=Paper=
{{Paper
|id=Vol-3209/8546
|storemode=property
|title=Fostering Explainable Online Review Assessment Through Computational Argumentation
|pdfUrl=https://ceur-ws.org/Vol-3209/8546.pdf
|volume=Vol-3209
|authors=Atefeh Keshavarzi Zafarghandi, Davide Ceolin
|dblpUrl=https://dblp.org/rec/conf/comma/ZafarghandiC22
}}
==Fostering Explainable Online Review Assessment Through Computational Argumentation==
https://ceur-ws.org/Vol-3209/8546.pdf
Fostering Explainable Online Review Assessment
Through Computational Argumentation
Atefeh Keshavarzi Zafarghandi, Davide Ceolin
Human-Centered Data Analytics, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands
Abstract
Explainable methods have received increased attention within artificial intelligence. Wherever an
automated system makes a decision an explanation is required to convince a user about the decision. Fur-
thermore, online information quality assessment is crucial to help users navigate information. However,
explaining the assessment of online information had not been clarified well. The current work provides
explanations to a user about the assessment of online information and specific, provides explanations
for the quality assessments of online reviews. We construct an abstract argumentation framework (AF)
based on a set of given reviews. We consider the grounded semantics of AFs to assess each topic. Then,
we discuss the question of why a score can be assigned to a topic of a product. Furthermore, we indicate
a proper score of a review based on the scores of topics within the review in question. We also collect
arguments that can support the chosen score of a review.
Keywords
Online reviews, Abstract Argumentation frameworks, Explainable Artificial Intelligence
1. Introduction
Argumentation is one research area that is frequently mentioned in explainable AI [1]. To our
knowledge, the role of argumentation formalisms in the sense of explanation for the assessment
of the quality of reviews has not been investigated in depth. In this work we aim to cover
this gap, i.e., to use an argumentation formalism not only for assessing the quality of online
information but also as a means to explain why a given score is assigned by a system to a
topic or a review. This is particularly compelling because online reviews are available in large
amounts, but for them to be beneficial to users, their quality needs to be determined. Given
the volume of the information at stake here, an automated approach is necessary to address
the problem properly. Given that the result of this automated assessment is meant to be used
by humans, the ability to explain the assessment process is likewise crucial. Computational
argumentation is, in our opinion, a promising methodology in this sense.
Abstract argumentation frameworks (AFs for short), as introduced by Dung [2] is a directed
graph in which nodes represent arguments and edges denote attack relation among arguments.
In this work, we use AFs as a means of modeling and evaluating reviews and as an explanation
for a chosen decision.
1st International Workshop on Argumentation for eXplainable AI (ArgXAI, co-located with COMMA ’22), September 12,
2022, Cardiff, UK
$ akz@cwi.nl (A. Keshavarzi Zafarghandi); davide.ceolin@cwi.nl (D. Ceolin)
0000-0002-5806-1012 (A. Keshavarzi Zafarghandi); 0000-0002-3357-9130 (D. Ceolin)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
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http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
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Atefeh Keshavarzi Zafarghandi et al. CEUR Workshop Proceedings 1–12
In the work presented in this paper, we aim to model a set of reviews with AFs and use the
grounded semantics of AFs as a means of evaluation and explanation. That is, this model allows
reasoning on the ‘acceptability of topics within reviews’ when reviews are conflicting with each
other. Such conflicts are solved by defining a weight for topics within reviews, which extends
and generalizes a review weight we defined in previous work [3]. To this end, we first consider
each set of reviews containing the same topic with the same score as a single argument. Then,
we introduce an attack relation if the weight of arguments is not the same. We first use the
grounded semantics of AFs to assess the score of each topic, and secondly to explain why a
system chooses a specific score for a topic in question. That is, we aim at providing the final user
with an explanation of why a specific score for a topic in question is acceptable (or trustable).
In other words, we aim to indicate what the score of a topic about a target/product is based on
the set of reviews. Some specific features of our work are as follows:
1. We consider all topics within a review, instead of only picking the most important one.
Thus, we do not miss any information presented in a review.
2. By our method, after the assessment, a user can ask about the score (strength) of topics
of a product, instead of just asking about the scores of the reviews.
3. Our method is solid enough to explain to a user the reason of assigning a score to a topic.
Also, explaining why an argument does not have a roll in the assessment of the score of a
topic.
4. We also accumulate the scores of topics within a review to assess a review score. Further-
more, we present an explanation for a review score from a machine point of view, which
is a subset of the grounded semantics of AFs. Thus, this explanation is beyond any doubt.
5. For indicating the scores of topics about a product within a set of reviews, based on a
system’s points of view, we do not need to consider any generalization of AFs. Since the
weight of each argument is used to indicate the direction of the attack relation.
The rest of the paper is structured as follows. Section 2 presents related work, and Section 3,
introduces abstract argumentation frameworks. Section 4 presents a model to formally represent
and reason on reviews. Section 5 concludes and outlines future work directions.
2. Related Work
Explainable artificial intelligence (XAI) has received increased attention to explain decisions of
automated systems [4]. Several machine learning methods are used to support decision-making.
However, these methods are required to convince a user about the machine decision. In other
words, an AI system needs to explain its decision to a user. Argumentation theory can help
the process of explanation, (see [1, 5] for a survey). Some argumentation frameworks with
respect to their use in support of explainable artificial intelligence (XAI) are presented in [6].
In [7] a new type of argumentation semantics is presented for AFs for capturing explanation.
Furthermore, argumentation is used to explain why and/or whether a certain argument can be
accepted under certain semantics [8, 9, 10, 11].
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On the other hand, a significant amount of research investigates the quality of reviews. In [3]
a generalization of abstract argumentation framework is used to assess the quality of the reviews
on a product, extending and combining preferred argumentation frameworks [12, 13] and valued-
based argumentation frameworks [14, 15] to model and evaluate a set of reviews. Furthermore,
to analyze product reviews, different methods for generating probability distributions over
constellations of arguments graph have been presented in [16, 17]. In [17] authors assume that
an agent(s) specifies a belief in the acceptability status of arguments. However, in [16] the
authors propose a scoring method for identifying the probability distribution for a review. After
the extraction of support and attack relations between reviews, a set of reviews is modeled by
an abstract dialectical framework [18] which generalizes AFs [2].
3. Background: Argumentation Formalisms
We start the preliminaries of our work by recalling the basic notion of Dung’s abstract argu-
mentation frameworks (AFs) [2].
Definition 1. [2] An abstract argumentation framework (AF) is a pair (𝐴, 𝑅) in which 𝐴 is a
set of arguments and 𝑅 ⊆ 𝐴 × 𝐴 is a binary relation representing attacks among arguments.
Let 𝐹 = (𝐴, 𝑅) be a given AF. For each 𝑎, 𝑏 ∈ 𝐴, the relation (𝑎, 𝑏) ∈ 𝑅 is used to represent
that 𝑎 is an argument attacking the argument 𝑏. An argument 𝑎 ∈ 𝐴 is, on the other hand,
defended by a set 𝑆 ⊆ 𝐴 of arguments (alternatively, the argument is acceptable with respect
to 𝑆) (in 𝐹 ) if for each argument 𝑐 ∈ 𝐴, it holds that if (𝑐, 𝑎) ∈ 𝑅, then there is a 𝑠 ∈ 𝑆 such
that (𝑠, 𝑐) ∈ 𝑅 (𝑠 is called a defender of 𝑎).
Different extension-based semantics of AFs present which sets of arguments in a given AF
can be accepted jointly [2]. We only recall grounded semantics here,1 because it is proven in [2]
that 1. every AF has a unique grounded extension, 2. there is no doubt on the acceptance of the
arguments in the grounded extension, 3. in any acyclic finite AF all sets of semantics coincide,
4. and in this work we only have acyclic frameworks.
Set 𝑆 ⊆ 𝐴 is called a conflict-free set (extension) (in 𝐹 ) if there is no 𝑎, 𝑏 ∈ 𝑆 such that (𝑎, 𝑏) ∈
𝑅. The characteristic function 𝐹 : 2𝐴 ↦→ 2𝐴 is defined as 𝐹 (𝑆) = {𝑎 | 𝑎 is defended by 𝑆}. A
set 𝑆 ∈ cf(𝐹 ) is the grounded extension in 𝐹 if 𝑆 is a unique fixed point of 𝐹 𝑛 (∅).
Example 1. Let 𝐹 = ({𝑎, 𝑏, 𝑐}, {(𝑎, 𝑏), (𝑏, 𝑐)}) be an AF. In 𝐹 , (𝑎, 𝑏) means that argument 𝑎
attacks 𝑏, and (𝑏, 𝑐) means that 𝑏 attacks 𝑐. Here, argument 𝑐 is defended by set {𝑎} (alternatively, 𝑐
is acceptable with respect to {𝑎}), since 𝑎 attacks the attacker of 𝑐, namely 𝑏. The set of conflict-free
sets of 𝐹 is cf(𝐹 ) = {∅, {𝑎}, {𝑏}, {𝑐}, {𝑎, 𝑐}}. A unique grounded extension of 𝐹 is {𝑎, 𝑐}. The
intuition is that 𝑎 is not attacked by any argument, thus no one has any doubt about accepting
argument 𝑎. Argument 𝑐 is attacked by 𝑏, however, it is defended by 𝑎 which was accepted by
everyone.
1
The reader interested in semantics of AFs can see [2].
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4. Modeling Reviews with Formal Argumentation
Here, we first model reviews in a formal manner by means of abstract argumentation frameworks
(AFs), and then show how to use AFs to evaluate the score of a topic of a product based on given
reviews (see Section 4.2). To this end, we collect the reviews with the same score containing the
same topic and we consider them as a single argument. After indicating the attack relations
between arguments, we construct an AF. Then, we use the grounded semantics of AFs for
indicating the most trusted arguments and for a reason of explaining why a score is assigned to
a topic and a review in our automated method.
4.1. Formal Modeling of Reviews
Let 𝑡 be a product (target) and let {r𝑖 (𝑡)} be a set of reviews of 𝑡 (alternatively, {r𝑡𝑖 }). Each review
r𝑡𝑖 consists of a numerical score 𝑠𝑐(r𝑡𝑖 ) (e.g., in 5-level Likert scale) and a textual description.
The description characterizes the product focusing to specific topics. E.g., in the case of a pair
of shoes, the topics can be ‘sole’, ‘upper’ or ‘comfort’. We represent the list of all topics relevant
to the product 𝑡 as 𝒯𝑡 , where 𝒯𝑡 = {𝜑1 , . . . , 𝜑𝑛 }.
Each review r𝑡𝑖 contains a finite set of topics 𝒯r𝑡𝑖 ⊆ 𝒯𝑡 . E.g., review ‘r𝑡1 : the color of the shoes
are not my favorite but I use it for a long time and they are still looking good’ contains two topics,
i.e., 𝒯r𝑡1 = {𝜑1 = color, 𝜑3 = quality}. The review score represents the actual reviewer’s
opinion on the product, while the text aims at motivating such judgment. An agreeing score of
two reviews containing the same topic about the same product indicates a support between
reviews while disagreeing score indicates a conflict.
Our goal is to identify the score of each topic of a product, based on the set of given reviews,
i.e., which score is proper for a topic in question. We address this by constructing an AF based
on a set of given reviews. Then, we use the grounded semantics of AFs to indicate a score to
a topic in question and explain why it is the case. In the end, we further update the scores of
reviews based on their topics. We also, prepare an explanation for the updated score of the
reviews by using the grounded semantics of AFs.
In review r𝑖𝑗 in Table 1, index 𝑖 indicates the product and 𝑗 indicates the reviewer. Reviews
can support one another if they have the same score and they have a common topic. If a set of
reviews has the same score and has a common topic, then it means that these reviews support
one another. Thus, we consider them as a single argument. In Table 1, topic ’𝜑 : quality’,
indicated by a topic detection, is a common topic between r21 and r22 , however, these reviews
do not have the same score. Reviewer r21 gave a score of 4 out of 5 to this product. The last
sentence in r21 presents the main reason why the reviewer gave a score of 4 out of 5 to this
product because she/he was satisfied with the quality of this product. However, the reviewer of
r22 is not as satisfied as the reviewer of r21 with the quality of this product. Thus, there is an
attack relation between reviews r21 and r22 , because 𝑠𝑐(r21 ) ̸= 𝑠𝑐(r22 ).
Reviews can be classified based on their topics. Assume that 𝜑 is a topic of a set of reviews
𝐸 = {r𝑡1 , . . . , r𝑡𝑗 }, if there is 𝐸 ′ ⊆ 𝐸, such that for any r𝑡𝑖 , r𝑡𝑗 ∈ 𝐸 ′ , it holds that 𝑠𝑐(r𝑡𝑖 ) =
𝑠𝑐(r𝑡𝑗 ), then we say that reviews in 𝐸 ′ support one another and we consider all reviews as a
single argument. This leads to the classification of 𝐸 based on the scores of reviews. Between
arguments with different scores, there is a symmetric attack relation. If there is no intersection
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Id Score Review Text
r11 ***** Comfortable
r12 * Waaaay too BIG
r21 **** Fit perfectly. I bought dark grey, and they didn’t fade
r22 *** They fit great. But they fade bad
Table 1
Example reviews. r11 and r12 are about the same product, and r21 and r22 are. The reviews, pairwise,
disagree on the scores given. The topics tackled, though, are slightly different.
between topics within r𝑡𝑖 and r𝑡𝑗 , then there is no relation between these two reviews.
4.2. Modeling Reviews with AFs
Let {r𝑡1 , . . . , r𝑡𝑛 } be a finite set of reviews on product 𝑡. Let 𝒯𝑡 = {𝜑𝑖 } be the set of topics
relevant to the product 𝑡. Each review r𝑡𝑖 consists of a numerical score 𝑠𝑐(r𝑡𝑖 ) (e.g., in 5-level
Likert scale) and a textual description. Let 𝒯𝑡,r𝑡𝑖 be the set of all topics presented in review
r𝑡𝑖 . Different topics have different importance in each review, to indicate this importance we
introduce a weight function in Definition 2 which shows the initial weight of topic 𝜑 in review
r𝑡𝑖 with score 𝑠𝑐(r𝑡𝑖 ).
Definition 2. Let r𝑡𝑖 be a review, let 𝜑 be a topic in r𝑡𝑖 , and let 𝑠𝑐(r𝑡𝑖 ) be a score of r𝑡𝑖 .
𝑤(𝑠𝑐(r𝑡𝑖 ), 𝜑, r𝑡𝑖 ) is called the initial weight of 𝜑 in review r𝑡𝑖 and score 𝑠𝑐(r𝑡𝑖 ), where 𝑤 is
a value in [0, ∞] such that 𝑤 is computed by aggregating one or multiple factors meeting the
following criteria:
1. at least one of such factors is the result of an abstraction function computed on the
review itself. Such abstraction functions should be computable over any review and allow
establishing a total order of reviews. Example of such abstraction functions include, for
instance, readability scores (e.g., Dale-Chall readability [19]) and complexity measures
(e.g., Kolmogorov complexity [20]);
2. optional factors can be computed as abstractions over the combination of the review r𝑡𝑖
and/or its topic 𝜑.
We aim to use a formalism of argumentation, i.e., abstract argumentation frameworks (AFs), to
assess the score of the topics within reviews of a product 𝑡. To this end, we construct an AF based
on a set of reviews. Our method associates each argument to the set of reviews with the same
score about a common topic. That is, we consider all reviews with the same score that presents
the same topic as a single argument. Formally, let [𝜑]𝑘 = {r𝑡𝑖 | r𝑡𝑖 contains topic 𝜑 and 𝑠𝑐(r𝑡𝑖 ) =
𝑘}, i.e., [𝜑]𝑖 collect all the reviews that contains topic 𝜑 and have score 𝑘. We consider [𝜑]𝑘
as a single argument, that contains all the reviews that have topic 𝜑 and score 𝑘. We are
interested in evaluating the weight of [𝜑]𝑘 as a single argument. To this end, for each 𝑘 with
𝑘 ∈ {1, 2, 3, 4, 5}, we sum up the initial weights of topic 𝜑 in review r𝑡𝑖 and score 𝑘. Note that
in Definition 3 if 𝜑 is not a topic of r𝑡𝑖 then 𝑤(𝑘, 𝜑, r𝑡𝑖 ) = 0.
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Definition 3. Let 𝜑 be a topic of a product 𝑡, let 𝑘 be a natural number between 1 and 5. The
weight of topic 𝜑 with respect to score 𝑘, alternatively, the weight of argument [𝜑]𝑘 is as follows:
𝑤([𝜑]𝑘 ) = Σ𝑛𝑖=1 𝑤(𝑘, 𝜑, r𝑡𝑖 )
where 𝑛 is the number of reviews about product 𝑡, and 𝑤(𝑘, 𝜑, r𝑡𝑖 ) is the initial weight 𝜑 in
review r𝑡𝑖 and score 𝑘 as introduced in Definition 2.
To construct an AF based on a set of reviews, we consider an attack relation from an argument
[𝜑]𝑖 to [𝜑]𝑗 iff 𝑤([𝜑]𝑖 ) > 𝑤([𝜑]𝑗 ).
Definition 4. Let 𝑡 be a product, let 𝒯𝑡 = {𝜑𝑖 } be a set of topics, and let 𝑖 be a natural number
between 1 and 5. For each 𝑖, with 𝑖 ∈ {1.2, 3, 4, 5}, and for each 𝜑 ∈ 𝒯𝑡 , we introduce an
argument 𝑎𝑖,𝜑 = [𝜑]𝑖 . Furthermore, 𝑤(𝑎𝑖,𝜑 ) is the weight of argument 𝑎𝑖,𝜑 , equal to 𝑤([𝜑]𝑖 ), as
introduced in Definition 3. An AF constructed based on topics is 𝐹 = (𝐴, 𝑅) where,
• 𝐴 = {𝑎𝑖,𝜑 }
• 𝑅 = {(𝑎𝑖,𝜑 , 𝑎𝑗,𝜑 ) | 𝑎𝑖,𝜑 , 𝑎𝑗,𝜑 ∈ 𝐴 and 𝑤(𝑎𝑖,𝜑 ) > 𝑤(𝑎𝑗,𝜑 )}.
An AF, constructed based on topics of a product, is a directed graph. Each node, indicated
by 𝑎𝑖,𝜑 contains all sets of reviews that contain topic 𝜑 with score 𝑖. The reason for collecting
all such reviews is that if two reviews contain the same topic 𝜑 and give the same score to the
product, then their content support one another. Thus, we accumulate them in a single node
and we consider them as one argument. After indicating the set of arguments from a given set
of reviews, we designate attack relations. If two arguments give different scores to product 𝑡, but
contain the same topic, it means that there may exist a conflict between these two arguments
with respect to the topic in question. We consider an attack relation between 𝑎𝑖,𝜑 and 𝑎𝑗,𝜑
when their weights are not the same. In order to indicate the direction of the attack relation
between two arguments we consider the weight of the topic with respect to the score, presented
in Definition 3. Note that in Definition 4 we only consider relations among arguments with the
same topics. Thus, for 𝜑, 𝜑′ ∈ 𝒯𝑡 , if 𝜑 ̸= 𝜑′ , then there is no relation between any arguments of
𝑎𝑖,𝜑 and 𝑎𝑗,𝜑′ , for 𝑖, 𝑗 ∈ {1, 2, 3, 4, 5}. That is, the associated graph to AF 𝐹 , constructed based
on the topics of a product, is a forest, presented formally in Lemma 1. Note that in graph theory
a graph is called connected if for every pair of vertices 𝑎 and 𝑏, there is a path between 𝑎 and 𝑏.
Furthermore, a connected component is a maximal connected subgraph of an undirected graph.
Definition 5. Let 𝑡 be a product, and let 𝒯𝑡 = {𝜑𝑖 } be a set of topics of 𝑡. Let 𝐹 = (𝐴, 𝑅) be
an AF constructed based on topics. Let 𝜑 ∈ 𝒯𝑡 , set 𝑎𝜑 = {𝑎𝑖,𝜑 } is called a component contains 𝜑
in 𝐹 . Furthermore, component 𝑎𝜑 is called connected component iff for every 𝑎𝑖,𝜑 , 𝑎𝑗,𝜑 ∈ 𝑎𝜑 it
holds that (𝑎𝑖,𝜑 , 𝑎𝑗,𝜑 ) ∈ 𝑅.
Lemma 1. Let 𝐹 be an AF, constructed based on topics of product 𝑡. If the reviews of the product
𝑡 contain at least two topics, then the graph associated with 𝐹 is disconnected. Furthermore, If
𝑚 is the number of topics presented in the reviews, i.e., |𝒯𝑡 | = 𝑚, then the associated graph of 𝐹
contains at least 𝑚 connected component.
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Proof. If the reviews contain more than one topic, for instance 𝜑 and 𝜑′ , then it is clear that
there is no relation between arguments containing 𝜑 and 𝜑′ . Thus, the associated graph is
disconnected. That is, there is no link between the arguments of components 𝑎𝜑 and 𝑎𝜑′ . Thus,
if we have at least two topics in the set of reviews, then the associated graph is disconnected.
We now show that the associated graph contains at least 𝑚 connected components if the set
of reviews contains 𝑚 number of different topics, by induction on 𝑚.
Base case: assume that 𝑚 = 1, that is all reviews contain the single topic 𝜑. If all reviews
give the same score to the product, then we only have one argument in the AF constructed
based on these reviews. Thus, we have exactly one component. Note that if we have different
arguments with the same weight, i.e., |𝑎𝜑 | > 1 and 𝑤(𝑎𝑖,𝜑 ) = 𝑤(𝑎𝑗,𝜑 ) for every 𝑎𝑖,𝜑 , 𝑎𝑗,𝜑 ∈ 𝑎𝜑 ,
then there are more than one connected component.
Inductive hypothesis: Assume that 𝑚 = 𝑗, then the associated graph contains at least 𝑗
connected components.
Inductive step: Assume that 𝑚 = 𝑗 + 1, then we have to show that the associated graph
contains at least 𝑗 + 1 components. Let 𝐾 be 𝑗 different topics of 𝑡, i.e., 𝐾 ⊆ 𝒯𝑡 and |𝐾| = 𝑗. By
the inductive hypothesis, the associated graph contains at least 𝑗 connected components. Let 𝜑
be a topic such that 𝜑 ̸∈ 𝐾, and let 𝜑′ ∈ 𝐾. Thus, there is no relation between arguments of 𝑎𝜑
and 𝑎𝜑′ . Thus, if 𝑚 = 𝑗 + 1 the associated graph has at least 𝑗 + 1 connected component.
An AF 𝐹 = (𝐴, 𝑅) is called acyclic (or well-founded) if there is no infinite sequence of
arguments 𝑎1 , . . . , 𝑎𝑖 , . . . such that (𝑎𝑖+1 , 𝑎𝑖 ) ∈ 𝑅. By Definition 4, in an AF 𝐹 = (𝐴, 𝑅),
it holds that (𝑎𝑖,𝜑 , 𝑎𝑗,𝜑 ) ∈ 𝑅 iff 𝑤(𝑎𝑖,𝜑 ) > 𝑤(𝑎𝑗,𝜑 ). Furthermore, because of the transitive
property of relation < in real numbers, any AF constructed based on a set of reviews is acyclic.
It is proven in [2] that in any acyclic AF all sets of semantics coincide. Thus, in the following of
this work, to assess the topics, presented in reviews, we focus on the grounded extension of the
constructed AF based on a given set of reviews.
Corollary 1. Let 𝐹 be an AF, constructed based on topics of the product 𝑡. Every connected
component in the associated graph of 𝐹 is acyclic.
Proof. This corollary is the direct result of the fact that 𝐹 is acyclic. Thus, any connected
component of 𝐹 is also acyclic.
Since, by Corollary 1 every connected component in 𝐹 is acyclic, every component has an
initial argument, i.e., an argument that does not have any parents. Proposition 1 is the direct
result of Definition 4.
Proposition 1. Let 𝐹 be an AF constructed based on a set of topics of the product 𝑡. Let 𝑎𝑖,𝜑 be an
initial argument of 𝐹 . It holds that 𝑤(𝑎𝑖,𝜑 ) is maximum among the weights of other arguments.
Lemma 2. Let 𝐹 = (𝐴, 𝑅) be an AF constructed based on a set of topics of the product 𝑡. Let 𝐼
be the set of initial arguments of 𝐹 , i.e., 𝐼 = {𝑏 | there is no 𝑎 ∈ 𝐴 such that (𝑎, 𝑏) ∈ 𝑅}. The
grounded extension of 𝐹 is none empty and it is equal with 𝐼.
Proof. Since every AF constructed based on topics is acyclic and since each acyclic AF has a
none empty grounded extension, 𝐹 has a none empty grounded extension. By the definition
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of grounded semantics, every initial argument is in the grounded extension, i.e., 𝐼 ⊆ grd(𝐹 ).
It remains to show that grd(𝐹 ) ⊆ 𝐼. Toward a contradiction, assume that grd(𝐹 ) ̸⊆ 𝐼. That
is, there exists an argument in grd(𝐹 ) which is not an initial argument. Assume that 𝑎𝑖,𝜑 is
an argument such that 𝑎𝑖,𝜑 ∈ grd(𝐹 ) but 𝑎𝑖,𝜑 ̸∈ 𝐼. Since grd(𝐹 ) ̸= ∅ and 𝐼 ⊆ grd(𝐹 ), there
exists 𝑎𝑗,𝜑 ∈ grd(𝐹 ) ∩ 𝐼. By Proposition 1, 𝑤(𝑎𝑗,𝜑 ) is the maximum among the weights of other
arguments, in specific, 𝑤(𝑎𝑗,𝜑 ) > 𝑤(𝑎𝑖,𝜑 ). Thus, by Definition 4, (𝑎𝑗,𝜑 , 𝑎𝑖,𝜑 ) ∈ 𝑅. That is, 𝑎𝑖,𝜑
is attacked by 𝑎𝑗,𝜑 in 𝐹 . This is a contradiction of the assumption that 𝑎𝑖,𝜑 ∈ grd(𝐹 ). Thus, the
assumption that there exists an argument in the grounded extension which is not an initial
argument is wrong. Hence, grd(𝐹 ) = 𝐼.
4.3. What is an AI system explanation of the score of a topic?
In this section, we explain how AFs as an AI system can be used to indicate the score of each
topic of the product 𝑡, based on the set of reviews.
Proposition 2. Let 𝐹 = (𝐴, 𝑅) be the constructed AF based on topics of product 𝑡. Let 𝜑 be a
topic of product 𝑡. There exists 𝑖 ∈ {1, 2, 3, 4, 5} such that 𝑎𝑖,𝜑 is in the grounded extension of 𝐹 .
Proof. Let 𝐹 be an AF, constructed based on topics of the product 𝑡. Let 𝜑 be a topic and let
𝑎𝜑 be the connected component of 𝜑, as introduced in Definition 5. By Corollary 1, every
connected component in the associated graph of 𝐹 is acyclic. Thus, for each 𝜑, 𝑎𝜑 contains an
initial argument. By Lemma 2, the grounded extension of 𝐹 and the set of initial arguments of
𝐹 coincide. Thus, for each 𝜑 an argument of 𝑎𝜑 is in the grounded extension. Hence, for any 𝜑,
there exists 𝑖 such that 𝑎𝑖,𝜑 is in the grounded extension of 𝐹 .
We now define basic explanation in terms of functions. The function 𝑠𝑐𝐴𝐼 (−) is a unary func-
tion that takes a topic as an input and returns an appropriate score to that topic by considering
all the reviews containing that topic, presented in Definition 6.
Definition 6. (Score of a topic) Let 𝐹 = (𝐴, 𝑅) be an AF constructed based on topics of product
𝑡. Let 𝜑 be a topic of product 𝑡. The score 𝜑 based on an AI system is denoted by 𝑠𝑐𝐴𝐼 (𝜑),
defined as follows:
Σ𝑎𝑖,𝜑 ∈grd(𝐹 ) 𝑖
𝑠𝑐𝐴𝐼 (𝜑) = round( )
|{𝑖 | 𝑎𝑖,𝜑 ∈ grd(𝐹 )}|
Σ𝑎 ∈grd(𝐹 ) 𝑖
In 𝑠𝑐𝐴𝐼 (𝜑) the output of the function round is the nearest integer to |{𝑖 | 𝑎𝑖,𝜑
𝑖,𝜑 ∈grd(𝐹 )}|
.
Note that by Proposition 2 for each topic 𝜑 there exists at least an 𝑖 such that 𝑎𝑖,𝜑 ∈ grd(𝐹 ).
Hence, Definition 6 is well-defined. Note that for each 𝜑, if component 𝑎𝜑 is connected, then
there exists exactly one 𝑖 such that 𝑎𝑖,𝜑 ∈ grd(𝐹 ). Intuitively, for a 𝜑, if component 𝑎𝜑 is
connected and 𝑎𝑗,𝜑 is an initial argument, then it holds that 𝑠𝑐𝐴𝐼 (𝜑) = 𝑗. In this case, the choice
of machine, i.e., 𝑠𝑐𝐴𝐼 (𝜑) = 𝑗 can be explained that the score of topic 𝜑 is 𝑗 because argument
𝑎𝑗,𝜑 is an initial argument, i.e., 𝑤(𝑎𝑗,𝜑 ) is maximum among all other arguments in component
𝑎𝜑 . The highest weight of 𝑎𝑗,𝜑 among the arguments of 𝑎𝜑 means that sum of the weights of
reviews containing 𝜑 with score 𝑗 is the highest weight.
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Furthermore, in the following, we try to explain to a user why from a machine point of
view topic 𝜑 has the score sc𝐴𝐼 (𝜑). To this end, we define an explanation function, denoted
by Exp(𝜑, sc𝐴𝐼 (𝜑)) in Definition 7. Function 𝐸𝑥𝑝(𝜑, sc𝐴𝐼 (𝜑)) is a binary function that takes
a topic 𝜑 and its machine score sc𝐴𝐼 (𝜑) as inputs and returns the set of arguments that their
scores have a role in the machine decision in Definition 6.
Definition 7. (Explanation of a score of a topic) Let 𝐹 be an AF, constructed based on topics
{𝜑𝑖 } of product 𝑡. Let 𝜑 be a topic and let sc𝐴𝐼 (𝜑) be the score of 𝜑 from a machine point of
view, as introduced in Definition 6. An explanation of why the score of topic 𝜑 is sc𝐴𝐼 (𝜑) is as
follows:
Exp(𝜑, sc𝐴𝐼 (𝜑)) = {𝑎𝑖,𝜑 | 𝑎𝑖,𝜑 ∈ grd(𝐹 )}
Let 𝜑 be a topic, Exp(𝜑, sc𝐴𝐼 (𝜑)) collects all 𝑎𝑖,𝜑 that is in the grounded extension of 𝐹 , i.e.,
the set of arguments, with respect to topic 𝜑, that the acceptance of them are beyond of any
doubts. Assume that sc𝐴𝐼 (𝜑) = 𝑖, the notation ¬sc𝐴𝐼 (𝜑) is a number 𝑗 such that 𝑗 ̸= 𝑖.
Furthermore, the function NotDef(𝜑) collects all the arguments that contain topic 𝜑 but do
not have any role in the computation of the score of topic 𝜑, from a machine point of view. In
other words, NotDef(𝜑) contains all arguments which are attacked by Exp(𝜑, sc𝐴𝐼 (𝜑)).
Definition 8. Let 𝐹 be an AF, constructed based on topics {𝜑𝑖 } of product 𝑡. Let 𝜑 be a topic
and let sc𝐴𝐼 (𝜑) be the score of 𝜑 from a machine point of view, as introduced in Definition 6.
Function NotDef(𝜑) is a unary function that takes a topic as an input and returns the set of
arguments that do not have any role in the evaluation of sc𝐴𝐼 (𝜑).
NotDef(𝜑) = {𝑎𝑖,𝜑 | 𝑎𝑖,𝜑 ̸∈ grd(𝐹 )}
For each topic 𝜑, Exp(𝜑, sc𝐴𝐼 (𝜑)) and NotDef(𝜑) are disjoint functions, i.e., Exp(𝜑, sc𝐴𝐼 (𝜑))∪
NotDef(𝜑) = 𝑎𝜑 . For each 𝜑, if 𝑎𝑖,𝜑 ̸∈ Exp(𝜑, sc𝐴𝐼 (𝜑)), then 𝑎𝑗,𝜑 ̸∈ grd(𝐹 ), that is, there exists
𝑎𝑖,𝜑 ∈ grd(𝐹 ) such that 𝑎𝑖,𝜑 attack 𝑎𝑗,𝜑 . That is, 𝑤(𝑎𝑖,𝜑 ) > 𝑤(𝑎𝑗,𝜑 ), thus, it is reasonable that
the machine neither consider the score of 𝑎𝑗,𝜑 in the evaluation of sc𝐴𝐼 (𝜑) nor argument 𝑎𝑗,𝜑 in
Exp(𝜑, sc𝐴𝐼 (𝜑)). Furthermore, the function SC𝐴𝐼 (−) gives a score to a review r𝑡𝑖 based on the
score of each topic within r𝑡𝑖 . That is, SC𝐴𝐼 revise the score of each review given by a reviewer.
Definition 9. (Score of a review) Let r𝑡𝑖 be a review of product 𝑡. Let 𝒯𝑡,r𝑡𝑖 be a set of topics
presented in review r𝑡𝑖 . The score of the review r𝑡𝑖 based on a machine assessment is the output
of function SC𝐴𝐼 (r𝑡𝑖 ), evaluated as follows:
Σ𝜑∈𝒯𝑡,r𝑡𝑖 sc𝐴𝐼 (𝜑)
SC𝐴𝐼 (r𝑡𝑖 ) = round( )
|𝒯𝑡,r𝑡𝑖 |
The score of review r𝑡𝑖 , from a machine point of view, is the round of the average of scores
of the topics presented in r𝑡𝑖 , where the score of each topic from a machine point of view is
presented in Definition 6.
In Definition 10 grounded semantics of AFs are implicitly used to explain the reasons for the
score given to a review from a machine’s point of view.
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Definition 10. (Explanation of a score of a review) Let r𝑡𝑖 be a review of product 𝑡. An
explanation of why the score SC(r𝑡𝑖 ) is given to a review r𝑡𝑖 is as follows:
⋃︁
Exp(r𝑡𝑖 , SC(r𝑡𝑖 )) = Exp(𝜑, sc𝐴𝐼 (𝜑))
𝜑∈𝒯𝑡,r𝑡𝑖
In Definition 10, function Exp(r𝑡𝑖 , SC(r𝑡𝑖 )) collects all the explanations for all the topics
within r𝑡𝑖 . In other words, this function collects all the initial arguments of components 𝑎𝜑 ,
where 𝜑 ∈ 𝒯𝑡,r𝑡𝑖 . That is, Exp(r𝑡𝑖 , SC(r𝑡𝑖 )) ⊆ grd(𝐹 ), thus, there is no doubt on the acceptance
of these arguments.
5. Conclusion and Future Work
We present a method to consider reviews containing a comment topic with the same score as a
single argument. We aggregate the initial weights of the reviews in an argument to indicate
the main weight of the arguments. We introduce an attack relation between arguments by
considering the weight of arguments. Then, we use the notion of grounded semantics of AFs
to evaluate the most trusted arguments. Since each argument 𝑎𝑖,𝜑 in the constructed AF is
attached by 𝑎𝑗,𝜑 if 𝑗 ̸= 𝑖 and 𝑤(𝑎𝑗,𝜑 ) > 𝑤(𝑎𝑖,𝜑 ), we evaluate the score of topics in the grounded
extension. Next, we introduce a function to explain the reason for choosing the associated score
of a topic by a system. Then, we present a function to accumulate the scores of topics within
a review to assign a score to a review from a machine point of view. In the next step, as an
explanation method, we also introduce a function to give a review and its score from a system
point of view as inputs and returns all the arguments that have an effect on the assessment of a
review in question from a system point of view.
In our approach, we identify an attack relation between arguments if they are about the same
topic but their weights are different. As future work, we are eager to present relations among
arguments that do not have a common topic (we are eager to consider some other features of
arguments for presenting relations among them). Furthermore, we are interested in using the
non-monotonic nature of argumentation theory for working on a temporal way of reasoning
instead of considering a fixed set of reviews. That is, we aim to show how we can evaluate the
quality of reviews if we consider the order of time of presenting of reviews. To have further
human-machine interaction we aim to consider user preferences over the topics of a product to
evaluate the score of a review. It is a possible topic for future work to use the generalizations of
AFs, namely, valued-based AFs [14, 15] or ADFs [21], for modeling and assessing the quality of
the set of the reviews.
Note that the tasks of argument mining from a given KR and automatically constructing of
the associated AF are not within the scope of this work because we focus on studying the use
of the grounded semantics of AFs as a means to assess product reviews. Given that this shows
to be a promising direction, future work will focus on optimizing the task of AF construction
by combining human and automated computation.
Acknowledgments This research has been supported by the Centrum Wiskunde & Informat-
ica (CWI) and Supported by the Netherlands eScience Center project “The Eye of the Beholder”
(project nr. 027.020.𝐺15).
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