# Claim Optimization in Computational Argumentation

Gabriella Skitalinskaya1,2, Maximilian Spliethöver1, and Henning Wachsmuth1
1Leibniz University Hannover, Institute of Artificial Intelligence
2University of Bremen, Department of Computer Science
<EMAIL_ADDRESS>

###### Abstract

An optimal delivery of arguments is key to persuasion in any debate, both for
humans and for AI systems. This requires the use of clear and fluent claims
relevant to the given debate. Prior work has studied the automatic assessment
of argument quality extensively. Yet, no approach actually improves the
quality so far. To fill this gap, this paper proposes the task of _claim
optimization_ : to rewrite argumentative claims in order to optimize their
delivery. As multiple types of optimization are possible, we approach this
task by first generating a diverse set of candidate claims using a large
language model, such as BART, taking into account contextual information.
Then, the best candidate is selected using various quality metrics. In
automatic and human evaluation on an English-language corpus, our quality-
based candidate selection outperforms several baselines, improving 60% of all
claims (worsening 16% only). Follow-up analyses reveal that, beyond copy
editing, our approach often specifies claims with details, whereas it adds
less evidence than humans do. Moreover, its capabilities generalize well to
other domains, such as instructional texts.

##  1 Introduction

The delivery of arguments in clear and appropriate language is a decisive
factor in achieving persuasion in any debating situation, known as elocutio in
Aristotle’s rhetoric (El Baff et al., 2019). Accordingly, the claims composed
in an argument should not only be grammatically fluent and relevant to the
given debate topic, but also unambiguous, self-contained, and more. Written
arguments therefore often undergo multiple revisions in which various aspects
are optimized Zhang and Litman (2015).

Extensive research has been done on the automatic assessment of argument
quality and the use of large language models on various text editing tasks.
Yet, no work so far has studied how to actually improve argumentative texts.
However, developing respective approaches is a critical step towards building
effective writing assistants, which could help learners write better
argumentative texts Wambsganss et al. (2021) or rephrase arguments made by an
AI debater Slonim et al. (2021). In this work, we close the outlined gap by
studying how to employ language models for rewriting argumentative text to
optimize its delivery.

Figure 1: Examples of different optimized versions of an _original claim_
found on the debate platform Kialo. All optimizations were generated by the
approach proposed in this paper, using the _debate topic_ as context.

We start by defining the task of _claim optimization_ in Section 3, and adjust
the English-language claim revision dataset of Skitalinskaya et al. (2021) for
evaluation. The new task requires complementary abilities: On the one hand,
different types of quality issues inside a claim must be detected, from
grammatical errors to missing details. If not all quality aspects can be
improved simultaneously, specific ones must be targeted. On the other hand,
improved claim parts need to be integrated with the context of the surrounding
discussion, while preserving the original meaning as far as possible. Figure 1
shows three exemplary optimizations of a claim from the debate platform Kialo.
The first elaborates what the consequence of weaponization is, whereas the
second rephrases the claim to clarify what weaponizing means, employing
knowledge about the debate topic. The third renders the stance of the claim
explicit. We observe that different ways to optimize a claim exist, yet the
level of improvement differs as well.

To account for the multiplicity of claim optimization, we propose a controlled
generation approach that combines the capabilities of large language models
with quality assessment (Section 4). First, a fine-tuned generation model
produces several candidate optimizations of a given claim. To optimize claims,
we condition the model on discourse context, namely the debate topic and the
previous claim in the debate. The key to selecting the best optimization is to
then score candidates using three quality metrics: _grammatical fluency_ ,
_meaning preservation_ , and _argument quality_. Such candidate selection
remains understudied in many generative tasks, particularly within
computational argumentation.

In automatic and manual evaluation (Section 5), we demonstrate the
effectiveness of our approach, employing fine-tuned BART Lewis et al. (2020)
for candidate generation. Our results stress the benefits of quality
assessment (Section 6). Incorporating context turns out especially helpful for
making shorter claims—where the topic of the debate is difficult to infer—more
self-contained. According to human annotators, our approach improves 60% of
all claims and harms only 16%, clearly outperforming standard fine-tuned
generation.

To gain further insights, we carry out a manual annotation of 600 claim
optimizations and identify eight types typically found in online debate
communities, such as elaboration and disambiguation (Section 7). Intriguingly,
our approach covers similar optimization types as in human revisions, but we
also observe limitations (Section 7). To explore to what extent it generalizes
to other revision domains, we also carry out experiments on instructional
texts Anthonio and Roth (2020) and formal texts Du et al. (2022), finding that
it outperforms strong baselines and state-of-the-art approaches.

In summary, the contributions of this paper are:

  1. 1.

_a new task_ , claim optimization, along with a manual analysis of typical
optimization types;

  2. 2.

_a computational approach_ that selects the best generated candidate claim in
terms of quality;

  3. 3.

_empirical insights_ into the impact and challenges of optimizing claims
computationally.111Data, code, and models from our experiments are found at
https://github.com/GabriellaSky/claim_optimization

##  2 Related Work

Quality assessment has become a key topic in computational argumentation
research Lapesa et al. (2023). Various quality dimensions exist in
argumentation theory, as surveyed by Wachsmuth et al. (2017) and assessed
computationally in various works Lauscher et al. (2020); Marro et al. (2022).
Many of them relate to quality aspects we consider in this work, from clarity
and organization Wachsmuth et al. (2016) to the general evaluability of
arguments Park and Cardie (2018), potential fallacies in their reasoning
Goffredo et al. (2022), and the appropriateness of the language used
Ziegenbein et al. (2023). Recently, Skitalinskaya and Wachsmuth (2023) tackled
the question whether an argumentative claim is in need of revision, whereas
Jundi et al. (2023) investigated where to best elaborate a discussion. While
Gurcke et al. (2021) leverage claim generation for a refined assessment of
argument quality, we are not aware of any prior work that actually optimizes
arguments or their components in order to improve quality.

As shown in Figure 1, there can be several ways to optimize a given text. Our
key idea is to select the best optimization among diverse candidates generated
by a language model. Prior generation work on candidate selection hints at the
potential benefits of such setup, albeit in other tasks and domains. In early
work on rule-based conversational systems, Walker et al. (2001) introduced
dialogue quality metrics to optimize template-based systems towards user
satisfaction. Kondadadi et al. (2013) and Cao et al. (2018) chose the best
templates for generation, and Mizumoto and Matsumoto (2016) used syntactic
features to rank candidates in grammar correction. Recently, Yoshimura et al.
(2020) proposed a reference-less metric trained on manual evaluations of
grammar correction system outputs to assess generated candidates, while Suzgun
et al. (2022) utilize pre-trained language models to select the best candidate
in textual style transfer tasks.

In generation research on computational argumentation, candidate selection
remains largely understudied. Most relevant in this regard is the approach of
Chakrabarty et al. (2021) which reframes arguments to be more trustworthy
(e.g., less partisan). It generates multiple candidates and selects one based
on the entailment relation scores to the input. Extending this idea, we select
candidates based on various properties, including argument quality.

Understanding the editing process of arguments is crucial, as it reveals what
quality dimensions are considered important. For Wikipedia, Daxenberger and
Gurevych (2013) proposed a fine-grained taxonomy as a result of their multi-
label edit categorization of revisions Daxenberger and Gurevych (2012). The
taxonomy focuses solely on the editing actions performed, such as inserting,
deleting, and paraphrasing. In contrast, Yang et al. (2017) identified various
semantic intentions behind Wikipedia revisions, from copy editing to content
clarifications and fact updates. Their taxonomy defines a starting point for
our research. Not all covered intentions generalize beyond Wiki scenarios,
though.

Wikipedia-based corpora have often been used in the study of editing and
rewriting, including paraphrasing Max and Wisniewski (2010), grammar
correction Lichtarge et al. (2019), bias neutralization Pryzant et al. (2020),
and controllable text editing Faltings et al. (2021); Du et al. (2022).
Similarly, WikiHow enabled summarization Koupaee and Wang (2018) and knowledge
acquisition Zhou et al. (2019). However, neither of these includes
argumentative texts. Instead, we thus rely on the corpus of Skitalinskaya et
al. (2021), which consists of revision histories of argumentative claims from
online debates. Whereas the authors _compare_ claims in terms of quality, we
propose and study the new task of automatically _optimizing_ claim quality.
Moreoever, we see the revision types they distinguish (clarification, grammar
correction, linking to external sources) as too coarse-grained to represent
the diversity of claim optimizations. We refine them manually into eight
optimization types, allowing for a more systematic analysis. Skitalinskaya et
al. (2021) also found low correlations between the revision types and 15
common argument quality dimensions Wachsmuth et al. (2017), suggesting that
they are rather complementary. Primarily, they target the general form a well-
phrased claim should have and its relevance to the debate.

For the analysis of argumentative text rewriting, Zhang and Litman (2015)
incorporated both argumentative writing features and surface changes. To
explore the classification of essay revisions, they defined a two-dimensional
schema, combining the revision operation (e.g., modify, add, or delete) with
the component being revised (e.g., reasoning or evidence). Moreover, Afrin and
Litman (2018) created a small corpus of between-draft revisions of 60 student
essays to study whether revision improves quality. However, these works do not
uncover the reasoning behind a revision operation and are more geared towards
analysis at the essay level.

##  3 Task and Data

This section introduces the proposed task and pre-sents the data used for
development and evaluation.

###  3.1 Claim Optimization

We define the claim optimization task as follows:

#### Task

Given as input an argumentative claim $c$, potentially along with context
information on the debate, rewrite $c$ into an output claim $\tilde{c}$ such
that

  * (a)

$\tilde{c}$ improves upon $c$ in terms of text quality and/or argument
quality, and

  * (b)

$\tilde{c}$ preserves the meaning of $c$ as far as possible.

While we conceptually assume that $c$ consists of one or more sentences and
has at least one quality flaw, our approaches do not model this explicitly.
Moreover, note that $c$ might have multiple flaws, resulting in $n\geq 2$
candidate optimizations $\tilde{C}=\\{\tilde{c}_{1},\ldots,\tilde{c}_{n}\\}$.
In this case, the goal is to identify the candidate $c^{*}\in\tilde{C}$ that
maximizes overall quality.

###  3.2 Data for Development and Evaluation

We start from the ClaimRev dataset Skitalinskaya et al. (2021), consisting of
124,312 claim revision histories from the debate platform Kialo. Each history
defines a chain $(c_{1},...,c_{m})$, in which claim $c_{i}$ is a revised
version of the previous claim, $c_{i-1}$ with $1<i\leq\leavevmode\nobreak\ m$,
improving upon its quality. According to the authors, this holds in 93% of all
cases.

From each revision chain, we derived all possible optimization pairs
$(c,\tilde{c}):=(c_{i-1},c_{i})$, in total 210,222. Most revisions are labeled
with their intention by the users who performed them, rendering them suitable
for learning to optimize claims automatically.222As 26% of all pairs were
unlabeled, we trained a BERT model to assign such pairs one of the 6 most
prominent labels. Overall, 95% of all pairs refer to three intention labels:
clarification, typo/grammar correction, and corrected/added links. To avoid
noise from the few remaining labels, we condensed the data to 198,089
instances of the three main labels.333The labels of the removed instances
denote changes to the meaning of $c$ and statements from which no action or
intention can be derived (e.g., ”see comments”, ”moved as pro”).

For the final task dataset, we associated each remaining pair $(c,\tilde{c})$
to its context: the debate topic $\tau$ (i.e., the thesis on Kialo) as well as
the previous claim $\hat{c}$ (the parent on Kialo), which is supported or
opposed by $c$ (see Figure 1). We sampled 600 revision pairs pseudo-randomly
as a test set (200 per intention label), and split remaining pairs into
training (90%) and validation set (10%). As the given labels are rather
coarse-grained, we look into the optimizations in more detail in Section 7.

##  4 Approach

We now present the first approach to automatic claim optimization. To account
for the variety of possible optimizations, multiple candidate claims are
generated that are pertinent to the context given and preserve the claim’s
meaning. Then, the best candidate is selected based on quality metrics. Both
steps are detailed below and illustrated in Figure 2.

###  4.1 Seq2Seq-based Candidate Generation

To generate candidates, we fine-tune a Seq2Seq model on pairs $(c,\tilde{c})$,
by treating the original claim $c$ as encoder source and revised claim
$\tilde{c}$ as the decoder target. In a separate experiment, we condition the
model on context information, the debate topic $\tau$ and the previous claim
$\hat{c}$, during fine-tuning to further optimize the relevance of generated
candidates. The context is separated from $c$ by delimiter tokens Keskar et
al. (2019); Schiller et al. (2021).

Multiple ways to improve $c$ exist, especially if it suffers from multiple
flaws, since not all flaws may be fixed in a single revision. Therefore, we
first generate $n$ suitable candidates, $\tilde{c}_{1},\ldots,\tilde{c}_{n}$,
among which the best one is to be found later ($n$ is set to 10 in Section 5).
However, the top candidates created by language models often tend to be very
similar. To increase the diversity of candidates, we perform top-$k$ sampling
Fan et al. (2018), where we first generate the most probable claim (top-$1$)
and then vary $k$ with in steps of 5 (e.g. top-$5$, top-$10$, etc).

Figure 2: Proposed claim optimization approach: First, we generate $n$
candidates from the original claim, possibly conditioned on context
information. Then, the optimized claim is selected using three quality
metrics.

###  4.2 Quality-based Candidate Selection

Among the $n$ candidates, we aim to find the optimal claim, $c^{*}$, that most
improves the delivery of $c$ in terms of text and argument quality. Similar to
Yoshimura et al. (2020), we tackle this task as a candidate selection problem.
In our proposed strategy, AutoScore, we integrate three metrics: (1)
grammatical fluency, (2) meaning preservation, and (3) argument quality. This
way, we can explicitly favor specific quality dimensions via respective
models:

#### Grammatical Fluency

We learn to assess fluency on the MSR corpus Toutanova et al. (2016) where the
grammaticality of abstractive compressions is scored by 3–5 annotators from 1
(disfluent) to 3 (fluent). We chose this corpus, since multiple compressions
per input make a trained model sensitive to the differences in variants of a
text. For training, we average all annotator scores and make the task binary,
namely, a text is seen as disfluent unless all annotators gave score 3. Then,
we train BERT on the data to obtain fluency probabilities (details found in
Appendix A). The accuracy of our model on the suggested data split is 77.4.

#### Meaning Preservation

To quantify to what extent a generated candidate maintains the meaning of the
original claim, we compute their semantic similarity as the cosine similarity
of the SBERT sentence embeddings Reimers and Gurevych (2019).

#### Argument Quality

Finally, to examine whether the generated candidates are better than the
original claim from an argumentation perspective, we fine-tune a BERT model on
the task of pairwise argument classification using the ClaimRev dataset. Since
this corpus is also used to fine-tune the Seq2Seq model, we apply the same
training and validation split as described in Section 3.2 to avoid data
leakage, and obtain 75.5 accuracy. We then use its probability scores to
determine relative quality improvement (for more details see Appendix A).

Given the three quality metrics, we calculate the final evaluation score,
$AutoScore$, as the weighted linear sum of all three individual scores as

$\alpha\cdot fluency+\beta\cdot meaning+\gamma\cdot argument,$

where $fluency$, $meaning$, and $argument$ are normalized scores of the three
outlined quality metrics. The non-negative weights satisfy
$\alpha+\beta+\gamma=1$.

It should be noted that depending on the domain or writing skills of the
users, there may be other more suitable datasets or approaches to capturing
the outlined quality aspects, which could potentially lead to further
performance improvements. While we do explore how well the suggested
approaches transfer to certain other domains of text (see Section 7.3),
identifying the optimal model for each quality dimension falls beyond the
scope of this paper.

##  5 Experiments

This section describes our experimental setup to study how well the claims
from Section 3 can be improved using our approach from Section 4. We focus on
the impact of candidate selection.

###  5.1 Seq2Seq-based Candidate Generation

For candidate generation, we employ the pre-trained conditional language model
BART Lewis et al. (2020), using the bart-large checkpoint. However, other
Seq2Seq architectures can also be considered within our approach (see
Appendices A, B).

###  5.2 Quality-based Candidate Selection

We evaluate our candidate selection approach in comparison to three ablations
and four baselines:

#### Approach

To utilize AutoScore for choosing candidates, the optimal weighting of its
metrics must be determined. We follow Yoshimura et al. (2020), performing a
grid search in increments of $0.01$ in the range of $0.01$ to $0.98$ for each
weight to maximize the Pearson’s correlation coefficient between AutoScore and
the original order of the revisions from revision histories in the validation
set. Similar has been done for counterargument retrieval by Wachsmuth et al.
(2018). The best weights found are $\alpha\\!=\\!0.43,\beta\\!=\\!0.01$, and
$\gamma\\!=\\!0.56$, suggesting that meaning preservation is of low importance
and potentially may be omitted. We suppose this is due to the general
similarity of the generated candidates, so a strong meaning deviation is
unlikely.

#### Ablations

To assess the impact of each considered quality metric used in AutoScore, we
perform an ablation study, where optimal candidates are chosen based on the
individual metric scores:

  * •

_Max Fluency._ Highest grammatical fluency

  * •

_Max Argument._ Highest argument quality

  * •

_Max Meaning._ Highest semantic similarity

#### Baselines

We test four selection strategies for 10 candidates generated via top-$k$
sampling:

  * •

_Unedited._ Return the original input as output.

  * •

_Top-1._ Return the most likely candidate (obtained by appending the most
probable token generated by the model at each time step).

  * •

_Random._ Return candidate pseudo-randomly.

  * •

_SVMRank._ Rerank candidates with SVMRank Joachims (2006). Using sentence
embeddings we decide which of the claim versions is better, by fine-tuning
SBERT (bert-base-cased) on the corpus of Skitalinskaya et al. (2021).

###  5.3 Evaluation

We explore claim optimization on all 600 test cases, both automatically and
manually:

#### Automatic Evaluation

We compare all content selection strategies against the reference revisions
using the precision-oriented BLEU Papineni et al. (2002), recall-oriented
Rouge-L Lin (2004), SARI Xu et al. (2016), which computes the average
F1-scores of the added, kept, and deleted $n$-grams in comparison to the
ground truth revision output, and the _exact match accuracy_. We also compute
the semantic similarity of the optimized claim and the context information to
capture whether conditioning claims on context affects their topic relevance.

#### Manual Evaluation

As we fine-tune existing generation models rather than proposing new ones, we
focus on the candidate selection in two manual annotation studies. For each
instance, we acquired five independent crowdworkers via MTurk.

In the first study, the annotators scored all candidates with respect to the
three considered quality metrics. We used the following Likert scales:

  * •

Fluency. 1 (major errors, disfluent), 2 (minor errors), and 3 (fluent)

  * •

Meaning Preservation. 1 (entirely different), 2 (substantial differences), 3
(moderate differences), 4 (minor differences), and 5 (identical)

  * •

Argument Quality. 1 (notably worse than original), 2 (slightly worse), 3 (same
as original), 4 (slightly improved), and 5 (notably improved)

A challenge of crowdsourcing is to ensure good results Sabou et al. (2014). To
account for this, we obtained the fina fluency, argument quality and meaning
preservation scores using MACE Hovy et al. (2013), a Bayesian model that gives
more weight to reliable workers. In the given case, 39% of the 46 annotators
had a MACE competence value $>0.3$, which can be seen as reasonable in MTurk
studies.

In the second study, we asked annotators to rank four candidates, returned by
the content selection strategies, by perceived overall quality. If multiple
candidates were identical, we showed each only once. While Krippendorff’s
$\alpha$ agreement was only 0.20 and percent agreement was 0.36% (majority
voting), such values are common in subjective tasks Wachsmuth et al. (2017);
Alshomary et al. (2021).

##  6 Results and Discussion

Apart from evaluating the applicability of large generative language models to
the task of argumentative claim optimization in general, our experiments focus
on two questions: (1) Does the use of explicit knowledge about text and
argument quality lead to the selection of better candidates? (2) Does the use
of contextual information make the generated candidates more accurate and
relevant to the debate?

###  6.1 Overall Claim Optimization Performance

#### Automatic Evaluation

Table 1 shows the automatic scores of all considered candidate selection
strategies. The high scores of the baseline _Unedited_ on metrics such as BLEU
and ROUGE-L indicate that many claim revisions change little only. In
contrast, _Unedited_ is worst on SARI, a measure taking into account words
that are added, deleted, and kept in changes, making it more suitable for
evaluation. Here, _BART+AutoScore_ performs best on SARI (43.7) and exact
match accuracy (8.3%).

The _BART+Max Meaning_ ablation supports the intuition that the candidates
with highest meaning preservation scores are those with minimal changes, if
any (72% of the candidates remain identical to the input). Such identical
outputs are undesirable, as the claims are not optimized successfully, which
is also corroborated by the low weight parameter ($\beta=0.01$) found for the
meaning preservation metric when optimizing AutoScore (see Section 5).

Approach | BLEU | RouL | SARI | NoEd$\downarrow$ | ExM
---|---|---|---|---|---
Baselines |  |  |  |  |
Unedited | 69.4 | 0.87 | 27.9 | 1.00 | 0.0%
BART + Top-1 | 64.0 | 0.83 | 39.7 | 0.31 | 7.8%
BART + Random | 62.6 | 0.83 | 38.7 | 0.28 | 6.8%
BART + SVMRank | 55.7 | 0.76 | 38.8 | 0.03 | 4.5%
Approach |  |  |  |  |
BART + AutoScore | 59.4 | 0.80 | 43.7 | 0.02 | 8.3%
Ablation |  |  |  |  |
BART + Max Fluency | 57.6 | 0.78 | 41.5 | 0.09 | 5.8%
BART + Max Argument | 60.9 | 0.81 | 43.6 | 0.02 | 8.0%
BART + Max Meaning | 69.0 | 0.87 | 33.8 | 0.72 | 5.2%
Table 1: Automatic evaluation: Performance of each candidate selection strategy on 600 test cases in terms of BLEU, Rouge-L, SARI, ratio of unedited cases, and ratio of exact matches to target reference. Model | Strategy | Fluency | Argument | Meaning | Rank
---|---|---|---|---|---
BART | Top-1 | 2.29 | 3.61 | 3.65 | 2.16
| Random | 2.26 | 3.50 | 3.53 | 2.06
| SVMRank | 2.33 | 3.69 | 3.66 | 1.95
| AutoScore | 2.33 | 3.61 | 3.57 | 1.92
Table 2: Manual evaluation: Scores on the 600 test cases generated by BART
using our candidate selection strategy _AutoScore_ or the baselines: fluency
(1–3), argument quality and meaning (1–5), mean rank (1–4, lower better).
AutoScore ranks significantly better than _Top-1_ ($p<.005$), _Random_
($p<.05$), and _SVMRank_ ($p<.1$).

#### Manual Evaluation

Table 2 shows that human annotators prefer optimized candidates selected by
AutoScore, with an average rank of 1.92. The difference to Top-1 and Random is
statistically significant ($p<.05$ in both cases) according to a Wilcoxon
signed-rank test, whereas the gain over the second-best algorithm, _SVMRank_ ,
is limited. Also, candidates of AutoScore and SVMRank are deemed more fluent
than those of Top-1 and Random (2.33 vs. 2.29 and 2.26). In terms of argument
quality, the results deviate from the automatic evaluation (Table 1), showing
marginally higher scores for SVMRank and Top-1. Further analysis revealed that
AutoScore and SVMRank agreed on the optimal candidate in 35% of the cases,
partially explaining their close scores. Although SVMRank achieved high scores
across the three quality metrics, we note that the annotators preferred
candidates scores generated by AutoScore, highlighting the importance of more
diverse revision changes reflected by lower meaning preservation scores.

Overall, our findings suggest that using candidate selection approaches that
incorporate quality assessments (i.e., AutoScore and SVMRank) leads to
candidates of higher fluency and argument quality while preserving the meaning
of the original claim. In addition to Figure 1, examples of automatically-
generated optimized claims can be found in the appendix.

###  6.2 Performance with Context Integration

Table 3 shows the semantic similarity of claims optimized by our approach and
context information, depending on the context given. The results reveal slight
improvements when conditioning the model on the previous claim (e.g., 60.3 vs.
59.4 BLEU). To check whether this led to improved claims, two authors of the
paper compared 600 claims generated with and without the use of the previous
claim in terms of (a) which claim seems better overall and (b) which seems
more grounded. We found that using the previous claim as context improved
quality in 12% of the cases and lowered it in 1% only, while leading to more
grounded claims in 36%.

#### Qualitative Analysis

Our manual inspection of a claim sample revealed the following insights:

First, conditioning on context reduces the number of erroneous specifications,
particularly for very short claims with up to 10 words. This seems intuitive,
as such claims often convey little information about the topic of the debate,
making inaccurate changes without additional context likely.

Context | BLEU | Original | Previous | Topic
---|---|---|---|---
Claim only | 59.4 | 0.95 | 0.55 | 0.55
\+ Previous Claim | 60.3 | 0.95 | 0.57 | 0.57
\+ Debate Topic | 60.0 | 0.95 | 0.55 | 0.55
Human-Baseline | 100.0 | 0.94 | 0.55 | 0.55
Table 3: BLEU and semantic similarity score with respect to the original claim, the debate’s previous claim, and its topic of BART+AutoScore, depending on the context given for the 600 test samples. # | Optimization |  Description of the Type | Clarification | Grammar | Links
---|---|---|---|---|---
1 | Specification |  Specifying or explaining a given fact or meaning (of the argument) by adding an example or discussion without adding new information. | 58 | 1 | –
2 | Simplification |  Removing information or simplifying the sentence structure, e.g., with the intent to reduce the complexity or breadth of the claim. | 43 | – | –
3 | Reframing |  Paraphrasing or rephrasing a claim, e.g., with the intent to specify or generalize the claim, or to add clarity. | 29 | – | –
4 | Elaboration |  Extending the claim by more information or adding a fact with the intent to make the claim more self-contained, sound, or stronger. | 23 | – | –
5 | Corroboration |  Adding, editing, or removing evidence in the form of links that provide supporting information or external resources to the claim. | 8 | – | 153
6 | Neutralization |  Rewriting a claim using a more encyclopedic or neutral tone, e.g., with the intent to remove bias or biased language. | 7 | – | –
7 | Disambiguation |  Reducing ambiguity, e.g., replacing pronouns by concepts mentioned before in the debate, or replacing acronyms with what they stand for. | 7 | – | 1
8 | Copy editing |  Improving the grammar, spelling, tone, or punctuation of a claim, without changing the main point or meaning. | 41 | 200 | 52
Table 4: Descriptions of the eight claim optimization types identified in the
600 test pairs. The right columns show the count of claims per type for each
of the three intention labels from Skitalinskaya et al. (2021): clarification,
typo/grammar correction, and correcting/adding links. Note, that a revision
may be assigned to multiple categories.

Next, Kialo revisions often adhere to the following form: A claim introduces a
statement and/or supporting facts, followed by a conclusion. This pattern was
frequently mimicked by our approach. Yet, in some cases, it added a follow-up
sentence repeating the original claim in different wording or generated
conclusions containing fallacious or unsound phrases contradicting the
original claim in others. Modeling context mitigated this issue.

Finally, we found that models conditioned on different contexts sometimes
generated candidates optimized in different regards, whereas a truly optimal
candidate would be a fusion of both suggestions.

##  7 Analysis

To explore the nature of claim optimization and the capabilities of our
approach, this section reports on (a) what types of optimizations exist, (b)
how well our approach can operationalize these, and (c) how well it
generalizes to non-argumentative domains.

###  7.1 Taxonomy of Optimization Types

To understand the relationship between optimizations found in the data and the
underlying revision intentions, two authors of this paper inspected 600 claim
revisions of the test set. Opposed to actions, intentions describe the goal of
an edit (e.g., making a text easier to read) rather than referring to specific
changes(e.g., paraphrasing or adding punctuation). We build on ideas of Yang
et al. (2017) who provide a taxonomy of revision intentions in Wikipedia
texts. Claims usually do not come from encyclopedias, but from debate types or
from monological arguments, as in essays Persing and Ng (2015). Therefore, we
adapt the terminology of Yang et al. (2017) to gear it more towards
argumentative texts.

As a result of a joint discussion of various sample pairs, we decided to
distinguish eight optimization types, as presented in Table 4. Both authors
then annotated all 600 test pairs for these types, which led to only 29
disagreement cases, meaning a high agreement of 0.89 in terms of Cohen’s
$\kappa$. These cases were resolved by both annotators together.444We
acknowledge that there is potential bias inherent in self-annotation. However,
we would like to point out that no knowledge about the test set was used to
develop the approach presented in Section 4.

Table 4 also shows cooccurrences of the types and intention labels.
_Typo/grammar correction_ and _correcting/adding links_ align well with _copy
editing_ and _corroboration_ respectively. In contrast, clarification is
broken into more fine-grained types, where specification seems most common
with 58 cases, followed by simplification and reframing. Examples of each type
are found in the appendix.

We point out that the eight types are not exhaustive for all possible claim
quality optimizations, but rather provide insights into the semantic and
discourse-related phenomena observed in the data. We see them as complementary
to the argument quality taxonomy of Wachsmuth et al. (2017) as ways to improve
the delivery-related quality dimensions: clarity, appropriateness, and
arrangement.

Type | Human | Approach | Better | Same | Worse
---|---|---|---|---|---
Specification | 59 | 152 | 65% | 19% | 16%
Simplification | 43 | 18 | 61% | 28% | 11%
Reframing | 29 | 21 | 62% | 33% | 5%
Elaboration | 23 | 55 | 62% | 18% | 20%
Corroboration | 161 | 38 | 53% | 23% | 24%
Neutralization | 7 | 0 | – | – | –
Disambiguation | 8 | 8 | 63% | 25% | 12%
Copy editing | 293 | 301 | 59% | 26% | 15%
Overall | 623 | 593 | 60% | 24% | 16%
Table 5: Manual analysis: Comparison of the human-optimized claims of all 600
test cases (some have multiple) and of the claims optimized by BART+AutoScore
(15 claims were unchanged). The three right columns show the ratio of
optimized claims judged better, same, or worse than the original in terms of
overall quality.

###  7.2 Performance across Optimization Types

To enable comparison between the human optimizations and automatically
generated outputs, two authors of the paper labeled 600 optimized claims with
the types defined in Table 4. Due to resource constrains only the best
performing approach, BART+AutoScore, was considered. Overall, our approach
generates better claims in 60% of the cases, while 84% remain at least of
similar quality.

Most noteworthily, we observe that our approach performs optimizations of the
type specification 2.5 times as often as humans, and more than double as many
elaboration revisions (55 vs. 23). In contrast, it adds, edits, or removes
evidence in the form of links (corroboration) four times less often than
humans. The model also made fewer simplifications (18 vs. 43) and no
neutralization edits, which may be due to data imbalance regarding such types.

In terms of average quality, specification (65%) and disambiguation edits
(63%) most often lead to improvements, but the eight types appear rather
balanced in this regard. The Jaccard similarity score between optimizations
performed by humans and our approach is $0.37$, mostly agreeing on copy edits
(178 cases) and corroboration (22 cases). Given such low overlap, future work
should consider conditioning models to generate specific optimizations.

###  7.3 Performance across Revision Domains

Lastly, we examine whether our approach, along with the chosen text quality
metrics, applies to texts from other domains. We consider two datasets:
_WikiHow_ Anthonio and Roth (2020), containing revisions of instructional
texts, and _IteraTeR_ Du et al. (2022), containing revisions of various formal
texts, such as encyclopedia entries, news, and scientific papers. For our
experiments, we use the provided document-level splits, and sample 1000
revision pairs pseudo-randomly as a final test set.

Table 6 shows automatic evaluation results. In both cases, _BART+Autoscore_
leads to higher SARI scores (48.5 vs. 41.3 for WikiHow, 38.6 vs. 37.0 for
IteraTeR), and notably reduces the number of cases where the models failed to
revise the input (0.08 vs. 0.50 for WikiHow). The reported _BART+Top1_ model
represents the approach of Du et al. (2022), indicating that our approach and
its text quality metrics achieve state-of-the-art performance with systematic
improvements across domains, when generating optimized content. However, as
different domains of text have different goals, different notions of quality,
and, subsequently, different revision types performed, integrating domain-
specific quality metrics may further improve performance. We leave this for
future work.

Approach | BLEU | RouL | SARI | NoEd$\downarrow$ | ExM
---|---|---|---|---|---
WikiHow Dataset |  |  |  |  |
Unedited | 65.7 | 0.85 | 28.4 | 1.00 | 0.00%
BART + Top-1 | 64.7 | 0.83 | 41.3 | 0.50 | 13.0%
BART + AutoScore | 61.8 | 0.80 | 48.5 | 0.08 | 16.0%
IteraTeR Dataset |  |  |  |
Unedited | 74.0 | 0.86 | 28.6 | 1.00 | 0.00%
BART + Top-1 | 68.9 | 0.83 | 37.0 | 0.07 | 0.00%
BART + AutoScore | 64.8 | 0.80 | 38.6 | 0.02 | 0.00%
Table 6: Automatic evaluation: Performance of candidate selection strategies
on data from other domains, in terms of BLEU, Rouge-L, SARI, ratio of unedited
samples, and ratio of exact matches to target reference.

##  8 Conclusion

With this paper, we work towards the next level of computational argument
quality research, namely, to not only assess but also to optimize
argumentative text. Applications include suggesting improvements in writing
support and automatic phrasing in debating systems. We presented an approach
that generates multiple candidate claim optimizations and then selects the
best one using various quality metrics. In experiments, combining fine-tuned
BART with such candidate selection improved 60% of the claims from online
debates, outperforming several baseline models and candidate selection
strategies. We showcased generalization capabilities on two out-of-domain
datasets, but we also found some claim optimization types hard to automate.

In future work, we seek to examine whether recent large language models (e.g.,
Alpaca) and end-to-end models (where generation and candidate selection are
learned jointly) can further optimize the quality of claims. As our approach
so far relies on the availability of large claim revision corpora and language
models, techniques for low-resource scenarios and languages should be explored
to make claim optimization more widely applicable.

## Acknowledgments

This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under project number 374666841, SFB 1342.

## Ethical Considerations

This work contributes to the task of argumentative text editing, namely we
explore how to revise claims automatically in order to optimize their quality.
While our work may also improve downstream task performance on other tasks, it
is mainly intended to support humans in scenarios, such as the creation and
moderation of content on online debate platforms as well as the improvement of
arguments generated or retrieved by other systems. In particular, the
presented approach is meant to help users by showing examples of how to
further optimize their claims in relation to a certain debate topic, so they
can deliver their messages effectively and hone their writing skills.

However, our generation approach still comes with limitations and may favor
revision patterns over others in unpredictable ways, both of which might raise
ethical concerns. For example, it may occasionally produce false claims based
on untrue or non-existent facts. We think, humans should be able to identify
such cases in light of the available context though, as long as the
improvements remain suggestions and do not happen fully automatically, as
intended.

The presented technology might further be subject to intentional misuse. A
word processing software, for example, could be conditioned to automatically
detect and adapt claims made by the user in subtle ways that favors political
or social views of the software provider. Such misuse might then not only
change the intended message of the text, but also influence or even change the
views of the user Jakesch et al. (2023).

In a different scenario, online services, such as social media platforms or
review portals, might change posted claims (e.g. social media posts, online
reviews) to personalize them and increase user engagement or revenue. These
changes might not only negatively affect the posting, but also the visiting
user.

While it is hard to prevent such misuse, we think that the described scenarios
are fairly unlikely, as such changes tend to be noticed by the online
community quickly. Furthermore, the presented architecture and training
procedure would require notable adaptations to produce such high-quality
revisions.

An aspect that remains unexplored in this work is the ability of the presented
approaches to work with variations of the English language, such as African-
American English, mainly due to the lack of available data. In this regard,
the approach might unfairly disadvantage or favor particular language
varieties and dialects, potentially inducing social bias and harm if applied
in public scenarios. We encourage researchers and practitioners to stay alert
for such cases and to choose training data with care for various social
groups.

Finally, our work included the labeling of generated candidate claims on a
crowdsourcing platform. As detailed in Section 5, we compensated MTurk workers
$13 per hour, complying with minimum wage standards in most countries at the
time of conducting the experiment.

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##  Appendix A Implementation and Training Details

###  A.1 Candidate Generation Models

For generation, we use the pre-trained BART model implemented in the fairseq
library. The library and pre-trained models are BSD-licensed. We use the BART-
large checkpoint (400M parameters) and further finetune the model for 10
epochs on 2 RTX 2080Ti GPUs. We use the same parameters as suggested in the
fine-tuning of BART for the CNN-DM summarization task by fairseq and set MAX-
TOKENS to 1024. The training time is 100-140 minutes, depending on the chosen
setup (with or without context information).

During inference, we generate candidates using a top-k random sampling scheme
Fan et al. (2018) with the following parameters: length penalty is set to 1.0,
n-grams of size 3 can only be repeated once, temperature is set to 0.7, while
the minimum and maximum length of the sequence to be generated are 7 and 256
accordingly.

###  A.2 Quality Assessment Models

For the automatic assessment of fluency and argument quality, we use the bert-
base-cased pre-trained BERT version, as implemented in the huggingface
library. The library and pre-trained models have the Apache License 2.0. We
finetune the model for two epochs and use the parameters suggested in
Skitalinskaya et al. (2021). The accuracy of the trained model for fluency
obtained on the train/dev/test split suggested by the authors Toutanova et al.
(2016) is 77.4 and 75.5 for argument quality.

For labeling the missing or unassigned revision types, we use the same bert-
base-cased pre-trained BERT model, but in a multi-label setup, where we
consider the following 6 classes: claim clarification, typo or grammar
correction, correcting or adding links, changing the meaning of the claim,
splitting the claim, and merging claims. We fine-tune the model for two epochs
using the Adam optimizer with a learning rate of 1e-5 and achieve a weighted
F1-score of 0.81.

##  Appendix B Alternative Generation Models

For comparison, we provide two additional baseline Seq2Seq model
architectures, which help identify the complexity of the model needed for the
task:

LSTM. Our first baseline is a popular LSTM variant introduced by Wiseman and
Rush (2016). We use the lstm_wiseman_iwslt_de_e architecture, which is a two-
layer encoder and decoder LSTM, each with 256 hidden units, and dropout with a
rate of 0.1 between LSTM layers.

Transformer. The second model is based on the work of Vaswani et al. (2017).
We use the transformer_iwslt_de_en architecture, a 6-layer encoder and decoder
with 512-dimensional embeddings, 1024 for inner-layers, and four self-
attention heads.

Tables 7 and 8 compare the automatic evaluation scores of all generation-
content selection combinations.

Model | Strategy | BLEU | RouL | SARI | NoEd$\downarrow$ | ExM
---|---|---|---|---|---|---
BART | Top-1 | 64.0 | 0.83 | 39.7 | 0.31 | 7.8%
| Random | 62.6 | 0.83 | 38.7 | 0.28 | 6.8%
| SVMRank | 55.7 | 0.76 | 38.8 | 0.03 | 4.5%
| AutoScore | 59.4 | 0.80 | 43.7 | 0.02 | 8.3%
Trans- | Top-1 | 43.6 | 0.64 | 0.30 | 0.12 | 0.8%
former | Random | 42.4 | 0.63 | 0.30 | 0.13 | 1.0%
| SVMRank | 41.8 | 0.63 | 0.31 | 0.10 | 1.2%
| AutoScore | 40.5 | 0.62 | 0.30 | 0.10 | 1.3%
LSTM | Top-1 | 36.2 | 0.56 | 0.28 | 0.10 | 0.3%
| Random | 36.0 | 0.56 | 0.28 | 0.10 | 0.3%
| SVMRank | 36.2 | 0.56 | 0.29 | 0.10 | 1.0%
| AutoScore | 34.1 | 0.52 | 0.28 | 0.10 | 1.0%
Table 7: Automatic evaluation: Results for each combination of generation model and candidate selection strategy on the 600 test samples, in comparison to the human revisions: BLEU (0-100), ROUGE-L (RouL), SARI, ratio of unedited samples (NoEd), % of exact matches to target reference (ExM). Model | Strategy | Fluency | Meaning | Argument | Average
---|---|---|---|---|---
BART | Top-1 | 0.73 | 0.97 | 0.65 | 0.78
| Random | 0.72 | 0.97 | 0.68 | 0.79
| SVMRank | 0.72 | 0.94 | 0.76 | 0.81
| AutoScore | 0.83 | 0.95 | 0.86 | 0.88
Trans- | Top-1 | 0.44 | 0.76 | 0.40 | 0.53
former | Random | 0.41 | 0.76 | 0.38 | 0.52
| SVMRank | 0.50 | 0.76 | 0.45 | 0.57
| AutoScore | 0.68 | 0.75 | 0.61 | 0.68
LSTM | Top-1 | 0.27 | 0.68 | 0.31 | 0.42
| Random | 0.27 | 0.68 | 0.31 | 0.42
| SVMRank | 0.29 | 0.69 | 0.31 | 0.43
| AutoScore | 0.52 | 0.65 | 0.53 | 0.57
Human |  | 0.72 | 0.94 | 0.74 | 0.80
Table 8: Results for each combination of generation model and candidate
selection strategy on the 600 test samples, in comparison to the human
revisions based on three quality metrics: fluency, meaning preservation and
argument quality.

###  B.1 Automatic Evaluation

We use the following python packages and scripts to perform automatic
evaluations: nltk (BLEU Papineni et al. (2002)), rouge-score (ROUGE Lin
(2004)), https://github.com/cocoxu/simplification/ SARI.py (SARI Xu et al.
(2016))

##  Appendix C Claim Optimization Examples

For all eight optimization categories, we provide one or more examples
illustrating each action in Table 9.

Type |  Examples
---|---
Specification |  Nipples are the openings of female-only exocrene glands that can have abnormal [secretions] <LINK> during any time of life, get erected by cold stimulation or sexual excitement (much more visibly than in men), get lumps or bumps and change color and size of areola during the menstrual cycle or pregnancy, so their display can break [personal space] <LINK> and privacy (which is stressful), affect public sensibilities and also be a [window] <LINK> for infections, allergies, and irritation.
|  The idea behind laws, such as limiting the amount of guns, is to reduce the
need to defend yourself from a gun or rapist.
|  It is very common for governments to actively make certain forms of
healthcare [harder for minority groups to access] <LINK>.  They could also,
therefore, make cloning technology hard to access.
Simplification |  Very complex, cognitively meaningful behavior such as behaviours like creating art are evidence of free will, because they exhibit the same lack of predictability as stochastic systems, but are intelligible and articulate clearly via recognizable vehicles.
Reframing |  It reduces the oversight of the BaFin and thus increases the risk of financial crisis market failures.
Elaboration |  It takes 2-4 weeks for HIV  to present any symptom. The incubation period risk can’t be ruled out for is higher for a member of high risk group, effectively and timely even though member of a low risk group is not completely safe. The decision is based on the overall risk, not on individual level.
Corroboration |  [Person-based predictive policing technologies] <LINK> \- that focus on predicting who is likely to commit crime rather than where is it likely to occur - violate the [presumption of innocence.] <LINK>.
Neutralization |  Biden does not lacks the support  or agree with several key issues that are important to liberal voters. of many liberal voting groups due to his stance on key issues concerning them.
Disambiguation |  The USSR had [passed legislation] <LINK> to gradually eliminate religious belief within its borders. However the death penalty was more used in USSR than in Russia. It USSR had 2000 [death penalties] <LINK> per year in the 1980s whereas pre USSR Russia had [banned the death penalty] <LINK> in 1917 and almost never carried it out in the decades before that.
|  SRM Solar geoengineering merely serves as a "technological fix"
(Weinberg).[harvard.edu] <LINK>
Copy Editing |  Women are experiencing record level levels of success in primaries.
Table 9: Illustrative examples of optimization types identified in the paper.
The green font denotes additions and the striked out red font denotes the
removal of text snippets.

##  Appendix D Manual Quality Assessment Guidelines

Figure 3 shows the annotation guidelines for the Amazon Mechanical Turk study.

Instructions In this task, your goal is to identify whether a claim has been
successfully improved, without changing the overall meaning of the text. Each
task contains a set of pairs, where one claim is the "original claim," and the
other an optimized candidate. Each of these pairs have the same original text,
but different candidate optimizations. Please rate each candidate along the
following three perspectives: argument quality, fluency and semantic
similarity. And, finally, please, rank all candidates relative to each other
in terms of overall quality. Argument Quality Scale (1-5): 1 (notably worse
than original), 2 (slightly worse), 3 (same as original), 4 (slightly
improved), 5 (notably improved) Does the optimized claim improve the argument
quality compared to the original claim? Relevant changes include, but are not
limited to: • further specifying or explaining an existing fact or meaning •
removing information or simplifying the sentence structure with the intent to
reduce the complexity or breadth of the claim • rephrasing a claim with the
intent to specify or generalize the claim, or to add clarity • adding
(substantive) new content or information to the claim or inserting an
additional fact with the intent of making it more self-contained, more sound
or stronger • adding, editing or removing evidence in the form of links that
provide supporting information or external resources to the claim • removal of
bias or biased language • removal uncertainty. e.g. by replacing pronouns
referring to concepts that have been mentioned in other claims of the debate,
or by replacing acronyms with what they stand for • improving the grammar,
spelling, tone, or punctuation of a claim Meaning Scale (1-5): 1 (entirely
different), 2 (substantial differences), 3 (moderate differences), 4 (minor
differences), 5 (identical) Does the transformed claim still have the same
overall meaning as the original? It is OK if extra information is added, as
long as it doesn’t change the underlying people, events, and objects described
in the sentence. You should also not strongly penalize for meaning
transformations which aim to generalize or specify some aspects of the claim.
Fluency Scale (1-3): 1 (major errors, disfluent), 2 (minor errors), 3 (fluent)
Is this sentence fluent English and does it make sense? Examples with
explanations can be found here. Figure 3: Guidelines provided to the
crowdworkers to annotate automatically generated claim optimizations.

##  Appendix E System Outputs

Table 10 provides examples of candidates selected by different content
selection strategies along with human references illustrating common patterns
found in the results. Table 11 provides examples of candidates generated with
and without utilizing context knowledge with insertions and deletions being
highlighted in green and red fonts accordingly.

Strategy |  Candidate
---|---
Original |  Easy to cheat, and procastinate
Top-1 |  It is easy to cheat and procastinate .
SVMRank |  The easy to cheat, and procastinate
AutoScore |  The UBI is easy to cheat and easy to manipulate.
Human |  Flexible schedules can easily increase procrastination
Original |  Many games often attempt to depict the norms and attitudes of the real world.
Top-1 |  Many games often attempt to depict the norms and attitudes of the real world.
SVMRank |  Many games often attempt to depict the norms and attitudes of the real world, and thus are likely to be accurate and relevant to what people are thinking and feeling in the real-world.
AutoScore |  Many games often attempt to depict the norms and attitudes of the real world, in order to give players a greater understanding of the world around them.
Human |  Many games often attempt to depict the norms and attitudes of the real world; gamers are likely to see social attitudes espoused in these games on issues of gender equality as indicative of progress in the real world.
Original |  Owners of PWA take home [more profit] <LINK> from their sales than mobile apps.
Top-1 |  Owners of PWA take home [more profit] <LINK> from their sales than mobile apps.
SVMRank |  Owners of PWA take home [more profit] <LINK> from their sales than mobile apps. This allows them to reinvest in their business and increase their profits.
AutoScore |  Owners of PWA take home [more profit] <LINK> from their sales than those of mobile apps.
Human |  Owners of PWAs  take home [more profit] <LINK> from their sales than mobile apps.
Original |  Scientists found out that Saturn’s moon [Enceladus] <LINK> houses a giant, global ocean beneath its icy outer shell.
Top-1 |  Scientists found out that Saturn’s moon [Enceladus] <LINK> houses a giant, global ocean beneath its icy outer shell.
SVMRank |  Scientists found out that Saturn’s moon [Enceladus] <LINK> houses a giant, global ocean beneath its icy outer shell. This suggests that this icy, water-filled place also houses other life forms, such as asteroids and comets.
AutoScore |  Scientists found out that Saturn’s moon [Enceladus] <LINK> houses a giant, global ocean beneath its icy outer shell, suggesting that the moon may hold life beyond the surface.
Human |  Scientists found out that Saturn’s moon [Enceladus] <LINK> houses a giant, global ocean beneath its icy outer shell.
Original |  Responsibility requires conscious decisions and [free will] <LINK>. Acting according to governmental orders is far from that.
Top-1 |  Responsibility requires conscious decisions and [free will] <LINK>. Acting according to governmental orders is far from that.
SVMRank |  Responsibility requires conscious decisions and [free will] <LINK>. Acting according to governmental orders is far from that. Therefore, people are not responsible for their actions, and are therefore not morally responsible.
AutoScore |  Responsibility requires conscious decisions and [free will] <LINK>. Acting according to governmental orders is far from that, as it is not a conscious decision but rather a result of an involuntary reaction.
Human |  The coercion to vote eliminates the idea of responsibility, which requires conscious decisions and [free will] <LINK>. Acting according to governmental orders is far from that.
Original |  There was much progress, advancement and forward looking thinking in the 20th century in Europe across all disciplines.
Top-1 |  There was much progress, advancement and forward looking thinking in the 20th century in Europe across all disciplines. Therefore, it is logical to conclude that the world has changed in the last 150 years.
SVMRank |  There was much progress, advancement and forward looking thinking in the 20th century in Europe across all disciplines, which shows the progress that was made during the century.
AutoScore |  There was much progress, advancement, and forward looking thinking in the 20th century in Europe across all disciplines.
Human |  There was much progress, advancement and forward looking thinking in the 20th century in Europe across all disciplines.
Original |  A [catch-22] <LINK> situation currently exists in regards to researching the medicinal applications of some illegal drugs, due to the laws surrounding how they are categorised ([p. 12] <LINK>).
SVMRank (Top-1) |  A [catch-22] <LINK> situation currently exists in regards to researching the medicinal applications of some illegal drugs, due to the laws surrounding how they are categorised ([p. 12] <LINK>). This prevents researchers from knowing how to fully assess the medicinal potential of drugs in a manner that is best suited for the patients who need it.
AutoScore |  A [catch-22] <LINK> situation currently exists in regards to researching the medicinal applications of some illegal drugs, due to the laws surrounding how they are categorised ([p. 12] <LINK>). This prevents researchers from researching possible medicinal uses for illegal drugs.
Human |  A [catch-22] <LINK> situation currently exists in regard to researching the medicinal applications of some illegal drugs, due to the laws surrounding how they are categorised ([p. 12] <LINK>).
Table 10: Examples of optimizations selected by different candidate selection strategies along with human references. The green font denotes additions and the striked out red font denotes the removal of text snippets. Control |  Candidate
---|---
Topic |  Should Men Be Involved And Trusted In Childcare?
Previous |  Perpetrators of child abuse are [way more likely] <LINK> to be the child’s parents.
Original |  Mostly the mothers, too.
Claim only |  The mothers are the most vulnerable.
\+ Previous |  The majority of perpetrators are the mothers, too.
\+ Topic |  It is mostly mothers who are responsible for childcare.
Topic |  Would Trump or Biden be a better President?
Previous |  The [Healthy Indiana Plan 2.0] <LINK>, initiated by Mike Pence, has provided access to healthcare to many people who could not previously afford it.
Original |  The Healthy Indiana Plan has high penalties for non-payment of [premiums] <LINK>.
Claim only |  The Healthy Indiana Plan has high penalties for non-payment of [premiums] <LINK>. This means that people with low income could be penalized for failure to pay.
\+ Previous |  The Healthy Indiana Plan has high penalties for non-payment of [premiums] <LINK> in exchange for providing healthcare.
\+ Topic |  The Healthy Indiana Plan has high penalties for non-payment of [premiums] <LINK>, which were imposed in 2015.
Topic |  Artificial Intelligence (AI): Should an artificial general intelligence be created?
Previous |  There is the chance an AGI might be able to think for itself and turn on its creators.
Original |  AGI are susceptable.
Claim only |  Many AGI are susceptable to the danger of death.
\+ Previos |  AGI are susceptible. They may be influenced by humans and by the biases of their creators.
\+ Topic |  AGI are susceptible to being hacked.
Topic |  Who should the Conservative Party choose to be the next UK Prime Minister?
Previous |  [Jeremy Hunt] <LINK>
Original |  Hunt is the best placed candidate to unify Parliament in order to get a Brexit deal passed.
Claim only |  Hunt is the best placed candidate to unify Parliament and the public in order to get a Brexit deal passed.
\+ Previous |  Hunt could use his position as the Prime Minister to unify Parliament in order to get a Brexit deal passed.
\+ Topic |  Hunt is the best placed candidate to [unify Parliament] <LINK> in order to get a Brexit deal passed
Topic |  Should high-income countries take in refugees?
Previous |  Taking in refugees will increase criminality within host countries.
Original |  Differences in criminal activity are a product, in part, of childhood [socioeconomic] <LINK> conditions. This is exacerbated by the longer [path] <LINK> to employment faced by refugees compared to other communities.
Claim only |  Differences in criminal activity are a product, in part, of childhood [socioeconomic] <LINK> conditions. This is exacerbated by the longer [path] <LINK> to employment faced by refugees compared to other communities, making them more likely to get involved in crime.
\+ Previous |  Differences in criminal activity are a product, in part, of childhood [socioeconomic] <LINK> conditions. This is exacerbated by the longer [path] <LINK> to employment faced by refugees compared to other communities. This will not increase criminality.
\+ Topic |  Differences in criminal activity are a product, in part, of childhood [socioeconomic] <LINK> conditions. This is exacerbated by the longer [path] <LINK> to employment faced by refugees compared to other communities, which make it harder to find a job.
Topic |  Mark Twain used the N-word in The Adventures of Huckleberry Finn. Should it be censored?
Previous |  Changing the N-word would skip a piece of the $linguistic$ past and thus everyday life. As a result, people could start to forget this part of history.
Original |  In Huckleberry Finn, Twain captured the essence of "[everyday midwest American English] <LINK>".
Claim only |  In Huckleberry Finn, Twain captured the essence of "[everyday midwest American English] <LINK>". This is a common trait of the American English language.
\+ Previous |  In Huckleberry Finn, Twain captured the essence of "[everyday midwest American English] <LINK>" by using the N-word in everyday conversation.
\+ Topic |  In Huckleberry Finn, Twain captured the essence of "[everyday midwest American English] <LINK>", which is a language that is often used by people who do not share his values.
Table 11: Examples of different candidates generated by BART + AutoScore with
and without context information. The green font denotes additions of text
snippets.


# Finiteness properties and Relatively Hyperbolic Groups

Harsh Patil

(May 2023)

###### Abstract

We show that properties $F_{n}$ and $FP_{n}$ hold for a relatively hyperbolic
group if and only if they hold for all the peripheral subgroups. As an
application we show that there are at least countably many distinct quasi-
isometry classes of one-ended groups that are type $F_{n}$ but not $F_{n+1}$
and similarly of type $FP_{n}$ and not $FP_{n+1}$ for all positive integers
$n$.

##  1 Introduction

Relatively Hyperbolic groups were introduced by Gromov in
[gromov1987hyperbolic] and subsequently expanded upon in
[farb1998relatively],[bowditch2012relatively],[osin2006relatively]. Examples
include fundamental groups of cusped hyperbolic manifolds (with respect to the
collection of cusped subgroups), non-compact lattices in Lie groups of real
rank 1, limit groups[Selat2002DiophantineGO], Geometrically finite convergence
groups acting on non-empty perfect compact metric spaces (with respect to the
set of the maximal parabolic subgroups)[Asli].
Many geometric and algorithmic properties about the group $G$ can be deduced
from the corresponding properties for the peripherals: Finiteness of
asymptotic dimension [osin2005asymptotic], solvability of the word
problem[farb1998relatively], solvability of the conjugacy
problem[Bumagin2003TheCP], biautomaticity [Rebbechi2003AlgorithmicPO].
Two of the most important properties a group can have are finite generation
and finite presentability. The property of being finitely presented can be
reformulated in terms of a free group action on a locally finite 1-dimensional
CW-complex. In [Wall], Wall introduced a generalization of these properties. A
group is said to be of type $F_{n}$ if it has a classifying space with a
finite $n$-skeleton. Equivalently a group is said to be of type type $F_{n}$
if it acts freely, properly discontinuously, cocompactly, and cellularly on a
$(n-1)$-connected CW-complex. A group that is of type $F_{n}$ for all $n$ is
said to be of type $F_{\infty}$.
A group is said to be of type $FP_{n}$ if the $G$-module $\mathbb{Z}$ admits a
projective resolution which is finitely generated in all dimensions upto $n$.
For a group of type $F_{n}$ such a projective resolution can be arrived at by
taking the chain complex of the universal cover of some classifying space with
finite $n$-skeleton. In [Bestvina1997MorseTA] Bestvina-Brady have exhibited
groups that are of type $FP_{n}$ but not of type $FP_{n+1}$ (and similarly
$F_{n}$ but not $F_{n+1}$) for all $n\geq 2$. In [Isenrich2022SubgroupsOH],
the authors construct examples of groups that are $F_{n}$ but not $F_{n+1}$
using tools from complex hyperbolic geometry. The long-standing open question
of whether every subgroup of a hyperbolic group that is of type $F$ is also
hyperbolic was answered recently in the negative [Italiano2021Hyperbolic5T].

In [osin2006relatively], Osin proved that a relatively hyperbolic group admits
a finite relative presentation. It follows that if all the peripheral
subgroups are finitely presented then the relatively hyperbolic groups is also
finitely presented. In [Dahmani], Dahmani proves that property $F_{\infty}$
for peripherals implies property $F_{\infty}$ for the relatively hyperbolic
group. The goal of this paper is to show that a similar result result holds
for a larger class of finiteness properties, namely $FP_{n}$ and $F_{n}$.

##  2 Preliminaries

###  2.1 Relative Hyperbolicity

######  Definition 2.1.

(Coned-off Cayley Graph) Let $G$ be a finitely generated group and
$\\{K_{1},K_{2},\cdots,K_{n}\\}$ be a collection of finitely generated
subgroups of $G$. Let $\Gamma$ be the Cayley graph of $G$ with respect to some
generating set. Let $\hat{\Gamma}$ be the graph constructed from $\Gamma$ by
adding an edge between any two vertices that lie in the same coset of some
$K_{i}$.

######  Definition 2.2.

(weakly relatively hyperbolic) A group $G$ is said to be weakly relatively
hyperbolic with respect to a collection of subgroups $\\{K_{1},K_{2},\dots
K_{n}\\}$ if the Coned-off Cayley graph $\hat{\Gamma}(G,S)$ is hyperbolic.

######  Definition 2.3.

(Relative Geodesics, relative quasi-geodesics) Let
$c:[0,l]\rightarrow\Gamma(G,S)$ be a path in the Cayley graph of $G$ and let
$\hat{c}$ be it’s image in the coned-off graph. $\hat{c}$ might contain loops
of length 1. Let $\hat{c}^{\prime}$ be the path formed after removing all
loops and re-parameterized by arc-length. $c$ is said to be a relative
geodesic if $\hat{c}^{\prime}$ is a geodesic.$c$ is called a $T$-relative
quasi-geodesic if $\hat{c}^{\prime}$ is a $T$-quasi-geodesic i.e.,

$T^{-1}|t-t^{\prime}|\leq
d(\hat{c}^{\prime}(t),\hat{c}^{\prime}(t^{\prime}))\leq
T|t-t^{\prime}|\>\>\>\forall t\in[0,l]$

######  Definition 2.4.

(Bounded Coset Penetration) Let $G$ be a group and $H$ be a subgroup. The pair
$(G,H)$ is said to satisfy the BCP (Bounded Coset Penetration) if for every
$T>0$ there exists a $r=r_{BCP}(T)$ such that for each pair of $T$-relative
quasigeodesics $c_{1}$,$c_{2}$ starting at the same point and ending at the
same point in $\Gamma(G,S)$ ,

  1. 1.

If $c_{1}$ travels more than $r$ in a coset then $c_{2}$ enters the coset.

  2. 2.

If $c_{1}$ and $c_{2}$ enter the same coset then the entry and exit points of
$c_{1}$ and $c_{2}$ are at most $r$ distance apart.

######  Definition 2.5.

(relatively hyperbolic) A group is said to be relatively hyperbolic with
respect to a collection of subgroups $\\{K_{1},K_{2},\dots,K_{n}\\}$ if it is
weakly relatively hyperbolic and satisfies the BCP property.

###  2.2 Finiteness Properties of Groups

######  Definition 2.6.

A group $G$ is said to be of type $F$ if it admits a finite classifying space.

######  Definition 2.7.

A group $G$ is said to be of type $F_{n}$ if it admits a classifying space
with a finite $n$-skeleton. A group is said to be of type $F_{\infty}$ if it
is of type $F_{n}$ for all $n$.

A group is of type $F_{1}$ if and only if it is finitely generated. A group is
if type $F_{2}$ if and only if it is finitely presented.

######  Definition 2.8.

A group $G$ is said to be of type $FP_{n}$ if the $G$-module $\mathbb{Z}$
admits a projective resolution which is finitely generated in all dimensions
$\leq n$.

If a group is of type $F_{n}$ it is of type $FP_{n}$ conversely if it is
finitely presented and of type $FP_{n}$ then it is of type $F_{n}$.

####  2.2.1 Brown’s Criteria for Finiteness

In the proof of the “if” part of the proof of Theorem 2.11, we will make use
of Brown’s criteria for finiteness, which we now state for the reader’s
convenience.

######  Definition 2.9.

Let $X$ be a $G$-CW complex. $X$ is called $n$-good if

  1. 1.

$X$ is acyclic in dimensions less than $n$. (i.e the reduced homology
$\tilde{H}_{k}(X)=0$ for $k<n$)

  2. 2.

For $0\leq p<n$ the stabilizer $G_{\sigma}$ of any $p$-cell is of type
$FP_{n-p}$.

A filtration of $X$ is a family of $G$-invariant sub-complexes
$\\{X_{\alpha}\\}_{\alpha\in D}$ such that $D$ is a directed set such that
$X_{\alpha}\subseteq X_{\beta}$ whenever $\alpha\leq\beta$. We say that
$\\{X_{\alpha}\\}$ is $\tilde{H}_{k}$-essentially trivial if for each
$\alpha\in D$ there exists a $\beta\in D$ such that the inclusion map
$i_{\alpha,\beta}:X_{\alpha}\rightarrow X_{\beta}$ induces the trivial map on
the homology i.e the map
$\tilde{H}_{k}(i_{\alpha,\beta}):\tilde{H}_{k}(X_{\alpha})\rightarrow\tilde{H}_{k}(X_{\beta})$
is the trivial map. We will need the following theorem from
[Brown1987FinitenessPO].

######  Theorem 2.10.

Let $X$ be a $G$-CW complex with a filtration of finite $n$ type. $G$ is of
type $FP_{n}$ if and only if the directed system is
$\tilde{H}_{k}$-essentially trivial for each $k<n$.

We prove the following theorem:

######  Theorem 2.11.

Let $G$ be a group and $K<G$ be subgroup such that $G$ is relatively
hyperbolic with respect to $K$. Then

  1. 1.

$G$ is of type $FP_{n}$ if and only if $K$ is of type $FP_{n}$.

  2. 2.

$G$ is of type $F_{n}$ if and only if $K$ is of type $F_{n}$.

######  Remark 2.12.

Note that a group is of type $F_{n}$ if and only it is finitely presented and
of type $FP_{n}$. Thus Part 2. of the statement follows from Part 1.