X’ in
‘XAI’ stands for ‘explainable’, it seems straightforward and uncontroversial
to summarize the central aim of the field plain and simple as follows: XAI
seeks to provide instruments that produce explanations of ML methods.222To be
precise, this applies to the field insofar it is concerned with the
application of XAI techniques to opaque ML methods, which is the focus of this
paper. It does not directly apply to that part of XAI that seeks to develop
and apply inherently interpretable methods, thereby avoiding the use of opaque
ML methods from the outset (Rudin, 2019).

Yet on the one hand, there is profound conceptual disagreement regarding the
precise _meaning_ of this aim (Lipton, 2018): what is it that explanations of
ML methods should achieve? Suggestions in the literature comprise the
straightforward requirements of _explainability_ and _interpretability_
(Doshi-Velez and Kim, 2017, Erasmus et al., 2020), the more intuitive
_understandability_ (Páez, 2019) as well as the larger category of
_transparency_ (Günther and Kasirzadeh, 2021, Zerilli et al., 2019). Others
argue that all these notions lack precise definitions altogether and only hide
the real goals such as safety of or non-discrimination by ML methods
(Krishnan, 2020).

On the other hand, the literature also diverges with respect to the
_instruments_ that are deemed appropriate to achieve the aim of XAI. Popular
approaches range from local approximations of complex models (Ribeiro et al.,
2016) to visual (Xu et al., 2015), textual (Hendricks et al., 2016),
counterfactual-based (Wachter et al., 2018) as well as attribution-based
explanations (Lundberg and Lee, 2017). Overall, it is unclear whether the
field of XAI is scattered into various disconnected subprojects or whether
there is a common structure that is shared by the variety of approaches
pursued in the literature.

In this article, I propose an account that structures the field. To do so, I
employ insights from means-end epistemology.333The idea of exploiting existing
research from philosophy and the social sciences when analyzing XAI is put
forward, e.g., in Miller, (2019). _Means-end epistemology_ takes epistemology
to be a normative discipline; it is based on the principle of instrumental
rationality (Huber, 2021: 1). Rational agents are assumed to have certain
epistemic ends (e.g., the end to hold true beliefs), and such agents ought to
adopt certain means (e.g., to base their beliefs on total evidence) if and
only if they further these epistemic ends (Huber, 2021: 125, Schulte, 1999:
7). Providing an explanation is such an epistemic end, because it relates to
the epistemic state of the agent receiving the explanation.444This is also a
well-established result in psychology as reported, for instance, by Keil,
(2006) or Lombrozo, (2006). Thus, when trying to provide instruments that
produce explanations of ML methods, the field of XAI essentially seeks to
provide the means to further an epistemic end. Consequently, means-end
epistemology is a very suitable framework to analyze XAI. I call this the
_means-end account of XAI_. The account’s motivation is based on the
fundamental observation that means-end relations are crucial to the field of
XAI. Indeed, as I will point out, researchers explicitly or implicitly specify
them in their contributions. I will show how these means-end relations can be
specified on a fine-grained level by distinguishing _what_ should be explained
(topic), _to whom_ something should be explained (stakeholder), _why_
something should be explained (goal), and _how_ something should be explained
(instrument).

I will argue that overall, the means-end account has several important
consequences. First, it explains why disagreement arises in the field: the
divergence in methods of XAI follows from the disagreement on fine-grained
ends being pursued. Second, it unifies and structures the field: there is a
shared methodology of developing appropriate means for given ends. Third, this
structure has a descriptive component: different authors specify different
topics, address different stakeholders, and have different goals. Thus, they
pursue different ends and different means are appropriate to achieve them.
This gives rise to a taxonomy that classifies existing contributions to the
field along the specific means-end relations that are considered. Fourth, the
means-end structure also has a normative component: according to means-end
epistemology, different means ought to be rationally adopted to achieve
different epistemic ends. Therefore, the fine-grained ends of an explanation
normatively constrain the set of admissible means to achieve it. The means-end
account thus reveals how the suitability of particular instruments of XAI is
prescribed by the ends for which an explanation is sought. I argue that this
analysis gives rise to a normative framework that can be used to assess the
suitability of XAI techniques.

Consequently, this article extends that strand of the literature that
emphasizes the relevance of pragmatic considerations in the context of
XAI.555Examples include Besold and Uckelmann, (2018), Nyrup and Robinson,
(2022), and Páez, (2019). Indeed, I show that pragmatic considerations are
relevant, especially in what concerns the topics, stakeholders, and goals.
However, by focusing on the principle of instrumental rationality as a
cornerstone of epistemic normativity, I additionally provide a normative
justification for why pragmatic considerations _ought_ to be relevant.
Furthermore, while I do not claim to be the first developing a normative
framework for XAI, this article is the first to thoroughly base such a
framework on an underlying epistemological theory.666Other normative
frameworks for XAI have been proposed, for instance, by Langer et al., (2021),
Mohseni et al., (2021), and Zednik, (2019).

The remainder of this article is structured as follows: In Section 2, I
outline the main characteristics of XAI by providing concrete examples from
the field. I also give an introduction to means-end epistemology. In Section
3, I argue that problems of XAI can be framed as problems of means-end
epistemology. I thereby establish the means-end account of XAI and discuss
both its normative and its descriptive component. In Section 4, I discuss an
extension of the account before concluding in Section 5.

## 2 Preliminaries

This section outlines the main characteristics of XAI by examining two
examples from the field. It also gives a short introduction to those aspects
of means-end epistemology that are relevant for the rest of the paper.

### 2.1 Explainable Artificial Intelligence

XAI is commonly employed to eliminate the inherent opacity of many ML methods
and models. In a first step, there is usually some opaque ML model, for
instance a deep neural network, whose opacity should be (at least partly)
eliminated. In a second step, some XAI technique is applied to the opaque ML
model to achieve that elimination. Yet as straightforward as it may seem,
there is considerable disagreement about what ‘eliminating opacity’ amounts
to. This disagreement is perhaps best illustrated by outlining two of the most
well-known methods of XAI.

First, consider local interpretable model-agnostic explanations (LIME)
(Ribeiro et al., 2016). Explanations produced by LIME are _local_ in the sense
that they explain ML predictions only within a specific part of the data. To
do so, LIME approximates the possibly highly complex ML model by a simpler
model around the specific prediction(s) of interest. Thus, a complex decision
surface might be approximated locally by a linear function. This makes the
overall ML model locally _interpretable_ , thereby revealing the model’s
structure within a specific part of the data. Since LIME is _model-agnostic_ ,
it is applicable to a wide range of ML methods.

Second, consider counterfactual explanations (CFE) (Wachter et al., 2018).
They are usually provided as verbalized counterfactual statements that take
the following form: “You were denied a loan because your annual income was
£30,000. If your income had been £45,000, you would have been offered a loan.”
Thus, CFE provide reasons for a given decision and seem to specify how to
reach a desired result in the future.777I use the rather cautious ‘seem’,
since this view is controversial. See Section 3.3 for a brief overview about
the debate in XAI. See also Raidl and Rott, (2022) as well as references
therein for the general philosophical debate about the relation of
counterfactuals and ‘because’-statements. As becomes obvious, CFE exclusively
focus on a model’s input-output relation: they explain why a certain input led
to a certain output “without opening the black box”, that is, without
considering a model’s internal functioning. They justify the model’s output by
giving reasons rather than by detailing the decision rule that led to the
output.

Overall, the deliberately simplistic sketch of two of the most popular methods
in XAI illustrates the observation from above: that instruments of XAI differ
widely and that there is no consensus on which instruments are appropriate to
use. This raises the question whether there is nevertheless something that XAI
techniques, ranging from LIME to CFE, have in common. As a first step, let us
try to distill an overall aim of XAI, general enough to be shared by LIME,
CFE, and other XAI techniques as different as they may be: what is it, that
XAI tries to achieve?

First, XAI develops _instruments_ , for instance, LIME or CFE. Second, these
instruments are meant to produce _explanations_ of the ML methods to which
they are applied. Thus at the highest level, the aim of XAI might be
summarized by stating that XAI seeks to

. Provide instruments that produce explanations of ML methods.

Clearly, the term ‘explanations’ in 2.1 is dangerously loaded, both within XAI
and within philosophy. In this article, I use it to designate the different
kinds of outputs that are produced by XAI techniques, regardless of whether
they qualify as a proper explanation according to some definition or not. At
this stage, my sole aim is to ensure a maximally general formulation of the
high-level goal of XAI that is meant to be as uncontroversial as possible. I
will return to it below when putting forward the main argument.

### 2.2 Means-End Epistemology

The second building block of the account that I propose in this paper is
means-end epistemology. It takes epistemology to be a normative discipline. In
this context, normativity has an epistemic rather than a moral meaning.
Contrary to moral normativity that is concerned with what one ought to _do_ ,
epistemic normativity is concerned with what one ought to _believe_. In the
case of means-end epistemology, the central normative criterion is spelt out
by the principle of instrumental rationality (Huber, 2021, Schulte, 1999):

. Given an epistemic end, certain means ought to be adopted if and only if
they further the epistemic end.

Thus, agents are assumed to have certain epistemic ends and the principle of
instrumental rationality requires them to adopt those means that are
appropriate to achieve the given end(s).888Note, that 2.2 expresses a
_hypothetical_ rather than a _categorical_ imperative. It is controversial
whether ‘ought’ needs to be replaced by ‘should’ in this case (Finlay, 2009,
Foot, 1972, Huber, 2021: Ch. 5.4). Since engaging with this debate is beyond
the scope of this text, my use of ‘ought’ is only meant to emphasize the
pronounced normative perspective of means-end epistemology. For instance,
consider Anne, who pursues the epistemic end of holding only true beliefs. She
falsely believes that she was denied a loan because her annual salary is too
low. Now suppose that she receives the (true) information that, in fact, she
was denied the loan because her loan application contained transposed digits
for her annual salary. According to means-end epistemology, Anne—if
rational—ought to adopt means that lead to a revision of her initial and false
belief in favor of the true belief that her loan application contained
transposed digits for her annual salary, since these means would further her
epistemic end of holding only true beliefs.

Equating epistemic normativity with instrumental rationality and expressing it
in terms of means-end relationships as in 2.2 involves several aspects that
are important for the subsequent discussion. First, different ends call for
different means. Thus, while the adoption of certain means might be rational
for agents with certain epistemic ends, agents with different ends need not or
even _ought_ not adopt the same means (Schulte, 1999: 26). This is a
consequence of the normative perspective adopted by means-end epistemology.

Second, note that ‘certain means’ in 2.2 generally refers to a set of means,
$M$, rather than to one particular means, $m\in M$. Thus, different ends may
call for different _sets_ of means, $M$ and $M^{\prime}$, but the latter can
be partially overlapping, such that $M\cap M^{\prime}\neq\emptyset$. So on the
one hand, _different_ ends might be achieved by the _same_ particular means
$m$. On the other hand, the _same_ end might be achieved by _different_
particular means, $m$ and $m^{\prime}$.

Third, epistemic ends come in different levels of granularity. For instance,
Schulte, (1999) conducts a means-end analysis of inductive inference. His
starting point is the epistemic end of beliefs converging to the truth.
Subsequently, however, further details are added to this initial end by
requiring the convergence to possess certain properties, most importantly to
evolve fast and with minimal retractions. Clearly, the latter ends are more
fine-grained than the former, thereby allowing to identify a more specific set
of means that ought to be rationally adopted.

Fourth, note that the means-end statement in 2.2 has the logical form of a
biconditional and is therefore equivalent to a conjunction of two conditional
statements pointing in two opposite ‘directions’999This is due to the
elementary fact that for two propositions $P$ and $Q$, the biconditional
$P\leftrightarrow Q$ holds if and only if the conjunction of the single
conditionals $P\rightarrow Q$ and $Q\rightarrow P$ holds.: according to one
direction, _if_ certain means ought to be adopted, _then_ they further the
epistemic end; according to the other and, arguably, more natural direction,
_if_ they further the epistemic end, _then_ certain means ought to be adopted.
The importance of taking both directions into account and thus preserving the
logical form of the biconditional will become important below.

## 3 A Means-End Account of XAI

This section establishes what I shall call the _means-end account_ of XAI. It
also discusses the account’s descriptive and normative component.

### 3.1 Establishing the Account

Recall the overall goal of XAI that I proposed in 2.1: XAI seeks to provide
instruments that produce explanations of ML methods. On the one hand, this
means that XAI clearly seeks to affect the epistemic states of individuals, be
it their beliefs about or their understanding of ML methods—the observation
does not hinge on a particular epistemological concept such as belief,
knowledge, or understanding being affected. Consequently, it is fair to say
that by producing explanations, XAI pursues an epistemic end. On the other
hand, XAI seeks to provide methods to achieve this epistemic end. Put
differently, XAI seeks to find appropriate means to further a given epistemic
end. Taken together, these aspects reveal that

. Problems of XAI can be framed as problems of means-end epistemology.

One might object that it is somewhat circular to argue for 3.1 based on the
high-level goal of XAI proposed in 2.1, since the latter could have been
purposefully designed for precisely this argument. However, as mentioned
above, 2.1 is simply formulated on the highest level possible so as to give
rise to a maximally broad and uncontroversial statement.

Let me illustrate the insight in 3.1 using the examples from Section 2.1.
First, consider LIME: as outlined above, LIME seeks to explain an individual
prediction or several predictions in a specific region of the data. This
constitutes the epistemic end that is pursued in this case. The means proposed
to achieve this end are local approximations to a possibly complex ML model.
Second, consider CFE: here, the epistemic end is to explain the input-output
relation of a model. The means proposed in this case are counterfactual
statements like the one about loan denial given above. So indeed, means-end
relations seem useful and easily applicable to analyze XAI techniques.

However, when framing problems of XAI as problems of means-end epistemology,
it might seem trivial to proceed by simply specifying means and ends
corresponding to existing methods like LIME or CFE. The more important
question is how means-end relations are determined in practice, for instance,
in the development of new methods. Analyzing the means-end relations governing
XAI more closely reveals that researchers either explicitly or implicitly
answer a variety of different questions: _what_ should be explained, _to whom_
it should be explained, and _how_ it should be explained. I argue that the
answers that are specified for each of the questions determine the relevant
means-end relations.

Answering the question as to _what_ should be explained determines the _topic_
of the explanation. At first blush, this might seem unnecessary: when trying
to produce an explanation of some ML method, the topic should obviously be the
ML method itself. Yet the topic can also be spelled out at a more fine-grained
level as a particular aspect of an ML method and, indeed, it regularly is.
This is shown in Table 1: in the case of LIME, the focus is on explanations
for predictions within a specific part of the data while in the case of CFE,
it is on the input-output relation of an ML model.

Answering the question _to whom_ something should be explained determines the
relevant _stakeholder_ who is asking for and receiving the explanation. This
is important, since there is a variety of different stakeholders in the ‘ML
ecosystem’. The latter term was coined by Tomsett et al., (2018) who
distinguish creators (agents that create an ML system), operators (agents
interacting directly with an ML system), and executors (agents making
decisions informed by an ML system) as well as decision-subjects (agents
affected by ML-based decisions) and data-subjects (agents whose personal data
has been used to train the system).101010This is only one possible
classification of stakeholders and I will use it here as a reference point.
For another classification, see, for instance, Preece et al., (2018). Clearly,
this variety of stakeholders suggests a variety of cognitive abilities,
previous knowledge, or interests across the different agents. It has therefore
been pointed out repeatedly that different stakeholders have different
explanatory requirements (Langer et al., 2021, Mohseni et al., 2021, Zednik,
2019).111111Recently, it has been argued that, in addition, what matters is
the relation between the stakeholder receiving and the stakeholder providing
the explanation (Bordt et al., 2022). This is reflected in practice: for
instance, LIME is explicitly meant to provide explanations to the users of an
ML system while CFE are meant to do the same for data-subjects (Ribeiro et
al., 2016: 1135, Wachter et al., 2018: 843).121212However, note that there is
no standard terminology for the stakeholders in the ML ecosystem yet: the
users mentioned by Ribeiro et al., (2016: 1135) are likely to be either
operators or executors as defined in the classification by Tomsett et al.,
(2018). Similarly, based on the remarks by Wachter et al., (2018), it seems
likely that CFE should rather be provided to _decision_ \- rather than to
_data_ -subjects as defined in the classification by Tomsett et al., (2018).
Thus, to avoid ambiguities, Table 1 was constructed using the latter
classification.

The previous paragraphs reveal that the specification of a topic and the
relevant stakeholders further characterizes what aspects should be taken into
account when an XAI technique produces an explanation. This determines an
epistemic end that is one component of the epistemic means-end relations
governing XAI. Clearly then, the corresponding means are the other component.
They are determined by answering the question as to _how_ an explanation
should be achieved, for this specifies the _instruments_ deemed appropriate to
achieve that explanation at hand. As reflected by the high-level aim in 2.1,
this is the main occupation of methodological research in XAI: to develop and
improve instruments that produce explanations of ML methods. In the case of
LIME, local approximations of complex models are the instruments or means
proposed to attain the given epistemic end, while CFE seek to attain the given
epistemic end via counterfactual statements (see Table 1).

Table 1: Possible determination of fine-grained means-end relations for LIME and CFE. | Epistemic End | Means
---|---|---
|  _What?_ |  _To whom?_ |  _How?_
Example |  (topic) |  (stakeholder) |  (instrument)
LIME |  prediction(s) in specific part of the data |  operators; executors |  local approximation to complex model
CFE |  input-output relation |  decision-subjects |  counterfactual statements

Although the exact characterization of LIME and CFE presented in Table 1 might
be debatable, the overall framework discussed so far clearly gives rise to a
situation that is considerably more fine-grained than the high-level aim of
XAI formulated in 2.1: epistemic ends can be split into topic and stakeholder,
instruments constitute the corresponding means to achieve given ends. Thus,
the high-level aim can be reformulated by stating that XAI seeks to

.[(1’)] Provide instruments that produce explanations of topic $t$ for
stakeholder $s$.

On the one hand, this goes slightly beyond standard means-end epistemology
that takes epistemic ends to come in different levels of granularity, yet also
takes them as rather monolithic and not separable into further constituents.
On the other hand, it hints at a possible strategy to determine the different
levels of granularity of epistemic ends in practice: there is a coarse-grained
level as expressed in 2.1, stating that an explanation of an ML method should
be produced; yet there is a sequence of more fine-grained levels as expressed
in (1’), at which explanations of specific parts of said ML method should be
produced for specific stakeholders. Stating topic, stakeholder, and instrument
with increasing precision allows to move from the coarse- to the fine-grained
level. As I will show in the following, this kind of analysis has a
descriptive and a normative component.

### 3.2 The Account’s Descriptive Component

The means-end account proposed in the previous section has a rather
straightforward descriptive component: as illustrated in Table 1, it allows to
_describe_ the means-end considerations of XAI researchers by stating what
topic and stakeholder constitute their epistemic end and what instruments they
propose as means to attain it. As two further examples will show, this is a
useful framework for structuring the field of XAI.

First, consider a technique proposed by Hendricks et al., (2016). It is meant
to produce explanations of how some visual input to an ML-based image
classification system, that is, an image, leads to a specific output, that is,
a particular classification. Their solution is to generate textual
explanations that describe those parts of the visual input that distinguish it
from images in other categories.

Second, consider a technique proposed by Kim et al., (2018). It is meant to
produce explanations for the internal state of an ML system that is
controlling an autonomous vehicle. Their solution is to generate textual
explanations derived from the visual attention of the ML system that controls
the vehicle.

Exploiting the means-end account’s descriptive component, it is
straightforward to analyze both techniques just like LIME and CFE above. As
for the _topic_ , Hendricks et al., (2016) focus on the relationship between
an input to the image classification system and its corresponding output. In
fact, they make their specification of the topic explicit by stating that they
concentrate on “ _justification_ explanation systems producing sentences
detailing how visual evidence [i.e., some input] is compatible with a system
output” (Hendricks et al., 2016: 3). Furthermore, they contrast their approach
with “ _introspective_ explanations” that focus on the internal functionality
of a system. The latter, however, are the explicit topic defined by Kim et
al., (2018: 564) who state that they aim at providing “explanations that are
based on the system’s internal state”. As for the _stakeholder_ who should
receive the explanation, both techniques are meant to address either the
operators or the executors of an ML system.131313To be precise, both Hendricks
et al., (2016) and Kim et al., (2018) mention (end-)users as the relevant
stakeholders, which in terms of the classification by Tomsett et al., (2018)
are either operators or executors.

Finally, as for the _instruments_ , Hendricks et al., (2016) propose a
technique that consists in describing those parts of input images that are
decisive for their classification. To use the authors’ terminology, they
propose to generate textual explanations that describe properties that are
both “image-relevant” in the sense that the property is really contained in
the input at hand and “class-discriminative” in the sense that the property is
relevant for distinguishing between different categories (Hendricks et al.,
2016: 4). For the particular application that the authors investigate, the
classification of birds, this leads to explanations like “[t]his is a _Western
Grebe_ because this bird has a long white neck, pointy yellow beak and red
eye” (Hendricks et al., 2016: 2). The explanation mentions the output of the
image classification system, ‘Western Grebe’, as well as specific properties
that occur in the input image and that distinguish the Western Grebe from
other, similar looking birds.

Kim et al., (2018) propose another instrument that is known as visual
attention heatmapping to achieve their epistemic end (Kim and Canny, 2017, Xu
et al., 2015). This means that their technique to achieve explanations relies
on analyzing the visual attention of the ML system controlling the autonomous
vehicle. More precisely, the system is continuously confronted with an input
of traffic scenes consisting of dashcam images and sensor measurements such as
the vehicle’s speed. The authors employ a so-called attention model to extract
salient features of this input that the system ‘looks at’ and that it uses for
its decisions regarding the vehicle’s acceleration as well as its change of
course. Subsequently, textual descriptions for these salient features are
generated, leading to explanations for the vehicle’s behavior such as: “The
car is driving forward + because there are no other cars in its lane” (Kim et
al., 2018: 564). Although this explanation resembles the ones produced by the
technique of Hendricks et al., (2016), it is generated by a strictly different
approach: whereas explanations by Hendricks et al., (2016) are generated
conditional on visual properties of the ML system’s _input_ (e.g., ‘long white
neck’, ‘pointy yellow beak’, ‘red eye’), explanations by Kim et al., (2018)
rely on attention heatmaps and are thus generated conditional on _internal
states_ of the ML system. To emphasize this distinction, I refer to the former
approach as ‘textual explanations’ and to the latter as ‘verbalized attention
heatmapping’.

The new examples just discussed can be used to extend Table 1, giving rise to
the situation in Table 2: four XAI techniques are described based on the
specific means-end considerations by which they are governed. This is useful
for at least two reasons.

Table 2: Tentative structure for a taxonomy of XAI techniques. | Epistemic End | Means
---|---|---
|  _What?_ |  _To whom?_ |  _How?_
Example |  (topic) |  (stakeholder) |  (instrument)
… |  … |  … |  …
LIME |  prediction(s) in specific part of the data |  operators; executors |  local approximation to complex model
CFE |  input-output relation |  decision-subjects |  counterfactual statements
Hendricks et al., (2016) |  input-output relation |  operators; executors |  textual explanations
Kim et al., (2018) |  system’s internal state |  operators; executors |  verbalized attention heatmapping
… |  … |  … |  …

First, it reveals that although the XAI literature diverges both conceptually
and methodologically, there is a common structure that is shared by the
different approaches pursued in the literature. This structure consists in
means-end relations that arise from the specification of topics, stakeholders,
and instruments.

Second, extending the analysis from above to other XAI techniques allows for a
taxonomy of the existing literature in the field. Accordingly, it is possible
to investigate the means-end relations governing other XAI techniques, to
identify the relevant topic, stakeholder, and instrument and to extend Table 2
as indicated by the dots in the first and last row. Thus, the table is not
only a description of four XAI techniques, it is also a starting point for a
more comprehensive taxonomy of existing methods.

### 3.3 The Account’s Normative Component

Using the descriptive component of the means-end account, it is possible to
unravel the different epistemic ends pursued by different authors and the
different means they propose to achieve them. Apparently, authors come up with
different instruments when they specify different topics or stakeholders. Thus
differences in the ‘what’ and ‘to whom’ of an explanation seem to trigger
differences in the ‘how’ of achieving it. This observation might seem entirely
unsurprising at first. After all, means-end considerations are common to a
variety of contexts different from XAI in which instruments or techniques have
to be chosen based on some given end: if I pursue the end of driving a nail
into the wall, I better use a hammer instead of a violin bow. Yet if my end
consists in practicing my favorite violin sonata, the latter will be much more
appropriate.141414Grüne-Yanoff, (2021) puts forward a similar argument for the
case of scientific methodology. The perspective of means-end epistemology
allows to move beyond such intuitively plausible observations. In particular,
it helps to make means-end relationships in XAI more precise, thereby
ultimately leading to the normative component of the present account.

First, recall from 2.2 that means-end epistemology is inherently normative and
governed by the principle of instrumental rationality: given an epistemic end,
certain means ought to be adopted if and only if they further the given end.
Second, we have seen in 3.1 that problems of XAI can be framed as problems of
means-end epistemology. In particular, specifying a topic and stakeholder
determines the epistemic end that is pursued, while specifying the
corresponding XAI instruments determines the means to attain the given end.
Taking these aspects together shows that XAI is inherently normative as well:

. Given a topic $t$ and stakeholder $s$, certain instruments of XAI ought to
be adopted if and only if they further the epistemic end determined by $t$ and
$s$.

Put differently, the suitability of XAI techniques depends on what exactly
should be explained and to whom the explanation should be given. However, this
dependence is a normative one. Indeed, differences in the topic and
stakeholder determining an epistemic end trigger differences in the
instruments to achieve it, but they do so with normative force.

For instance, it is not by mere coincidence that the last column of Table 2
displays four different instruments. Rather, the topics and stakeholders
defined by the different authors determine different epistemic ends. The
means-end account’s normative component tells us that different ends call for
different means. So clearly, given different topics or stakeholders, the
specific instrument proposed by Hendricks et al., (2016) differs from the one
proposed by Kim et al., (2018) which in turn differs from CFE. Furthermore,
Table 2 highlights the importance of analyzing epistemic ends at a high level
of granularity. For instance, both the technique proposed by Kim et al.,
(2018) and the one proposed by Hendricks et al., (2016) are meant to provide
explanations to either operators or executors of an ML system, yet the former
authors aim at explanations of a system’s internal states whereas the latter
aim at explanations of its input-output relation. Thus, while addressing the
same stakeholders, the techniques are meant to produce explanations of
different topics, that is, of different aspects of an ML system. In sum, this
leads to different epistemic ends being pursued and different means ought to
be adopted to achieve them.151515The same reasoning could be applied when
comparing the technique proposed by Hendricks et al., (2016) to CFE. In that
case, the topic is the same, but explanations should be produced for different
stakeholders which, in sum, also leads to different epistemic ends (see Table
2).

Consequently, the examples hint at what the normative component allows to
achieve on a more general level: it allows to spell out in great detail what
an explanation for an ML method should ‘look like’ in a specific setting.
Thus, analyzing particular ends, that is, particular topics and stakeholders,
can reveal which instruments ought to be adopted to achieve them and which
instruments can be ruled out as inappropriate. In order to allow for such
insights, it is important to recognize the logical form in which the principle
of instrumental rationality 2.2 is stated in means-end epistemology and to
preserve this form also in 3.3. Topic and stakeholder constitute the epistemic
end which is in turn tied by a biconditional to the adoption of certain means,
that is, certain intruments of XAI: if certain instruments ought to be
adopted, then they further the epistemic end determined by the given topic and
stakeholder; if they further the epistemic end determined by the given topic
and stakeholder, then certain instruments ought to be adopted. Considering
only one of the latter conditional statements could give rise to two types of
problematic cases: on the one hand, cases in which certain instruments ought
_not_ to be adopted, although they further the given epistemic end.161616There
might be cases in which certain instruments _cannot_ be adopted, although they
further the given epistemic end, for instance due to privacy issues or
proprietary software. Yet this does not affect the normative result that, in
principle, they nevertheless _ought_ to be adopted. On the other hand, cases
in which certain instruments do not further the given epistemic end, yet
nevertheless ought to be adopted.

However, if such problematic cases are prevented, the normative component can
be used to show how the set of appropriate XAI instruments is constrained by
the particular ends for which an explanation is sought. As outlined above, in
means-end epistemology and in the means-end account of XAI alike, the set of
appropriate instruments gets narrower as the epistemic end gets more precise.
This implies that one should aim for maximally specific topics and
stakeholders to identify a maximally specific set of appropriate instruments
that one ought to adopt.171717Note that no matter how specific topic and
stakeholder are defined, there will be several appropriate instruments and
hence a set of different particular means to the same end in most cases
(Mothilal et al., 2021). Furthermore, the central insight of means-end
epistemology that “all we need to provide a means-end analysis […] is a
sufficiently clear description of the goals in question” (Schulte, 1999: 26)
hints at the precondition for assessing the suitability of XAI techniques in a
given context: we can only ever determine whether an XAI technique is
appropriate, if _ex ante_ , the epistemic end being pursued is specified in
sufficient detail. This implication of the present investigation is so far
largely neglected in the discourse on XAI. In particular, high-level
regulation such as the EU General Data Protection Regulation or the European
Union’s draft Artificial Intelligence Act does not spell out the precise
epistemic end corresponding to the transparency requirements imposed on ML
methods.

Thus overall, the means-end account’s normative component establishes a
normative framework for the field of XAI. The framework is based on the
insight that a close analysis of _what_ specific part of an ML method should
be explained and _to whom_ it should be explained allows to determine the set
of instruments that is appropriate to bring about that specific explanation.
This unifies and extends existing proposals that point to a similar direction.

First, the means-end account’s normative component unifies rather descriptive
frameworks of XAI like the one proposed by Sokol and Flach, (2020). They carve
out “a set of descriptors that can be used to characterise and systematically
assess explainable systems” (Sokol and Flach, 2020: 56). However, although
leading to a useful and very detailed taxonomy of XAI techniques, the
framework does not provide an overarching account of how the assessment of XAI
techniques connects them to specific situations. This can be achieved using
the means-end account’s normative component: a specific situation will be
characterized by a specific epistemic end being pursued which in turn
normatively prescribes a set of appropriate instruments. For instance,
consider a loan applicant—without expertise in ML—who asks for an explanation
of why her loan application was accepted or rejected by the bank’s ML-based
decision system. The applicant’s explanatory topic—the decision, that is, the
output of the ML-based system—and her own role as a specific stakeholder with
specific explanatory requirements that need to be fulfilled constitute an
epistemic end that clearly rules out a highly specific explanation of the
system’s internal processes as the appropriate means. Instruments that provide
some high-level explanation of why the system’s input led to a specific output
might be more appropriate in this case. Once such a set of appropriate
instruments has been established, a purely descriptive account can help to
assess whether a given XAI technique belongs to that set or not. Yet
beforehand, it is epistemic normativity that links the characteristics of a
situation to a set of instruments that are appropriate due to their specific
characteristics and that hence ought to be adopted.

Second, the means-end account’s normative component goes beyond other
proposals of normative frameworks that solely focus on the explanatory
requirements of different stakeholders. For instance, on Zednik,’s (2019)
account, these requirements can be characterized by spelling out the
epistemically relevant elements of an ML system for a given stakeholder. Since
these elements differ across stakeholders, different explanatory requirements
have to be satisfied by tailor-made explanations. Thus, an XAI technique
should be used if it produces explanations that fulfill a stakeholder’s
explanatory requirements in virtue of addressing the specific epistemically
relevant elements. However, fulfilling the requirements of different
stakeholders can hardly be all there is to the suitability of XAI techniques,
since one can easily imagine a situation in which the _same_ stakeholder asks
for _different_ explanations. For instance, consider once more a loan
applicant, but this time with a genuine interest in ML. In that case, she
might on the one hand still ask for an explanation of why her loan application
was accepted or rejected, that is, why certain inputs led to a certain output.
On the other hand, however, she might also ask for an explanation of the ML
system’s internal functioning. As already shown in Table 2 above, the means-
end account of XAI accomodates both situations as in this example and accounts
that derive different explanatory requirements from differences across
stakeholders in a straightforward way: on this account, the explanatory
requirements of different stakeholders are but one source of variation in the
epistemic end of XAI, another one consisting in the specification of different
topics. The means-end account’s descriptive component allows to distinguish
them accurately and to analyze their particular specifications as well as the
epistemic end that they determine. Additionally, given a certain epistemic
end, the account’s normative component allows to identify the set of
instruments that the end calls for.

## 4 Extending the Account

We have made quite some progress up to this point: we have seen that the high-
level aim of XAI can be reformulated in a more granular way (see (1’)), that
problems of XAI can be framed as problems of means-end epistemology (see 3.1),
and that, consequently, XAI is inherently normative (see 3.3). However, the
preceding discussion exclusively focused on epistemic aspects, considering the
epistemic end of producing explanations to be the main ingredient of the
means-end account. Albeit leading to an account that accurately reflects the
structure of XAI problems and is useful for their analysis, this perspective
needs to be broadened for at least two reasons.

First, there can be epistemic ends other than that of producing explanations.
Indeed, it has been pointed out that sometimes, XAI techniques should produce
explanations to achieve further epistemic ends such as understanding or
interpretability (Erasmus et al., 2020). Seen this way, achieving the
epistemic end of producing explanations can also turn into a means to achieve
another epistemic end.

Second, XAI techniques are commonly employed to achieve non-epistemic ends.
For instance, returning to the examples from above, LIME and the technique
proposed by Hendricks et al., (2016) are meant to foster trust in an ML
system; Kim et al., (2018) aim at enabling human agents to extrapolate the
behavior of the vehicle controlled by an ML system; CFE are meant to inform,
provide grounds to contest adverse decisions, and reveal how to reach a
desired result in the future (Wachter et al., 2018: 843).

Thus, beyond the epistemic ends discussed above, there are further ends
relevant to XAI that might stem from epistemic or non-epistemic
considerations. So in addition to answering what should be explained, to whom
it should be explained, and how it should be explained, researchers seem to
answer the question as to _why_ something should be explained. I call the
answer to this question the _goal_ of an explanation. Incorporating this into
the means-end account, one can extend (1’) by stating that XAI seeks to

.[(1*)] Provide instruments that produce explanations of topic $t$ for
stakeholder $s$ to achieve goal $g$.

This extension leads to a setup in which there are two types of means-end
relations: the strictly epistemic means-end relations discussed above and
means-end relations that can, but need not be strictly epistemic, depending on
the specification of the goal. Importantly, the former relations are
instrumental to the latter ones, since achieving the epistemic end of
producing explanations of topic $t$ for stakeholder $s$ can also be a means to
achieving goal $g$, provided that the particular epistemic end really is
suitable to achieve the particular goal. This setup could easily be extended
even further to what one might call a cascade of means-end relations in which
achieving the end of one relation is also a means to achieve the end of the
next relation and so on. To determine a suitable XAI technique, one would then
have to work backwards through the cascade, ultimately arriving at one of the
strictly epistemic means-end relations discussed above.181818Apart from being
intuitively plausible, this strategy of working backwards is suggested by the
literature on means-end reasoning in both philosophy and artificial
intelligence (Bratman, 1981, Pollock, 1998).

Extending the means-end account in this way is important, since it reflects
both the methodological and the conceptual literature on XAI. As for the
methodological literature, consider once more the example of CFE. As discussed
above, CFE are meant to reveal “what could be changed to receive a desired
result in the future” (Wachter et al., 2018: 843), a problem that is commonly
referred to as _algorithmic recourse_ (Venkatasubramanian and Alfano, 2020).
However, it has been claimed that CFE fall short of achieving this goal, for
they ignore “the _causal relationships_ governing the world in which actions
will be performed” (Karimi et al., 2021: 353). This means that although CFE
recommend a set of alternative actions (e.g., ‘increase annual income by
amount $X$’) these need not lead to the desired result (e.g., ‘you were
granted the loan’), since the mechanism by which the ML model operates might
not reflect the true underlying mechanism properly.191919An intuitive example
for this situation is provided in Karimi et al., (2021: 353). The debate
surrounding CFE reveals that, although implicitly, debates about the
suitability of XAI methods indeed center around means-end considerations and
their inherent normativity: according to the literature, counterfactual
statements are an appropriate means to achieve the epistemic end of producing
explanations of an ML system’s input-output relation for a decision-subject
(see Table 1). Furthermore, this epistemic end seems to be an appropriate
means to achieve the goal of identifying and contesting adverse decisions.
However, it seems to be an inappropriate means to achieve the goal of
providing information on how to turn them into a desired result in the future.
Consequently, CFE ought not be used when the latter is the
goal.202020Similarly, it has been questioned whether producing particular
explanations is an appropriate means to achieve the goal of establishing human
trust in an ML system (Kästner et al., 2021).

As for the conceptual literature, recall from above that Krishnan, (2020: 488)
argues that what is called explainability or interpretability “serves as a
means to an end, rather than being an end in itself” (Krishnan, 2020:
488).212121Similar arguments have been put forward, e.g., by Bordt et al.,
(2022). Thus, beyond the basic epistemic end of producing explanations and
beyond further epistemic ends such as interpretability, there are more
‘fundamental goals’ (Krishnan, 2020: 495) that she takes to be the _actual_
ends that should be achieved. Accordingly, problems of XAI should be framed in
a way that uncovers these fundamental goals to “facilitate a more pluralistic
approach to problem-solving” (Krishnan, 2020: 495). So on her view,
identifying XAI techniques that are appropriate in a particular situation
requires a fine-grained characterization of that situation in the first place.
The extension introduced in (1*), distinguishing epistemic ends from further
goals that might be specified, offers a straightforward way to accommodate
this line of argumentation within the means-end account of XAI. First, we have
seen that epistemic ends come in varying degrees of granularity. Second, the
account’s normative component reveals that more or less specific ends entail
more or less specific sets of appropriate instruments. Third, different (sets
of) means ought to be adopted to achieve different epistemic ends. Fourth,
different epistemic ends are required to achieve different goals.
Consequently, the means-end account of XAI allows for a fine-grained
investigation of what Krishnan refers to as ‘fundamental goals’. It also
reveals why a pluralistic approach to problem-solving is indeed necessary in
XAI: since one ought to adopt the means to one’s ends.

Having said all this, however, one might object that the perspective of
normative epistemology adopted in this article is no longer essential to the
means-end account. After all, what matters when faced with a cascade of means-
end relations seems to be the strategy of backward-planning mentioned above,
since this suffices to ensure means-end coherence across the different
relations. But we do not have to consider an entire cascade of means-end
relations, we do not even have to go beyond (1*) to notice the following: XAI
is an epistemic endeavor at heart. No matter what further goals are specified,
we have seen that a strictly epistemic means-end relation is the nucleus of
everything that follows. This is why the perspective of normative epistemology
is crucial.

## 5 Conclusion

This paper set out by observing considerable disagreement in the XAI
literature, both on a conceptual and on a methodological level. Does this mean
that the field of XAI is scattered into various disconnected subprojects?
Quite to the contrary. Indeed, I argue that there is a common structure that
is shared by the variety of approaches pursued in the literature. To do so, I
put forward a means-end account of XAI. The account relies on the insight from
means-end epistemology that one ought to adopt appropriate means to one’s
epistemic ends. It also relies on the observation that XAI can be framed as a
problem of means-end epistemology. Taking both aspects together, I show that
normative means-end relations are and should in fact be central to XAI. I
further show that these means-end relations are determined by a topic, a
stakeholder, a goal, and an instrument. By specifying these, one provides
answers to four central questions: What should be explained? To whom should it
be explained? Why should it be explained? And how should it be explained?

The means-end account of XAI has several important consequences. First, it
explains why disagreement arises in the field: the divergence in instruments
of XAI follows from the disagreement on epistemic ends. Second, it structures
the field: there is a common methodology of developing appropriate means for
given ends. Third, this structure has a descriptive component: different
authors specify different ends and come up with different means to achieve
them. This gives rise to a taxonomy that classifies existing contributions to
the field along the specific means-end relations that are considered. Fourth,
this structure also has a normative component: the ends of an explanation
normatively constrain the set of admissible means to achieve it. The means-end
account thus reveals how the suitability of particular instruments of XAI is
prescribed by the ends for which an explanation is sought.

Future research might investigate the different components of the means-end
account even further. On the one hand, I plan to establish a more
comprehensive taxonomy of existing XAI techniques using the account’s
descriptive component and to evaluate it using the normative component. On the
other hand, there is potential to apply the means-end account to regulatory
issues. From this perspective, the account paves the way for designing
effective guidelines of XAI that ensure that the right techniques are employed
in the right situations.

## References

  * Baldi et al., (2014) Baldi, P., Sadowski, P., and Whiteson, D. (2014).  Searching for Exotic Particles in High-Energy Physics with Deep Learning.  Nature Communications, 5(4308):1–9.
  * Besold and Uckelmann, (2018) Besold, T. and Uckelmann, S. (2018).  The What, the Why, and the How of Artificial Explanations in Automated Decision-Making.  arXiv, 1808.07074:1–20.
  * Bojarski et al., (2016) Bojarski, M., Del Testa, D., Dworakowski, D., Firner, B., Flepp, B., Goyal, P., Jackel, L. D., Monfort, M., Muller, U., Zhang, J., Zhang, X., Zhao, J., and Zieba, K. (2016).  End to End Learning for Self-Driving Cars.  arXiv, 1604.07316.
  * Bordt et al., (2022) Bordt, S., Finck, M., Raidl, E., and von Luxburg, U. (2022).  Post-Hoc Explanations Fail to Achieve their Purpose in Adversarial Contexts.  In 2022 ACM Conference on Fairness, Accountability, and Transparency, ACM Digital Library, pages 891–905, New York, NY. Association for Computing Machinery.
  * Bratman, (1981) Bratman, M. (1981).  Intention and Means-End Reasoning.  The Philosophical Review, 90(2):252–265.
  * Burrell, (2016) Burrell, J. (2016).  How the Machine ‘Thinks’: Understanding Opacity in Machine Learning Algorithms.  Big Data & Society, 3(1):1–12.
  * Creel, (2020) Creel, K. A. (2020).  Transparency in Complex Computational Systems.  Philosophy of Science, 87(4):568–589.
  * Doshi-Velez and Kim, (2017) Doshi-Velez, F. and Kim, B. (2017).  Towards A Rigorous Science of Interpretable Machine Learning.  arXiv, 1702.08608.
  * Erasmus et al., (2020) Erasmus, A., Brunet, T. D. P., and Fisher, E. (2020).  What is Interpretability?  Philosophy & Technology, 174(2):1–30.
  * Esteva et al., (2017) Esteva, A., Kuprel, B., Novoa, R. A., Ko, J., Swetter, S. M., Blau, H. M., and Thrun, S. (2017).  Dermatologist-Level Classification of Skin Cancer with Deep Neural Networks.  Nature, 542(7639):115–118.
  * Finlay, (2009) Finlay, S. (2009).  Oughts and Ends.  Philosophical Studies, 143(3):315–340.
  * Foot, (1972) Foot, P. (1972).  Morality as a System of Hypothetical Imperatives.  The Philosophical Review, 81(3):305.
  * Foreman-Mackey et al., (2015) Foreman-Mackey, D., Montet, B. T., Hogg, D. W., Morton, T. D., Wang, D., and Schölkopf, B. (2015).  A Systematic Search for Transiting Planets in the K2 Data.  The Astrophysical Journal, 806(2):215–228.
  * Grüne-Yanoff, (2021) Grüne-Yanoff, T. (2021).  Justifying Method Choice: A Heuristic-Instrumentalist Account of Scientific Methodology.  Synthese, 199(1-2):3903–3921.
  * Günther and Kasirzadeh, (2021) Günther, M. and Kasirzadeh, A. (2021).  Algorithmic and Human Decision Making: For a Double Standard of Transparency.  AI & SOCIETY.
  * Hendricks et al., (2016) Hendricks, L. A., Akata, Z., Rohrbach, M., Donahue, J., Schiele, B., and Darrell, T. (2016).  Generating Visual Explanations.  In Leibe, B., Matas, J., Sebe, N., and Welling, M., editors, Computer Vision – ECCV 2016, pages 3–19, Cham. Springer International Publishing.
  * Huber, (2021) Huber, F. (2021).  Belief and Counterfactuals. A Study in Means-End Philosophy.  Oxford University Press, New York.
  * Karimi et al., (2021) Karimi, A.-H., Schölkopf, B., and Valera, I. (2021).  Algorithmic Recourse: from Counterfactual Explanations to Interventions.  FAccT ’21: Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, pages 353–362.
  * Kästner et al., (2021) Kästner, L., Langer, M., Lazar, V., Schomäcker, A., Speith, T., and Sterz, S. (2021).  On the Relation of Trust and Explainability: Why to Engineer for Trustworthiness.  2021 IEEE 29th International Requirements Engineering Conference Workshops (REW), pages 169–175.
  * Keil, (2006) Keil, F. C. (2006).  Explanation and Understanding.  Annual Review of Psychology, 57(1):227–254.
  * Kim and Canny, (2017) Kim, J. and Canny, J. (2017).  Interpretable Learning for Self-Driving Cars by Visualizing Causal Attention.  Proceedings of the IEEE International Conference on Computer Vision, pages 2942–2950.
  * Kim et al., (2018) Kim, J., Rohrbach, A., Darrell, T., Canny, J., and Akata, Z. (2018).  Textual Explanations for Self-Driving Vehicles.  In Ferrari, V., Hebert, M., Sminchisescu, C., and Weiss, Y., editors, Computer Vision – ECCV 2018, pages 563–578, Cham. Springer International Publishing.
  * Krishnan, (2020) Krishnan, M. (2020).  Against Interpretability: a Critical Examination of the Interpretability Problem in Machine Learning.  Philosophy & Technology, 33(3):487–502.
  * Langer et al., (2021) Langer, M., Oster, D., Speith, T., Hermanns, H., Kästner, L., Schmidt, E., Sesing, A., and Baum, K. (2021).  What Do We Want from Explainable Artificial Intelligence (XAI)? – A Stakeholder Perspective on XAI and a Conceptual Model Guiding Interdisciplinary XAI Research.  Artificial Intelligence, 296:103473.
  * Lipton, (2018) Lipton, Z. C. (2018).  The Mythos of Model Interpretability.  Queue, 16(3):31–57.
  * Lombrozo, (2006) Lombrozo, T. (2006).  The Structure and Function of Explanations.  Trends in Cognitive Sciences, 10(10):464–470.
  * Lundberg and Lee, (2017) Lundberg, S. M. and Lee, S. (2017).  A Unified Approach to Interpreting Model Predictions.  NIPS’17: Proceedings of the 31st International Conference on Neural Information Processing Systems, pages 4768–4777.
  * Miller, (2019) Miller, T. (2019).  Explanation in Artificial Intelligence: Insights from the Social Sciences.  Artificial Intelligence, 267:1–38.
  * Mohseni et al., (2021) Mohseni, S., Zarei, N., and Ragan, E. D. (2021).  A Multidisciplinary Survey and Framework for Design and Evaluation of Explainable AI Systems.  ACM Transactions on Interactive Intelligent Systems, 11(3-4):1–45.
  * Mothilal et al., (2021) Mothilal, R. K., Mahajan, D., Tan, C., and Sharma, A. (2021).  Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End.  AIES ’21: Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society, pages 652–663.
  * Nyrup and Robinson, (2022) Nyrup, R. and Robinson, D. (2022).  Explanatory Pragmatism: A Context-Sensitive Framework for Explainable Medical AI.  Ethics and information technology, 24(1):1–15.
  * Páez, (2019) Páez, A. (2019).  The Pragmatic Turn in Explainable Artificial Intelligence (XAI).  Minds and Machines, 29(3):441–459.
  * Pollock, (1998) Pollock, J. L. (1998).  The Logical Foundations of Goal-regression Planning in Autonomous Agents.  Artificial Intelligence, 106(2):267–334.
  * Preece et al., (2018) Preece, A., Harborne, D., Braines, D., Tomsett, R., and Chakraborty, S. (2018).  Stakeholders in Explainable AI.  arXiv, 1810.00184.
  * Raidl and Rott, (2022) Raidl, E. and Rott, H. (2022).  Towards a Logic for ‘because’.  Unpublished Manuscript.
  * Ribeiro et al., (2016) Ribeiro, M. T., Singh, S., and Guestrin, C. (2016).  “Why Should I Trust You?” Explaining the Predictions of Any Classifier.  Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 1135–1144.
  * Rudin, (2019) Rudin, C. (2019).  Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead.  Nature Machine Intelligence, 1(5):206–215.
  * Schulte, (1999) Schulte, O. (1999).  Means-Ends Epistemology.  The British Journal for the Philosophy of Science, 50(1):1–31.
  * Sokol and Flach, (2020) Sokol, G. and Flach, P. (2020).  Explainability Fact Sheets: A Framework for Systematic Assessment of Explainable Approaches.  FAT* ’20: Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency, pages 56–67.
  * Tomsett et al., (2018) Tomsett, R., Braines, D., Harborne, D., Preece, A., and Chakraborty, S. (2018).  Interpretable to Whom? A Role-based Model for Analyzing Interpretable Machine Learning Systems.  arXiv, 1806.07552.
  * Venkatasubramanian and Alfano, (2020) Venkatasubramanian, S. and Alfano, M. (2020).  The Philosophical Basis of Algorithmic Recourse.  Proceedings of 2020 ACM Conference on Fairness, Accountability, and Transparency, pages 284–293.
  * Wachter et al., (2018) Wachter, S., Mittelstadt, B., and Russell, C. (2018).  Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR.  Harvard Journal of Law & Technology, 31(2):841–887.
  * Xu et al., (2015) Xu, K., Ba, J. L., Kiros, R., Cho, K., Courville, A., Salakhutdinov, R., Zemel, R. S., and Bengio, Y. (2015).  Show, Attend and Tell: Neural Image Caption Generation with Visual Attention.  International Conference on Machine Learning, pages 2048–2057.
  * Zednik, (2019) Zednik, C. (2019).  Solving the Black Box Problem: A Normative Framework for Explainable Artificial Intelligence.  Philosophy & Technology, 34(2):1–24.
  * Zerilli et al., (2019) Zerilli, J., Knott, A., Maclaurin, J., and Gavaghan, C. (2019).  Transparency in Algorithmic and Human Decision-Making: Is There a Double Standard?  Philosophy & Technology, 32(4):661–683.