=Paper=
{{Paper
|id=Vol-3768/paper5
|storemode=property
|title=Applying Attribution Explanations in Truth-Discovery Quantitative Bipolar Argumentation Frameworks
|pdfUrl=https://ceur-ws.org/Vol-3768/paper5.pdf
|volume=Vol-3768
|authors=Xiang Yin,Nico Potyka,Francesca Toni
|dblpUrl=https://dblp.org/rec/conf/comma/0007PT24
}}
==Applying Attribution Explanations in Truth-Discovery Quantitative Bipolar Argumentation Frameworks==
https://ceur-ws.org/Vol-3768/paper5.pdf
Applying Attribution Explanations in Truth-Discovery
Quantitative Bipolar Argumentation Frameworks
Xiang Yin1 , Nico Potyka2 and Francesca Toni1
1
Imperial College London, UK
2
Cardiff University, UK
Abstract
Explaining the strength of arguments under gradual semantics is receiving increasing attention. For
example, various studies in the literature offer explanations by computing the attribution scores of
arguments or edges in Quantitative Bipolar Argumentation Frameworks (QBAFs). These explanations,
known as Argument Attribution Explanations (AAEs) and Relation Attribution Explanations (RAEs), com-
monly employ removal-based and Shapley-based techniques for computing the attribution scores. While
AAEs and RAEs have proven useful in several applications with acyclic QBAFs, they remain largely
unexplored for cyclic QBAFs. Furthermore, existing applications tend to focus solely on either AAEs
or RAEs, but do not compare them directly. In this paper, we apply both AAEs and RAEs, to Truth
Discovery QBAFs (TD-QBAFs), which assess the trustworthiness of sources (e.g., websites) and their
claims (e.g., the severity of a virus), and feature complex cycles. We find that both AAEs and RAEs can
provide interesting explanations and can give non-trivial and surprising insights.
Keywords
Explainable AI, Quantitative Argumentation, Truth Discovery Application
1. Introduction
Abstract argumentation Frameworks (AFs) [1] are promising tools in the Explainable AI (XAI)
field [2] due to their transparency and interpretability, as well as their ability to support
reasoning about conflicting information [3, 4, 5]. Quantitative Bipolar AFs (QBAFs) [6] are
an extension of traditional AFs, which consider the (dialectical) strength of arguments and
the support relation between arguments. In QBAFs, each argument has a base score, and its
dialectical strength is computed by gradual semantics based on its base score and the strength
of its attackers and supporters [7]. QBAFs can be deployed to support several applications like
product recommendation [8], review aggregation [9] or stance aggregation [10].
Another interesting application that has been considered recently are truth discovery net-
works [11, 12, 13]. Figure 1 shows an example of a Truth-Discovery QBAFs (TD-QBAF) to evaluate
the trustworthiness of sources and the reliability of claims made about an exhibition. We have
11 sources and 6 claims, each represented as an abstract argument. The nodes on the left
represent the 11 source arguments (๐ 0 to ๐ 10), while the ones on the right represents the 6
claim arguments. The claim arguments are categorized into three types โ year, place, and theme
ArgXAI-24: 2nd International Workshop on Argumentation for eXplainable AI
$ x.yin20@imperial.ac.uk (X. Yin); potykan@cardiff.ac.uk (N. Potyka); ft@imperial.ac.uk (F. Toni)
000-0002-6096-9943 (X. Yin); 0000-0003-1749-5233 (N. Potyka); 0000-0001-8194-1459 (F. Toni)
ยฉ 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Xiang Yin et al. CEUR Workshop Proceedings 56โ66
Figure 1: Example of a TD-QBAF. (Nodes are arguments, where the ๐ ๐ and ๐๐ are identifiers for the
source and claim arguments, respectively (for ease of reference). Solid and dashed edges indicate attack
and support, respectively.)
of the exhibition โ each distinguished by different colors. For pairs of contradictory claims,
where different values are asserted for the same object, a bi-directional attack relationship
is introduced between the claims. For each report (one for each pair of source and claim), a
bi-directional support relationship is established between the source and the claim. Following
[13], we use a base score of 0.5 for source argument (we are initially indifferent about the
trustworthiness of a source), and a base score of 0 for claims (we do not believe claims without
evidence). We compute the dialectical strength of arguments using the Quadratic Energy (QE)
gradual semantics [14], and the final strengths of arguments are displayed on their side in Figure
1. While the strength values seem plausible, it can be challenging to understand why certain
claims and sources receive higher or lower trust scores.
To address this problem, attribution explanations (AEs) have been proposed. Specifically, given
an argument of interest (topic argument) in a QBAF, AEs can explain the impact of arguments
on the topic argument. AEs can be broadly categorized into Argument Attribution Explanations
(AAEs) (e.g., [15, 16, 17]) and Relation Attribution Explanations (RAEs) (e.g., [18, 19]). AAEs
explain the strength of the topic argument by assigning attribution scores to arguments: the
greater the attribution score, the greater the argumentโs contribution to the topic argument.
Similarly, RAEs assign the attribution scores to edges to measure their contribution. Removal-
based and Shapley-based techniques are commonly used for computing the attribution scores.
However, most existing studies focus on explaining acyclic QBAFs rather than cyclic ones,
leaving a gap in understanding the complexities of the latter. In addition, current research
typically examines only one type of attribution โ either AAEs or RAEs โ without providing a
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comprehensive comparison of both methods. In this paper, we aim to address these gaps by
investigating the applicability of removal and Shapley-based AAEs and RAEs in the context of
cyclic TD-QBAFs. Furthermore, we offer a comprehensive comparison between them to better
understand the applicability of these AEs.
2. Preliminaries
2.1. QBAFs and the QE Gradual Semantics
We briefly recall the definition of QBAFs and the QE gradual semantics [14].
Definition 1 (QBAF). A Quantitative Bipolar Argumentation Framework (QBAF) is a quadru-
ple ๐ฌ = โจ๐, โโ , โ+ , ๐ โฉ consisting of a finite set of arguments ๐, binary relations of attack
โโ โ ๐ร๐ and support โ+ โ ๐ร๐ (โโ โฉโ+ = โ
) and a base score function ๐ : ๐ โ [0, 1].
The base score function in QBAFs assigns an apriori belief to arguments. QBAFs can be
represented graphically (as in Figure 1) using nodes to represent arguments and edges to show
the relations between them. Then QBAFs are said to be (a)cyclic if the graphs representing them
are (a)cyclic.
In this paper, we use the QE gradual semantics [14] to evaluate the strength of arguments in
QBAFs. Like most QBAF semantics, it computes strength values iteratively by initializing the
strength value of each argument with its base score and repeatedly applying an update function.
Let us represent the strength of arguments in the ๐-th iteration by a function
๐ ๐ : ๐ โ [0, 1],
where ๐ 0 (๐ผ) = ๐ (๐ผ) for all ๐ผ โ ๐. In order to compute ๐ ๐+1 from ๐ ๐ , the update function first
computes the energy ๐ธ๐ผ๐ of attackers and supporters of each argument ๐ผ defined by
โ๏ธ โ๏ธ
๐ธ๐ผ๐ = ๐ ๐ (๐ฝ) โ ๐ ๐ (๐ฝ).
{๐ฝโ๐|(๐ฝ,๐ผ)โโ+ } {๐ฝโ๐|(๐ฝ,๐ผ)โโโ }
It then computes the strength in the next iteration via
โง
โจ๐ (๐ผ) โ ๐ (๐ผ) ยท (๐ธ๐ผ๐ )2 ๐๐ ๐ธ๐ผ๐ โค 0;
1+(๐ธ๐ผ๐ )2
๐ ๐+1 (๐ผ) = ๐ 2
โฉ๐ (๐ผ) + (1 โ ๐ (๐ผ)) ยท (๐ธ๐ผ )๐ 2 ๐๐ ๐ธ๐ผ๐ > 0.
1+(๐ธ๐ผ )
The final dialectical strength of each argument ๐ผ is then defined as the limit lim๐กโโ ๐ ๐ก (๐ผ). In
cyclic graphs, the strength values may start oscillating and the limit may not exist [20]. In all
known cases, the problem can be solved by continuizing the semantics [14, 13]. However, we
do not have space to discuss these issues in more detail here and will just restrict to examples
where the strength values converge.
To better understand the QE gradual semantics, let us look at an example.
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Figure 2: Example of a QBAF structure for computing the QE gradual semantics.
Example 1. Consider the QBAF in Figure 2, where the base scores are given as ๐ (๐ผ) = 0.8, ๐ (๐ฝ) =
0.6, ๐ (๐พ) = 0.9, and ๐ (๐ฟ) = 0.7. Since ๐ฝ and ๐พ have no parents, we have ๐ธ๐ฝ๐ = ๐ธ๐พ๐ = 0 for all ๐
and thus ๐(๐ฝ) = ๐ (๐ฝ) = 0.6 and ๐(๐พ) = ๐ (๐พ) = 0.9. For ๐ฟ, we have ๐ธ๐ฟ๐ = ๐ ๐ (๐พ) โ ๐ ๐ (๐ฝ) = 0.3
for all ๐, hence ๐(๐ฟ) = ๐ (๐ฟ) + (1 โ ๐ (๐ฟ)) ยท 0.32 /(1 + 0.32 ) = 0.72. For ๐ผ, we have ๐ธ๐ผ๐ = ๐ ๐ (๐พ) +
๐ ๐ (๐ฟ) โ ๐ ๐ (๐ฝ) = 1.02 for all ๐ โฅ 1. Hence, ๐(๐ผ) = ๐ (๐ผ) + (1 โ ๐ (๐ผ)) ยท 1.022 /(1 + 1.022 ) = 0.90.
In the remainder, unless specified otherwise, we assume as given a generic QBAF ๐ฌ =
โจ๐, โโ , โ+ , ๐ โฉ and we let โ = โโ โช โ+ We will often need to restrict QBAFs to a subset of
the arguments or edges, or change the base score function, as follows.
Notation 1. For ๐ฐ โ ๐, let ๐ฌ|๐ฐ = โจ๐ โฉ ๐ฐ, โโ , โ+ , ๐ โฉ. Then, for any ๐ผ โ ๐, we let ๐๐ฐ (๐ผ)
denote the strength of ๐ผ in ๐ฌ|๐ฐ .
Notation 2. For ๐ฎ โ โ, let ๐ฌ|๐ฎ = โจ๐, โโ โฉ ๐ฎ, โ+ โฉ ๐ฎ, ๐ โฉ. Then, for any ๐ผ โ ๐, we let ๐๐ฎ (๐ผ)
denote the strength of ๐ผ in ๐ฌ|๐ฎ .
Notation 3. For ๐ โฒ : ๐ โ [0, 1] a base score function, let ๐ฌ|๐ โฒ = โจ๐, โโ , โ+ , ๐ โฒ โฉ. Then, for
any ๐ผ โ ๐, we let ๐๐ โฒ (๐ผ) denote the strength of ๐ผ in ๐ฌ|๐ โฒ .
2.2. Truth Discovery QBAFs (TD-QBAFs)
TD-QBAFs allow reasoning about truth discovery problems using quantitative argumentation.
Truth discovery problems can be described concisely as truth discovery networks (TDNs) [11].
Formally, a TDN is a tuple N = (๐ฎ, ๐ช, ๐, ๐ซ) consisting of a finite set of sources ๐ฎ, a finite set
of objects ๐ช,โ๏ธa set ๐ = {๐ท๐ }๐โ๐ of domains of the objects, and a set of reports ๐ซ โ ๐ฎ ร ๐ช ร ๐ ,
where ๐ = ๐โ๐ ๐ท๐ , and for all (๐ , ๐, ๐ฃ) โ ๐ซ, we have ๐ฃ โ ๐ท๐ , and there is no (๐ , ๐, ๐ฃ โฒ ) โ ๐ซ
with ๐ฃ ฬธ= ๐ฃ โฒ . Given a TDN N , we are interested in a truth discovery operator that assigns a
trust score to each source and each claim [11].
Singleton suggested to reason about TDNs using bipolar argumentation frameworks, where
we have bi-directional support edges between sources and their claims (trustworthy sources
make claims more believable, and, conversely, believable claims make sources more trustworthy)
and contradictory claims attack each other [12]. TD-QBAFs implement this idea with QBAFs,
where sources have a base score of 0.5 (we are initially indifferent about the trustworthiness of
sources) and claims have a base score of 0 (we do not believe anything without evidence).
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Definition 2 (TD-QBAF induced from a TDN). The TD-QBAF induced from the TDN N =
(๐ฎ, ๐ช, ๐, ๐ซ) is defined as ๐ = (๐, โโ , โ+ , ๐ ), where ๐ = ๐ฎ โช{(๐, ๐ฃ) | โ๐ โ ๐ฎ : (๐ , ๐, ๐ฃ) โ ๐ซ},
โโ = {(๐, ๐โฒ ) โ ๐2 โฉ ๐ถ 2 | obj(๐) = obj(๐โฒ ), val(๐) ฬธ= val(๐โฒ )}, โ+ = {(๐ , (๐, ๐ฃ)), ((๐, ๐ฃ), ๐ ) |
(๐ , ๐, ๐ฃ) โ ๐ซ}. ๐ (๐ ) = 0.5 for all ๐ โ ๐ฎ and ๐ (๐) = 0 for all ๐ โ ๐ถ.
Every QBAF semantics gives rise to a truth discovery operator that is defined by associating
each source and claim with its final strength under the semantics. The semantical properties of
QBAF semantics like balance and monotonicity directly translate to meaningful guarantees for
the derived trust scores.
2.3. Argument Attribution Explanations
In order to explain trust scores in TD-QBAFs, we recall the removal-based and Shapley-based
AAEs. AAEs aim at evaluating the impact of an argument on a given topic argument. The
removal-based AAEs proposed by [15] measure how the strength of the topic argument changes
if an argument is removed.
Definition 3 (Removal-based AAEs). Let ๐ผ, ๐ฝ โ ๐. The removal-based AAE from ๐ฝ to ๐ผ
under ๐ is:
๐๐ผ๐ (๐ฝ) = ๐(๐ผ) โ ๐๐โ{๐ฝ} (๐ผ).
The Shapley-based AAEs [16, 21] use the Shapley value from coalitional game theory [22]
to assign attributions. Each argument in a QBAF is seen as a player that can contribute to the
strength of the topic argument. Intuitively, Shapley-based AAEs look at all possible ways how
the argument could be added to the QBAF and average its impact on the topic argument.
Definition 4 (Shapley-based AAEs). Let ๐ผ, ๐ฝ โ ๐. The Shapley-based AAE from ๐ฝ to ๐ผ
under ๐ is:
โ๏ธ (|๐ โ {๐ผ}| โ |๐ฐ | โ 1)! |๐ฐ|! [๏ธ
๐๐๐ผ (๐ฝ) =
]๏ธ
๐๐ฐ โช{๐ฝ} (๐ผ) โ ๐๐ฐ (๐ผ) .
|๐ โ {๐ผ}|!
๐ฐ โ๐โ{๐ผ,๐ฝ}
2.4. Relation Attribution Explanations
RAEs are similar to AAEs, but measure the impact of edges rather than the impact of arguments.
Analogous to the idea of removal-based AAEs [15], we consider the removal-based RAEs.
Definition 5 (Removal-based RAEs). Let ๐ผ โ ๐ and ๐ โ โ. The removal-based RAE from
๐ to ๐ผ under ๐ is:
๐๐ผ๐ (๐) = ๐(๐ผ) โ ๐โโ{๐} (๐ผ).
Shapley-based RAEs [18, 19] share the same idea with Shapley-based AAEs, but the attribution
objects are changed from arguments to edges.
Definition 6 (Shapley-based RAEs). Let ๐ผ โ ๐ and ๐ โ โ. The Shapley-based RAE from ๐
to ๐ผ under ๐ is:
โ๏ธ (|โ| โ |๐ฎ| โ 1)! |๐ฎ|! [๏ธ
๐๐ผ๐ (๐) =
]๏ธ
๐๐ฎโช{๐} (๐ผ) โ ๐๐ฎ (๐ผ) .
|โ|!
๐ฎโโโ{๐}
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3. Explaining TD-QBAFs with AAEs and RAEs
3.1. Settings
To compare the different AEs, we explain the strength of argument ๐5 in Figure 1. Since there
are 17 arguments and 32 edges in Figure 1, computing Shapley-based AAEs and RAEs exactly
is prohibitively expensive. We therefore apply the approximation algorithm from [19] that
approximates the Shapley values using sampling (we set the sample size to 1000).
We report the removal and Shapley-based AAEs and RAEs in Figure 3 and 4 1 . In addition,
to provide intuitive explanations for argument ๐5, we visualize the removal and Shapley-
based AAEs and RAEs as shown in Figure 3 and 4, where blue/red arguments or edges denote
positive/negative AAEs or RAEs. The darkness of the color of arguments and the thickness of
the edges denote the magnitude of the their AAEs and RAEs, respectively2 .
3.2. Results and Analysis for AAEs
Figure 3 shows the results of removal and Shapley-based AAEs.
For the removal-based AAEs, we observe that ๐ 7, ๐ 8, ๐ 9, and ๐ 10 have noticeably positive
influences on ๐5, followed by minor positive influences from ๐ 3, ๐1, and ๐2. This is because ๐ 7
to ๐ 10 are direct supporters for ๐5, whereas ๐ 3, ๐1, and ๐2 indirectly support ๐5. Specifically, ๐2
supports ๐ 3, ๐ 3 supports ๐1, ๐1 supports ๐ 7, and then ๐ 7 supports ๐5, meaning ๐ 3, ๐1, and ๐2 all
indirectly support ๐5. These indirect influences also explain why the AAEs of ๐ 3, ๐1, and ๐2 are
much smaller than those of ๐ 7 to ๐ 10. Besides, since ๐ 7 is supported by ๐1, its AAE is slightly
larger than those of ๐ 8 to ๐ 10, which have consistent AAEs due to their symmetrical structure
to ๐5. In contrast, ๐ 0, ๐ 1, ๐ 2, and ๐0 have minor negative influences on ๐5 because ๐0 attacks
๐1, an indirect supporter for ๐5. Furthermore, ๐ 0 to ๐ 2 support ๐0, and thus they have negative
influences on ๐5 as well. However, their negative influences are not obvious due to the indirect
influences. Finally, the remaining arguments have AAEs close to 0, indicating their negligible
influences on ๐5.
When considering the Shapley-based AAEs, the results are similar to those of removal-based
AAEs, where ๐ 7 to ๐ 10 still have significant influences on ๐5. Unlike removal-based AAEs,
however, we notice that both ๐4 and ๐ 6 have minor negative influences on ๐5. This is because
๐4 directly attacks ๐5, while ๐ 6 indirectly attacks ๐5 by supporting ๐4, although the QE strength
of ๐4 is very small (close to 0). Also, the negative influences of ๐ 0 to ๐ 2 and ๐0 and positive
influence of ๐2 are relatively negligible compared with those of in removal-based AAEs due to
their indirect connection to ๐5.
In this case study, both removal and Shapley-based AAEs can effectively capture the main
influential arguments despite having some tiny differences in those low contributing arguments.
This is mainly because of their different mechanisms of computing the AAEs. Another important
reason is probably due to the approximation algorithm used for Shapley-based AAEs, leading
to different AAEs even with the same sample size for the coalitions. We also noticed that
the qualitative influence (the sign) of those Shapley-based AAEs close to 0 is sensitive when
1
The numerical AAEs and RAEs can be found in the Appendix
2
The code of all experiments is available at https://github.com/XiangYin2021/TD-QBAF-AAE-RAE.
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Removal-based AAEs Shapley-based AAEs
(Strengths) Sources Claims Sources Claims (Strengths)
0.66 s0 c0: Year = 1958 s0 c0: Year = 1958 0.70
0.66 s1 s1
0.66 s2 c1: Year = 1962 s2 c1: Year = 1962 0.47
0.81 s3 s3
0.70 s4 c2: Place = Bath s4 c2: Place = Bath 0.83
0.70 s5 s5
0.50 s6 c3: Place = London s6 c3: Place = London ~0
0.83 s7 s7
0.72 s8 c4: Theme = History s8 c4: Theme = History ~0
0.72 s9 s9
0.72 s10 c5: Theme = Art s10 c5: Theme = Art 0.90
Figure 3: Removal and Shapley-based AAEs for the topic argument ๐5 of TD-QBAF in Figure 1.
(Blue/red/grey nodes denote positive/negative/negligible AAEs, respectively. The darkness of nodes
represents the magnitude of their AAE values.)
applying the approximation algorithm, thus we do not visualize those close to 0. However, this
should not be a concern since their influence is negligible.
3.3. Results and Analysis for RAEs
Figure 4 shows the results of removal and Shapley-based RAEs.
Let us first discuss the removal-based RAEs. We see that (๐ 7, ๐5) has the largest positive
impact on ๐5. Following closely are (๐ 8, ๐5), (๐ 9, ๐5), and (๐ 10, ๐5), which also have notably
positive influences on ๐5 because they are direct incoming supports to ๐5. There are also
four outgoing supports from ๐5, namely (๐5, ๐ 7), (๐5, ๐ 8), (๐5, ๐ 9), and (๐5, ๐ 10), with positive
influences but their RAEs are greatly smaller than that of the previous four as they are indirect
supports. For instance, ๐5 first supports ๐ 7, and then ๐ 7 supports ๐5, indicating the indirect
positive influence of (๐5, ๐ 7). Additionally, (๐5, ๐4) also contributes positively to ๐5 because
๐5 attacks its attacker ๐4, thus the attack from ๐4 to ๐5 is weakened. We can also observe
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Removal-based RAEs Shapley-based RAEs
(Strengths) Sources Claims Sources Claims (Strengths)
0.66 s0 c0: Year = 1958 s0 c0: Year = 1958 0.70
0.66 s1 s1
0.66 s2 c1: Year = 1962 s2 c1: Year = 1962 0.47
0.81 s3 s3
0.70 s4 c2: Place = Bath s4 c2: Place = Bath 0.83
0.70 s5 s5
0.50 s6 c3: Place = London s6 c3: Place = London ~0
0.83 s7 s7
0.72 s8 c4: Theme = History s8 c4: Theme = History ~0
0.72 s9 s9
0.72 s10 c5: Theme = Art s10 c5: Theme = Art 0.90
Figure 4: Removal and Shapley-based RAEs for the topic argument ๐5 of TD-QBAF in Figure 1.
(Blue/red/grey edges denote positive/negative/negligible RAEs, respectively. The darkness of edges
represents the magnitude of their RAE values.)
some marginal influences, such as the positive influences provided by (๐1, ๐ 7), (๐ 3, ๐1), and
(๐2, ๐ 3) on ๐5, while the negative influences from (๐0, ๐1), (๐ 0, ๐0), (๐ 1, ๐0), and (๐ 2, ๐0). The
remaining edges have RAEs close to 0, showing their negligible influence on ๐5.
When it comes to the Shapley-based RAEs, which have similar effects to removal-based
RAEs, the four incoming supports to ๐5 are still the major contributors, and the four outgo-
ing supports from ๐5 have minor RAEs. Different from removal-based RAEs, Shapley-based
RAEs capture some different negligible influences, such as the negative influence by (๐4, ๐5)
and (๐ 6, ๐4). However, Shapley-based RAEs also disregard some tiny influences, like (๐ 0, ๐0),
(๐ 1, ๐0), and (๐ 2, ๐0), which are shown by removal-based RAEs.
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In this case study, both removal and Shapley-based RAEs have a consistent ranking for the
main influential edges despite having some tiny differences in those low contributing edges.
The reasons are the same as we discussed above.
Let us further compare the results of AAEs and RAEs. In this case study, we observe some
connections between AAEs and RAEs. For example, in both AAEs, the top-4 influential argu-
ments are ๐ 7 to ๐ 10, while in both RAEs, the outgoing edges from these arguments ((๐ 7, ๐5),
(๐ 8, ๐5), (๐ 9, ๐5), and (๐ 10, ๐5)) also rank in the top-4. In addition, ๐ 0 to ๐ 4 and ๐0 to ๐2 have
minor influences in the removal-based AAEs, while their incoming or outgoing edges also
have minor influences in the removal-based RAEs. A similar phenomenon can be found in
the Shapley-based AAEs and RAEs. While it is expected that the RAEs for outgoing edges
of important arguments are relatively high, the consistency observed across different sets of
arguments and edges is noteworthy. Besides, we found that removal or Shapley-based AAE of
an argument does not necessarily equate to the sum of RAEs of all its incoming and outgoing
edges, which goes against a reasonable expectation. We will leave the investigation of their
formal relationships for future work.
4. Conclusion
Since most existing applications of AAEs and RAEs focus on acyclic QBAFs, this paper inves-
tigated their applicability in cyclic QBAFs. First, we found that AAEs and RAEs can provide
intuitive explanations. By displaying the ranking of arguments or edges, it is easy to identify
the most influential arguments or edges in the QBAF without delving into the complex (cyclic)
structure of the QBAFs, particularly in TD-QBAFs where the number of arguments is typically
large and the connections between source arguments and claim arguments are bi-directional.
Second, AAEs and RAEs can provide interesting or even surprising explanations. For example,
in the case study provided earlier, one might overlook the influence between claim arguments
๐1 and ๐5 because they are in different topics (Year=1962 and Theme=Art), but AEs demonstrate
that ๐1 can contribute to ๐5 through ๐ 7. Third, RAEs provide more fine-grained explanations
than AAEs. This is because when computing AAEs, such as removal-based AAEs, removing an
argument means removing all the incoming and outgoing edges associated with that argument,
whereas RAEs offer a more detailed insight by processing every incoming and outgoing edge
individually. One can choose between them depending on the granularity for practical use.
For future work, it would be worthwhile to investigate how different gradual semantics influ-
ence AAEs and RAEs, because the property satisfaction of semantics have an influence on the
property satisfaction of explanations. Additionally, the formal relationship between AAEs and
RAEs requires further exploration. However, we believe AAEs and RAEs can complement each
other, providing a deeper and more comprehensive understanding of the internal mechanisms
of QBAFs, particularly the interactions between arguments and edges in complex QBAFs.
Acknowledgments
This research was partially funded by the European Research Council (ERC) under the European
Unionโs Horizon 2020 research and innovation programme (grant agreement No. 101020934,
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Xiang Yin et al. CEUR Workshop Proceedings 56โ66
ADIX) and by J.P. Morgan and by the Royal Academy of Engineering under the Research Chairs
and Senior Research Fellowships scheme. Any views or opinions expressed herein are solely
those of the authors.
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Additional Results for AAEs and RAEs
Table 1
Comparison of removal-based AAEs and Shapley-based AAEs (in descending order) for the argument ๐5
of TD-QBAF in Figure 1. Note that they are in different scales.
Argument Removal-based AAE Argument Shapley-based AAE
s7 0.084304029 s7 0.285373360
s8 0.066738248 s9 0.259206533
s9 0.066738248 s10 0.257762474
s10 0.066738248 s8 0.256392126
s3 0.006673061 c1 0.020544840
c1 0.006635552 s3 0.007852405
c2 0.002938110 c2 0.001789997
s4 0.000076913 s5 0.000810191
s5 0.000076913 s4 0.000789093
s6 -0.000008421 s0 -0.000593859
c3 -0.000008421 s2 -0.000917430
c4 -0.000008423 s1 -0.001164825
s0 -0.002444482 c3 -0.001309005
s1 -0.002444482 c0 -0.001711158
s2 -0.002444482 c4 -0.010154039
c0 -0.002476209 s6 -0.010892383
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Table 2
Comparison of removal-based RAEs and Shapley-based RAEs (in descending order) for the argument ๐5
of TD-QBAF in Figure 1. Note that they are in different scales.
Relation Removal-based RAE Relation Shapley-based RAE
(s7, c5) 0.083473613 (s7, c5) 0.255513421
(s8, c5) 0.066745475 (s10, c5) 0.247761961
(s9, c5) 0.066745475 (s8, c5) 0.245927825
(s10, c5) 0.066745475 (s9, c5) 0.238930772
(c5, s7) 0.022507211 (c5, s7) 0.024524066
(c5, s8) 0.014968725 (c5, s9) 0.022019375
(c5, s9) 0.014968725 (c5, s10) 0.020724751
(c5, s10) 0.014968725 (c5, s8) 0.020059231
(c5, c4) 0.014703252 (c5, c4) 0.015153831
(c1, s7) 0.006793938 (c1, s7) 0.009541657
(s7, c1) 0.006577898 (s3, c1) 0.006460594
(s3, c1) 0.006576020 (s7, c1) 0.005974419
(c2, s3) 0.002946488 (s3, c2) 0.001282426
(c1, s3) 0.000805779 (s4, c2) 0.001206074
(c1, c0) 0.000695966 (c2, s3) 0.001140980
(s3, c2) 0.000212036 (s5, c2) 0.001083422
(s4, c2) 0.000085191 (c2, c3) 0.000928671
(s5, c2) 0.000085191 (c1, s3) 0.000881815
(c3, c2) -0.000007913 (c1, c0) 0.000834337
(s6, c3) -0.000007913 (c2, s5) 0.000670102
(c3, s6) -0.000007913 (c2, s4) 0.000631869
(s6, c4) -0.000007913 (c0, s2) 0.000586827
(c4, s6) -0.000007913 (c0, s1) 0.000558687
(c4, c5) -0.000007915 (c0, s0) 0.000558250
(c2, c3) -0.000115977 (c3, c2) 0.000164534
(c2, s4) -0.000120350 (s2, c0) 0.000144884
(c2, s5) -0.000120350 (s0, c0) -0.000017152
(c0, s0) -0.000641070 (s1, c0) -0.000036753
(c0, s1) -0.000641070 (s6, c3) -0.000276491
(c0, s2) -0.000641070 (c3, s6) -0.000465298
(s0, c0) -0.002436075 (c4, s6) -0.001147533
(s1, c0) -0.002436075 (c0, c1) -0.001659705
(s2, c0) -0.002436075 (c4, c5) -0.028383722
(c0, c1) -0.002598473 (s6, c4) -0.029099303
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