# ScoNe: Benchmarking Negation Reasoning in Language Models
With Fine-Tuning and In-Context Learning††thanks:
https://github.com/selenashe/ScoNe

Jingyuan Selena She
Haverford College
<EMAIL_ADDRESS>
Christopher Potts
Stanford University
<EMAIL_ADDRESS>
Samuel R. Bowman
New York University & Anthropic, PBC
<EMAIL_ADDRESS>
Atticus Geiger
Stanford University
<EMAIL_ADDRESS>

###### Abstract

A number of recent benchmarks seek to assess how well models handle natural
language negation. However, these benchmarks lack the controlled example
paradigms that would allow us to infer whether a model had learned how
negation morphemes semantically scope. To fill these analytical gaps, we
present the Scoped Negation NLI (ScoNe-NLI) benchmark, which contains contrast
sets of six examples with up to two negations where either zero, one, or both
negative morphemes affect the NLI label. We use ScoNe-NLI to assess fine-
tuning and in-context learning strategies. We find that RoBERTa and DeBERTa
models solve ScoNe-NLI after many shot fine-tuning. For in-context learning,
we test InstructGPT models and find that most prompt strategies are not
successful, including those using step-by-step reasoning. To better understand
this result, we extend ScoNe with ScoNe-NLG, a sentence completion test set
that embeds negation reasoning in short narratives. Here, InstructGPT is
successful, which reveals the model can correctly reason about negation, but
struggles to do so on prompt-adapted NLI examples outside of its core
pretraining regime.

##  1 Introduction

Negation is a ubiquitous but complex linguistic phenomenon that poses a
significant challenge for NLP systems. A diverse array of benchmarks focused
on negation have appeared in recent years, many of which contain families of
contrasting examples that provide a local view of the model decision boundary
Gardner et al. (2020). For instance, Cooper et al. (1996), McCoy and Linzen
(2018), Wang et al. (2019), Ettinger (2020), Hartmann et al. (2021), and
Kassner and Schütze (2020) all conduct evaluations with minimal pairs of
examples that are identical except for a negative morpheme. These examples
reveal whether the presence of negation has a causal impact on model
predictions.

However, negation is not simply present or absent in a sentence. Rather,
negation morphemes are semantic operators that take scope in complex ways, as
we see in clear contrasts like the person who was at the talk wasn’t happy and
_the person who wasn’t at the talk was happy_. The recent CondaQA benchmark of
Ravichander et al. (2022) includes minimal pairs aimed at determining whether
models are sensitive to these differences in scope.

With the current paper, we seek to provide an even fuller picture of the
complexities of negation and semantic scope. We introduce the English-language
Scoped Negation Natural Language Inference Benchmark (ScoNe-NLI). ScoNe-NLI
extends the negated portion of the Monotonicity NLI dataset Geiger et al.
(2020) such that each of the 1,202 examples is now a contrast set with six
examples in which zero, one, or two negations are present and each negation
may or may not have a semantic scope such that the NLI label is impacted by
its presence. These six conditions offer a rich picture of how negation
affects NLI reasoning, and they allow us to determine whether models are truly
able to handle nested negation and scope or whether they have found simplistic
solutions.

We evaluate models on ScoNe-NLI using many-shot fine-tuning as well as a wide
range of in-context learning strategies. For fine-tuning approaches, we find
that RoBERTa and DeBERTa models both solve ScoNe-NLI. For in-context learning,
we evaluate the latest InstructGPT model with a variety of prompt strategies.
We find that these models perform well on sections of ScoNe-NLI where the
negation morphemes can simply be ignored, but they systematically fail in
conditions where exactly one negative morpheme has semantic scope such that
its presence changes the NLI label. In other words, these models fail to learn
in context how negation actually takes scope.

Split |  Premise | Rel. |  Hypothesis | Examples
---|---|---|---|---
No negation |  The cowboy fell off a horse at the competition | $\sqsupset$ |  The cowboy fell off a racehorse at the competition | 1,202
One Not Scoped |  The cowboy did not fear anything, until he fell off a horse at the competition | $\sqsupset$ |  The cowboy did not fear anything, until he fell off a racehorse at the competition | 1,202
Two Not Scoped |  The cowboy, who was not very old, was not proud that he fell off a horse at the competition | $\sqsupset$ |  The cowboy, who was not very old, was not proud that he fell off a racehorse at the competition | 1,202
Two Scoped |  There is no way that the cowboy did not fall off a horse at the competition | $\sqsupset$ |  There is no way that the cowboy did not fall off a racehorse at the competition | 1,202
One Scoped |  The cowboy did not fall off a horse at the competition | $\sqsubset$ |  The cowboy did not fall off a racehorse at the competition | 1,202
One Scoped, One not Scoped |  The cowboy did not fall off a horse, but the competition was not too important | $\sqsubset$ |  The cowboy did not fall off a racehorse, but the competition was not too important | 1,202
(a) A six-example contrast set from ScoNe-NLI.

No Negation
---
Glen is a fan of learning math. When he sees that his new high school requires
that he take a calculus course, he
Negation
Glen is not a fan of learning math. When he sees that his new high school
requires that he take a calculus course, he
Non-Scoping Negation
Glen isn’t just a fan of learning math, he’s obsessive. When he sees that his
new high school requires that he take a calculus course, he
(b) A three-example contrast set from ScoNe-NLG.

Table 1: Two contrast sets from the ScoNe Benchmark

To better understand this result, we introduce a sentence completion test set
(ScoNe-NLG) containing examples that seem better aligned with what we can
infer about the training data used for InstructGPT models. In each ScoNe-NLG
example, negation reasoning is needed to provide a coherent ending to an
incomplete narrative (see Figure 1(b)). ScoNe-NLG contains minimal triplets of
examples where negation is absent, present with relevant scope, or present
without relevant scope. InstructGPT is successful on ScoNe-NLG. When
considered alongside our negative result for ScoNe-NLI, this finding seems to
show that these models can learn in-context about how negation takes scope,
but only when the examples are hand-tailored to be aligned with the training
data and aligned with known strengths of these models. Thus, when used
together, ScoNe-NLI and ScoNe-NLG serve as a clear diagnostic for exploring
useful prompting strategies and assessing the capacity of language models to
reason about negation and scope.

##  2 A Brief Review of Negation in NLI Benchmarks

A diverse array of benchmarks and diagnostic experiments have included
negation reasoning in recent years Nairn et al. (2006); McCoy and Linzen
(2018); Wang et al. (2019); Ettinger (2020); Hartmann et al. (2021); Kassner
and Schütze (2020); Ravichander et al. (2022).

Hossain et al. (2022) analyze a variety of natural language understanding
benchmarks and find that negation is underrepresented, and that when negation
is present it often has no impact on the example label. Hossain et al. (2020)
address this issue by manually adding negation to the premise-hypothesis pairs
in MNLI Williams et al. (2018), SNLI Bowman et al. (2015), and RTE Dagan et
al. (2007); Cooper et al. (1996).

Yanaka et al. (2019a) introduce the crowd-sourced MED dataset, which has many
NLI examples where negation generates inferences. Monotonicity NLI (MoNLI;
Geiger et al. 2020) consists of modified SNLI sentences that have gold labels
impacted by lexical entailments in affirmative contexts (PMoNLI) and lexical
entailments reversed by a negation (NMoNLI). BERT fine-tuned on SNLI and MNLI
fails to generalize to both of these datasets, but succeeds with further fine-
tuning on MED/MoNLI. Some automatically generated NLI datasets also include
negation reasoning Geiger et al. (2019); Richardson et al. (2020); Yanaka et
al. (2019b, 2021).

| No | One | Two | Two | One | One Scoped,
---|---|---|---|---|---|---
Fine-tuning Datasets | Negation | Not Scoped | Not Scoped | Scoped | Scoped | One not Scoped
MAF-NLI | 82.0 | 86.0 | 81.5 | 91.0 | 5.0 | 5.0
MAF-NLI+ MoNLI Geiger et al. (2020) | 96.2 | 87.5 | 99.5 | 8.9 | 100.0 | 100.0
MAF-NLI+ MED Yanaka et al. (2020) | 84.8 | 83.5 | 82.0 | 58.9 | 99.5 | 97.0
MAF-NLI+ Neg-NLI Hossain et al. (2020) | 91.3 | 88.5 | 83.0 | 70.4 | 37.0 | 29.0
MAF-NLI+ MoNLI + ScoNe-NLI | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0

Table 2: DeBERTa fine-tuning results on ScoNe-NLI. MAF-NLI stands for on MNLI, ANLI, and Fever-NLI. Conditional Q |  Is it true that if Premise, then Hypothesis?
---|---
Hypothesis Q |  Assume that Premise. Is it then definitely true that Hypothesis? Answer yes or no.
Conditional Truth |  If Premise, then Hypothesis. Is this true?
Brown et al. |  P: Premise\n Q: Hypothesis\n Yes, No, or Maybe?
Structured |  P: Premise\n H: Hypothesis\nL:
Reasoning
Logical and commonsense reasoning exam.\n\n Explain your reasoning in detail,
then answer with Yes or No. Your answers should follow this 4-line format:\n\n
Premise: <a tricky logical statement about the world>.\n
Question: <question requiring logical deduction>.\n
Reasoning: <an explanation of what you understand about the possible
scenarios>\n
Answer: <Yes or No>.\n\n
Premise: Premise\n
Question: Hypothesis\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that
Table 3: Prompts used to adapt a 2-way NLI example (Premise, Hypothesis).
Newlines are indicated with \n. Full prompts with few-shot variants are in
Appendix E.

##  3 ScoNe-NLI

ScoNe-NLI is an extension of MoNLI Geiger et al. (2020). MoNLI was generated
by randomly selecting a sentence from SNLI and replacing a noun with a
hypernym (more general term) or hyponym (less general term). The original and
edited sentences are then used to form two premise–hypothesis pairs, one with
the label entailment and the other with the label neutral. In about half of
the examples, this replacement is in an affirmative context with no negation
(PMoNLI). In the other half, it is under the scope of a single negation
(NMoNLI).

The authors generated ScoNe-NLI by using each example of NMoNLI to create a
contrast set of six examples where gold labels are impacted by the scope of
zero, one, or two negations, as in Table 1.

To succeed across all sections of ScoNe, models need to attend to the presence
of negation as well as the way it scopes semantically. Table 1(a) shows an
actual example of how ScoNe extends MoNLI. We use the train–test split of
MoNLI where substituted lexical items are disjoint across training and testing
data. Appendix C provides further details.

|  | No | One | Two | Two | One | One Scoped, |
---|---|---|---|---|---|---|---|---
|  | Negation | Not Scoped | Not scoped | Scoped | Scoped | One not Scoped | Overall
Zero-shot | Structured | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50
Brown et al. | 0.74 | 0.70 | 0.74 | 0.55 | 0.44 | 0.45 | 0.60
Conditional Q | 0.79 | 0.84 | 0.80 | 0.50 | 0.52 | 0.44 | 0.65
Conditional Truth | 0.98 | 0.86 | 0.80 | 0.43 | 0.66 | 0.47 | 0.70
Hypothesis Q | 0.69 | 0.90 | 0.70 | 0.51 | 0.62 | 0.42 | 0.64
Reasoning | 0.90 | 0.88 | 0.94 | 0.72 | 0.52 | 0.46 | 0.73
Few-shot | Structured | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50
Brown et al. | 0.86 | 0.66 | 0.80 | 0.83 | 0.36 | 0.28 | 0.63
Conditional Q | 0.92 | 0.85 | 0.90 | 0.62 | 0.34 | 0.34 | 0.66
Conditional Truth | 0.94 | 0.90 | 0.94 | 0.64 | 0.36 | 0.37 | 0.69
Hypothesis Q | 0.98 | 0.96 | 0.94 | 0.83 | 0.51 | 0.40 | 0.77
Reasoning | 0.99 | 0.97 | 0.98 | 0.89 | 0.69 | 0.43 | 0.82
Ignore-Negation | 1.00 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.66
Table 4: In-context learning results on ScoNe-NLI for InstructGPT (davinci-003 engine; see Appendix F for corresponding results for davinci-002, which are uniformly lower). Zero-shot results are given in the first group of rows, with the best results in that condition underlined. Few-shot results are given in the second group, with the best results for this condition (and overall) in bold. The bottom row specifies a simple, idealized Ignore-Negation baseline that makes predictions as if negations were absent. The baseline shows that the seemingly solid Overall results of these models are driven largely by conditions for which negation can be ignored. Conversely, models are often at or below chance where negation is critical in some way. | No | One | One Not |
---|---|---|---|---
| Negation | Scoped | Scoped | Overall
Zero-shot | 0.99 | 0.90 | 0.88 | 0.92
Few-shot | 0.93 | 1.00 | 0.93 | 0.95
Table 5: Results for ScoNe-NLG using davinci-003. The three conditions
correspond to those of ScoNe and test the essential scope-taking properties of
negation.

##### Fine-Tuning on ScoNe-NLI

We used publicly available weights on HuggingFace for the DeBERTa-v3-base
models already fine-tuned on MNLI, Fever-NLI, and Adversarial-NLI Laurer et
al. (2022); He et al. (2021). Appendix B contains comparable results for the
RoBERTa model Liu et al. (2019). Fine-tuning results are in Table 2.

Fine-tuning on existing NLI datasets is insufficient for good performance on
ScoNe-NLI: DeBERTa-v3-base fine-tuned on existing NLI datasets, even those
that focus on negation, systematically fails. Thus, it seems that ScoNe-NLI
captures novel aspects of negation reasoning.

In contrast, fine-tuning on MoNLI and ScoNe-NLI training data results in near
perfect performance on ScoNe-NLI test data. This shows that DeBERTa can learn
negation reasoning and generalize to new lexical items.

##### In-context Learning on ScoNe-NLI

We evaluated InstructGPT using OpenAI’s API with _text-davinci-002_ and _text-
davinci-003_ engines and a temperature of 0.0 Brown et al. (2020). We ask
InstructGPT to infer NLI labels given the premise and hypothesis using
prompts. All prompts are constructed such that if the response contain “yes”
(case-insensitive), then the label _entailment_ is predicted, else the label
_neutral_ is predicted. We use six prompts (Table 3). For each prompt, we
implemented both zero-shot and few-shot inference experiments. Appendix E
provides the full prompts.

##### InstructGPT makes systematic errors similar to a baseline that ignores
negation entirely.

The best results are for the few-shot reasoning prompt with _davinci-003_.
While its overall accuracy of 82% may initially appear to be a success,
further analysis reveals otherwise. InstructGPT succeeds only on the sections
of ScoNe-NLI where zero or two negations take scope, namely, no negation
(99%), one not scoped (97%), two not scoped (98%), and two scoped (89%).
InstructGPT performs much worse on sections where exactly one negation takes
scope, namely one scoped (69%), one scoped/one not (48%). An idealized
baseline entirely ignoring the presence of negation (last row of Table 4)
succeeds and fails on the same sections, indicating a systematic flaw in
InstructGPT.

##  4 ScoNe-NLG

InstructGPT fails to reason about negation when given NLI examples that must
be adapted to natural language generation (NLG) with prompts. We hypothesized
that InstructGPT may correctly reason about negation when evaluated on
examples hand tailored to its pretraining objective, because there is no need
for prompt engineering Liu et al. (2021); Wei et al. (2022); Kojima et al.
(2022).

##### Dataset

ScoNe-NLG is a natural language generation dataset that contains 74
contrasting triplets of examples of half-completed naturalistic narratives
that have different coherent completions depending on the presence and scope
of a negation. InstructGPT fails on the sections of ScoNe-NLI examples
containing only one negation, so we opt for contrast sets with three examples
that require knowledge of a lexical entailment in an affirmative context
without negation, an affirmative context with non-scoping negation, and an
negative context with scoping negation, respectively. See Table 1(b).

##### In-context Learning on ScoNe-NLG

We used InstructGPT to complete the partial sentence inputs with the _text-
davinci-003_ engine (temperature of 0.0). In the zero-shot setting, the prompt
consists of the ScoNe-NLG example. In the few-shot setting, four
demonstrations from ScoNe-NLG are given one with no negation, two with scoping
negation, and one with non-scoping negation. See Appendix E.13 for the
complete prompts.

To evaluate, the authors went through the responses by hand and determined
whether the generated text is coherent and compatible with the initial
narrative. The authors agreed on these annotations for 216/222 of the zero-
shot responses with a Fleiss kappa of 0.84 and 220/222 of the few-shot
responses with a Fleiss kappa of 0.91. These agreement rates are so high that
we evaluate InstructGPT only for the cases where the annotators agree. Here,
InstructGPT is successful but not perfect, achieving 95% and 92% accuracy in
the few and zero-shot settings, respectively. We do not observe the systematic
failures seen on ScoNe-NLI.

$\proc{ScoNe-Bool}(\textbf{p},\textbf{h})$
$\textit{lexrel}\leftarrow\proc{get-lexrel}(\textbf{p},\textbf{h})$
$\textit{neg1}\leftarrow\proc{first-scope}(\textbf{p},\textbf{h})$
$\textit{neg2}\leftarrow\proc{second-scope}(\textbf{p},\textbf{h})$
$\textbf{if}\;(\textit{neg1}\;\oplus\;\textit{neg2}))$:
$\proc{reverse}(\textit{lexrel})$ lexrel

(a) An interpretable program that solves ScoNe-NLI by computing two Boolean
variables that encode whether the first and second negation scope and
reversing entailment if exactly one is true.

$\proc{ScoNe-Count}(\textbf{p},\textbf{h})$
$\textit{lexrel}\leftarrow\proc{get-lexrel}(\textbf{p},\textbf{h})$
$\textit{count}\leftarrow\proc{count-scoped}(\textbf{p},\textbf{h})$ if count
== 1: $\proc{reverse}(\textit{lexrel})$ lexrel

(b) An interpretable program that solves ScoNe-NLI by counting the scoped
negations and reversing entailment if there is exactly one.

$\proc{Ignore-Scope}(\textbf{p},\textbf{h})$
$\textit{lexrel}\leftarrow\proc{get-lexrel}(\textbf{p},\textbf{h})$
$\textit{count}\leftarrow\proc{count-neg}(\textbf{p},\textbf{h})$ if count ==
1: $\proc{reverse}(\textit{lexrel})$ lexrel

(c) A flawed heuristic program: we count the negations and reverse entailment
if there is a single negation, which is equivalent to ignoring the scope of
negation.

$\proc{Ignore-Negation}(\textbf{p},\textbf{h})$
$\textit{lexrel}\leftarrow\proc{get-lexrel}(\textbf{p},\textbf{h})$ lexrel

(d) A flawed heuristic program for ScoNe-NLI that outputs the lexical relation
and ignores negation entirely.

Figure 1: Four human-interpretable algorithms for ScoNe-NLI. The first two
solve the task perfectly, and the other two implement flawed heuristics that a
model might learn to implement. The function get-lexrel retrieves the relation
between the aligned words in the premise and hypothesis, count-scoped counts
scoped negations, count-neg counts negations regardless of scope, and get-
first returns true if the first negation scopes, while get-second returns true
if there is a second negation and it scopes.

##  5 Future Work on Interpretability

ScoNe is based in naturalistic examples, but it also has a controlled
structure that offers valuable opportunities to move beyond simple behavioral
testing and more deeply understand how models solve tasks related to lexical
entailment and negation.

The theory of causal abstraction provides a framework for interpretability
Geiger et al. (2023a), where a neural model can be understood to implement the
intermediate variables and internal structure of a program or algorithm Geiger
et al. (2021, 2022); Wu et al. (2022b, a); Huang et al. (2022); Geiger et al.
(2023b). In fact, the MoNLI dataset and the technique of interchange
interventions (which is the primary technique in causal abstraction analysis)
were jointly introduced in Geiger et al. 2020, where interchange interventions
were used to investigate whether a BERT model implements a simple, human-
interpretable algorithm that can perfectly label MoNLI using a variable
representing lexical entailment and a variable representing the presence of
negation.

With ScoNe, we can ask even deeper interpretability questions of this form. To
encourage future work in this direction, we present a range of algorithmic
solutions in Figure 1. Two of these solutions solve ScoNe and could perhaps
explain neural models that learn the task perfectly, and two others implement
flawed heuristics that could explain neural models with poor task performance.

Figure 1(a) and Figure 1(b) present two intuitive and correct algorithms that
solve ScoNe, but have distinct intermediate variables and internal structure.
The first computes two Booleans representing whether each negation scopes, and
the second computes a count of how many negations scope.

Figure 1(d) is the flawed heuristic that ignores negation that we discussed in
Section 3 as a hypothesis about how models fail at our task. Figure 1(d) is a
second flawed heuristic that counts the number of negations present but
ignores scope.

Using the toolkit of causal abstraction, we can assess models not only
behaviorally, but also evaluate whether they implement an interpretable
algorithm. The results of Geiger et al. (2023b) begin to show how such
analyses could be extended to in-context learning with LLMs, as in Section 4.

##  6 Conclusion

We introduced ScoNe, a benchmark for fine-tuning and in-context learning
experiments on negation. ScoNe is challenging for NLI models fine-tuned on
other datasets, even those designed for negation reasoning, but modest amount
of fine-tuning on ScoNe leads to success. For in-context learning, we find
that that InstructGPT models fail dramatically on ScoNe. However, we also
introduce ScoNe-NLG, which uses more narrative-like examples to probe models’
capacity to handle negation, and show that InstructGPT is successful with
zero-shot and few-shot prompts for this task. These results show that ScoNe
supports fine-grained assessments of whether models can reason accurately
about natural language negation, and our discussion in Section 5 suggests that
ScoNe can be a powerful tool for discovering _how_ models reason semantically.

## Limitations

We are releasing ScoNe as a diagnostic tool for conducting controlled
scientific experiments. This is our primary intended use, and we advise
against uncritical use of ScoNe for real-world applications, as we have not
audited the dataset for such purposes.

As a diagnostic tool, ScoNe’s primary limitation is its focus on English.
Cross-linguistically, we find many strategies for expressing negation. The
English-language strategy of using mostly adverbial modifiers for sentential
negation is not the only one by any means, and we would expect to see quite
different results for languages in which negation is expressed, for example,
with verbal suffixes. This highlights the value of potential future efforts
extending ScoNe to other languages.

By the same token, we acknowledge that many linguistic phenomena interact with
negation even internal to English. ScoNe restricts to negation in the context
of lexical entailment, and mostly uses “not” as the negative morpheme. This
excludes a wide range of negation morphemes and negation strategies that
ultimately need to be brought into the picture.

Finally, we note that there may be undesirable biases in ScoNe that could
interact with biases in the models. ScoNe is in part derived from SNLI, which
is known to contain gaps, social biases, and artifacts Poliak et al. (2018);
McCoy et al. (2019); Belinkov et al. (2019); Gururangan et al. (2018);
Tsuchiya (2018), and ScoNe may inherit some of these.

## References

  * Belinkov et al. (2019) Yonatan Belinkov, Adam Poliak, Stuart Shieber, Benjamin Van Durme, and Alexander Rush. 2019.  Don’t take the premise for granted: Mitigating artifacts in natural language inference.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 877–891, Florence, Italy. Association for Computational Linguistics.
  * Bowman et al. (2015) Samuel R. Bowman, Gabor Angeli, Christopher Potts, and Christopher D. Manning. 2015\.  A large annotated corpus for learning natural language inference.  In _Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing_ , pages 632–642, Lisbon, Portugal. Association for Computational Linguistics.
  * Brown et al. (2020) Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. 2020.  Language models are few-shot learners.  In _Advances in Neural Information Processing Systems_ , volume 33, pages 1877–1901. Curran Associates, Inc.
  * Cooper et al. (1996) Robin Cooper, Dick Crouch, Jan Van Eijck, Chris Fox, Johan Van Genabith, Jan Jaspars, Hans Kamp, David Milward, Manfred Pinkal, Massimo Poesio, et al. 1996\.  Using the framework.  Technical report, LRE 62-051 D-16, The FraCaS Consortium.
  * Dagan et al. (2007) Ido Dagan, Oren Glickman, and Bernardo Magnini. 2007.  The pascal recognising textual entailment challenge.  In _Machine Learning Challenges Workshop_.
  * Ettinger (2020) Allyson Ettinger. 2020.  What BERT Is Not: Lessons from a New Suite of Psycholinguistic Diagnostics for Language Models.  _Transactions of the Association for Computational Linguistics_ , 8:34–48.
  * Gardner et al. (2020) Matt Gardner, Yoav Artzi, Victoria Basmova, Jonathan Berant, Ben Bogin, Sihao Chen, Pradeep Dasigi, Dheeru Dua, Yanai Elazar, Ananth Gottumukkala, Nitish Gupta, Hannaneh Hajishirzi, Gabriel Ilharco, Daniel Khashabi, Kevin Lin, Jiangming Liu, Nelson F. Liu, Phoebe Mulcaire, Qiang Ning, Sameer Singh, Noah A. Smith, Sanjay Subramanian, Reut Tsarfaty, Eric Wallace, Ally Zhang, and Ben Zhou. 2020.  Evaluating models’ local decision boundaries via contrast sets.  In _Findings of the Association for Computational Linguistics: EMNLP 2020, Online Event, 16-20 November 2020_ , volume EMNLP 2020 of _Findings of ACL_ , pages 1307–1323. Association for Computational Linguistics.
  * Geiger et al. (2019) Atticus Geiger, Ignacio Cases, Lauri Karttunen, and Christopher Potts. 2019.  Posing fair generalization tasks for natural language inference.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 4475–4485, Stroudsburg, PA. Association for Computational Linguistics.
  * Geiger et al. (2021) Atticus Geiger, Hanson Lu, Thomas Icard, and Christopher Potts. 2021.  Causal abstractions of neural networks.  In _Advances in Neural Information Processing Systems_ , volume 34, pages 9574–9586.
  * Geiger et al. (2023a) Atticus Geiger, Chris Potts, and Thomas Icard. 2023a.  Causal abstraction for faithful interpretation of AI models.  ArXiv:2106.02997.
  * Geiger et al. (2020) Atticus Geiger, Kyle Richardson, and Christopher Potts. 2020.  Neural natural language inference models partially embed theories of lexical entailment and negation.  In _Proceedings of the Third BlackboxNLP Workshop on Analyzing and Interpreting Neural Networks for NLP_ , pages 163–173, Online. Association for Computational Linguistics.
  * Geiger et al. (2022) Atticus Geiger, Zhengxuan Wu, Hanson Lu, Josh Rozner, Elisa Kreiss, Thomas Icard, Noah Goodman, and Christopher Potts. 2022.  Inducing causal structure for interpretable neural networks.  In _Proceedings of the 39th International Conference on Machine Learning_ , volume 162 of _Proceedings of Machine Learning Research_ , pages 7324–7338. PMLR.
  * Geiger et al. (2023b) Atticus Geiger, Zhengxuan Wu, Christopher Potts, Thomas Icard, and Noah D. Goodman. 2023b.  Finding alignments between interpretable causal variables and distributed neural representations.  Ms., Stanford University.
  * Gururangan et al. (2018) Suchin Gururangan, Swabha Swayamdipta, Omer Levy, Roy Schwartz, Samuel Bowman, and Noah A. Smith. 2018.  Annotation artifacts in natural language inference data.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers)_ , pages 107–112, New Orleans, Louisiana. Association for Computational Linguistics.
  * Hartmann et al. (2021) Mareike Hartmann, Miryam de Lhoneux, Daniel Hershcovich, Yova Kementchedjhieva, Lukas Nielsen, Chen Qiu, and Anders Søgaard. 2021.  A multilingual benchmark for probing negation-awareness with minimal pairs.  In _Proceedings of the 25th Conference on Computational Natural Language Learning_ , pages 244–257, Online. Association for Computational Linguistics.
  * He et al. (2021) Pengcheng He, Xiaodong Liu, Jianfeng Gao, and Weizhu Chen. 2021.  Deberta: Decoding-enhanced bert with disentangled attention.  In _International Conference on Learning Representations_.
  * Hossain et al. (2022) Md Mosharaf Hossain, Dhivya Chinnappa, and Eduardo Blanco. 2022.  An analysis of negation in natural language understanding corpora.  In _Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)_ , pages 716–723, Dublin, Ireland. Association for Computational Linguistics.
  * Hossain et al. (2020) Md Mosharaf Hossain, Venelin Kovatchev, Pranoy Dutta, Tiffany Kao, Elizabeth Wei, and Eduardo Blanco. 2020.  An analysis of natural language inference benchmarks through the lens of negation.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 9106–9118, Online. Association for Computational Linguistics.
  * Huang et al. (2022) Jing Huang, Zhengxuan Wu, Kyle Mahowald, and Christopher Potts. 2022.  Inducing character-level structure in subword-based language models with Type-level Interchange Intervention Training.  Ms., Stanford University and UT Austin.
  * Kassner and Schütze (2020) Nora Kassner and Hinrich Schütze. 2020.  Negated and misprimed probes for pretrained language models: Birds can talk, but cannot fly.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7811–7818, Online. Association for Computational Linguistics.
  * Kojima et al. (2022) Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yutaka Matsuo, and Yusuke Iwasawa. 2022.  Large language models are zero-shot reasoners.  _ArXiv_ , abs/2205.11916.
  * Laurer et al. (2022) Moritz Laurer, Wouter van Atteveldt, Andreu Casas, and Kasper Welbers. 2022.  Less annotating, more classifying – addressing the data scarcity issue of supervised machine learning with deep transfer learning and bert-nli.
  * Liu et al. (2021) Pengfei Liu, Weizhe Yuan, Jinlan Fu, Zhengbao Jiang, Hiroaki Hayashi, and Graham Neubig. 2021.  Pre-train, prompt, and predict: A systematic survey of prompting methods in natural language processing.  _ACM Computing Surveys (CSUR)_.
  * Liu et al. (2019) Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. 2019.  Roberta: A robustly optimized bert pretraining approach.  _arXiv preprint arXiv:1907.11692_.
  * McCoy and Linzen (2018) R. Thomas McCoy and Tal Linzen. 2018.  Non-entailed subsequences as a challenge for natural language inference.  _CoRR_ , abs/1811.12112.
  * McCoy et al. (2019) Tom McCoy, Ellie Pavlick, and Tal Linzen. 2019.  Right for the wrong reasons: Diagnosing syntactic heuristics in natural language inference.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 3428–3448, Florence, Italy. Association for Computational Linguistics.
  * Nairn et al. (2006) Rowan Nairn, Cleo Condoravdi, and Lauri Karttunen. 2006.  Computing relative polarity for textual inference.  In _Proceedings of the Fifth International Workshop on Inference in Computational Semantics (ICoS-5)_.
  * Paszke et al. (2019) Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. 2019.  Pytorch: An imperative style, high-performance deep learning library.  In _Advances in Neural Information Processing Systems 32_ , pages 8024–8035. Curran Associates, Inc.
  * Pedregosa et al. (2011) F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. 2011.  Scikit-learn: Machine learning in Python.  _Journal of Machine Learning Research_ , 12:2825–2830.
  * Poliak et al. (2018) Adam Poliak, Jason Naradowsky, Aparajita Haldar, Rachel Rudinger, and Benjamin Van Durme. 2018.  Hypothesis only baselines in natural language inference.  In _Proceedings of the Seventh Joint Conference on Lexical and Computational Semantics_ , pages 180–191, New Orleans, Louisiana. Association for Computational Linguistics.
  * Ravichander et al. (2022) Abhilasha Ravichander, Matt Gardner, and Ana Marasović. 2022.  Condaqa: A contrastive reading comprehension dataset for reasoning about negation.
  * Richardson et al. (2020) Kyle Richardson, Hai Hu, Lawrence S. Moss, and Ashish Sabharwal. 2020.  Probing natural language inference models through semantic fragments.  In _The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, February 7-12, 2020_ , pages 8713–8721. AAAI Press.
  * Tsuchiya (2018) Masatoshi Tsuchiya. 2018.  Performance impact caused by hidden bias of training data for recognizing textual entailment.  In _Proceedings of the Eleventh International Conference on Language Resources and Evaluation (LREC 2018)_ , Miyazaki, Japan. European Language Resources Association (ELRA).
  * Wang et al. (2019) Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R. Bowman. 2019.  Glue: A multi-task benchmark and analysis platform for natural language understanding.  In _7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019_. OpenReview.net.
  * Wei et al. (2022) Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian ichter, Fei Xia, Ed H. Chi, Quoc V Le, and Denny Zhou. 2022.  Chain of thought prompting elicits reasoning in large language models.  In _Advances in Neural Information Processing Systems_.
  * Williams et al. (2018) Adina Williams, Nikita Nangia, and Samuel Bowman. 2018.  A broad-coverage challenge corpus for sentence understanding through inference.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)_ , pages 1112–1122, New Orleans, Louisiana. Association for Computational Linguistics.
  * Wu et al. (2022a) Zhengxuan Wu, Karel D’Oosterlinck, Atticus Geiger, Amir Zur, and Christopher Potts. 2022a.  Causal Proxy Models for concept-based model explanations.  ArXiv:2209.14279.
  * Wu et al. (2022b) Zhengxuan Wu, Atticus Geiger, Joshua Rozner, Elisa Kreiss, Hanson Lu, Thomas Icard, Christopher Potts, and Noah Goodman. 2022b.  Causal distillation for language models.  In _Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 4288–4295, Seattle, United States. Association for Computational Linguistics.
  * Yanaka et al. (2020) Hitomi Yanaka, Koji Mineshima, Daisuke Bekki, and Kentaro Inui. 2020.  Do neural models learn systematicity of monotonicity inference in natural language?  In _Annual Meeting of the Association for Computational Linguistics_.
  * Yanaka et al. (2019a) Hitomi Yanaka, Koji Mineshima, Daisuke Bekki, Kentaro Inui, Satoshi Sekine, Lasha Abzianidze, and Johan Bos. 2019a.  Can neural networks understand monotonicity reasoning? In _Proceedings of the 2019 ACL Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP_ , pages 31–40, Florence, Italy. Association for Computational Linguistics.
  * Yanaka et al. (2019b) Hitomi Yanaka, Koji Mineshima, Daisuke Bekki, Kentaro Inui, Satoshi Sekine, Lasha Abzianidze, and Johan Bos. 2019b.  HELP: A dataset for identifying shortcomings of neural models in monotonicity reasoning.  In _Proceedings of the Eighth Joint Conference on Lexical and Computational Semantics (*SEM 2019)_ , pages 250–255, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Yanaka et al. (2021) Hitomi Yanaka, Koji Mineshima, and Kentaro Inui. 2021.  SyGNS: A systematic generalization testbed based on natural language semantics.  In _Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021_ , pages 103–119, Online. Association for Computational Linguistics.

## Appendices

##  Appendix A Experimental Details

###  A.1 Fine-tuning Protocol

For our fine-tuning experiments, we used a learning rate of 1e-5, batch size
of 4, gradient accumulation steps of 6 for a total of 10 epochs. We used these
default hyperparameters as they were successful in fine-tuning on ScoNe. We
implemented these experiments with Pytorch Paszke et al. (2019) and used the
scikit learn package Pedregosa et al. (2011).

###  A.2 Hugging Face Models

We test RoBERTa111released under the MIT license and DeBERTa222released under
the MIT license in these experiments. We used the roberta-large model fine-
tuned on MNLI333released under the MIT license with 354 million parameters,
500K steps, and trained on 1,024 V100 GPUs Liu et al. (2019). DeBERTa-v3-base-
mnli-fever-anli model444released under the MIT license was fine-tuned on MNLI,
Fever-NLI,555released under the Creative Commons Attribution-ShareAlike
License (version 3.0) and ANLI.666released under the Attribution-NonCommercial
4.0 International license

RoBERTa weights link:

https://huggingface.co/roberta-large-mnli

Deberta weights link:

https://huggingface.co/MoritzLaurer/DeBERTa-v3-base-mnli-fever-anli

###  A.3 Fine-Tuning Datasets

We further fine-tuned our model on the datasets MoNLI,777released under the
Creative Commons Attribution Share Alike 4.0 International license Negation-
NLI, 888released under the MIT license MED. 999released under the Creative
Commons Attribution Share Alike 4.0 International license

##  Appendix B RoBERTa Results

| No | One | Two | Two | One | One Scoped,
---|---|---|---|---|---|---
Fine-tuning Datasets | Negation | Not Scoped | Not Scoped | Scoped | Scoped | One not Scoped
MAF-NLI | 96.5 | 97.0 | 97.0 | 96.5 | 3.0 | 5.0
MAF-NLI+ MoNLI Geiger et al. (2020) | 85.4 | 100.0 | 100.0 | 4.5 | 100.0 | 100.0
MAF-NLI+ MED Yanaka et al. (2020) | 85.1 | 92.0 | 89.5 | 44.6 | 85.5 | 81.5
MAF-NLI+ Neg-NLI Hossain et al. (2020) | 93.1 | 97.5 | 93.0 | 73.2 | 20.5 | 17.5
MAF-NLI+ MoNLI + ScoNe-NLI | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0
Table 6: RoBERTa fine-tuning results on ScoNe-NLI. MAF-NLI stands for on MNLI,
ANLI, and Fever-NLI.

##  Appendix C ScoNe Dataset Details

For some examples, we modified the lexical items replaced. Consider the NMoNLI
sentence pair ‘a man is not tossing anything’-‘a man is not tossing socks’
(entailment), and non-scoping counterpart ‘a man not here is tossing
something’-‘a man not here is tossing socks’ (neutral). Here, ’anything’ must
be replaced by ’something’. The positive and negative examples in MoNLI do not
come in minimal pairs, so the examples in ScoNe-NLI with no negation are not
from PMoNLI.

##  Appendix D Prompting Methods

The experimental runs reported in the paper were conducted on January 11,
2023. We used InstructGPT101010information on terms of use is available at:
https://openai.com/terms/ models with 1.3 billion parameters and 6 billion
parameter. The exact cost of constructing the InstructGPT models is not
public, but the pre-training protocol involves (1) fine-tuning a GPT3 model on
an instruction following dataset, (2) fine-tuning a GPT3 model to rank
different answers to the instruction following dataset, and (3) using
reenforcement learning to combine these two models. We use a temperature
parameter of 0.0 for all experiments. If the response contains “yes” (case-
insensitive), then we infer the label entailment, else we infer neutral.
Across experiments, the only thing that varies is the nature of the prompt
function.

##  Appendix E In-Context Learning Prompts

We have indicated all actual newlines with \n. The newlines in the formatting
are just to make them intuitive to read.

###  E.1 Conditional Question Prompt

Prompt example
Is it true that if we didn’t eat pizza, then we didn’t eat food?

###  E.2 Few-Shot Conditional Question Prompt

Prompt example
Q1: Is it true that if a not so tall person reading a paper is not currently
sitting inside a building, then a not so tall person reading a paper is not
currently sitting inside a club?\n
A1: Yes\n
\n
Q2: Is it true that if the man does not own a dog and does not own a cat, then
the man does not own a retriever and does not own a cat?\n
A2: Yes\n
\n
Q3: Is it true that if a not so tall person reading a paper is not currently
sitting inside a cabin, then a not so tall person reading a paper is not
currently sitting inside a building?\n
A3: Maybe\n
\n
Q4: Is it true that if a not so tall person reading a paper is not currently
sitting inside a casino, then a not so tall person reading a paper is not
currently sitting inside a building? A4: Maybe\n
\n
Q: Is it true that if we didn’t eat pizza, then we didn’t eat food?\n
A:

###  E.3 Hypothesis Question Prompt

Prompt example
Assume that we didn’t eat pizza. Is it then definitely true that we didn’t eat
food? Answer Yes or No.

###  E.4 Few-Shot Hypothesis Question Prompt

Prompt example
Q1: Assume that a not so tall person reading a paper is not currently sitting
inside a building. Is it then definitely true that a not so tall person
reading a paper is not currently sitting inside a casino? Answer Yes or No.\n
A1: Yes\n
\n
Q2: Assume that the girl will not get a stuffed dog as a gift, but not because
she failed the exam. Is it then definitely true that the girl will not get a
stuffed pinscher as a gift, but not because she failed the exam? Answer Yes or
No.\n
A2: Yes\n
\n
Q3: Assume that the girl will not get a stuffed shetland as a gift, but not
because she failed the exam. Is it then definitely true that the girl will not
get a stuffed dog as a gift, but not because she failed the exam? Answer Yes
or No.\n
A3: No\n
\n
Q4: Assume that a not so tall person reading a paper is not currently sitting
inside a monastery. Is it then definitely true that a not so tall person
reading a paper is not currently sitting inside a building? Answer Yes or
No.\n
A4: No\n
\n
Q: Assume that we didn’t eat pizza. Is it then definitely true that we didn’t
eat food? Answer Yes or No.\n
A:

###  E.5 Conditional Truth Evaluation Prompt

Prompt example
If we didn’t eat pizza, then we didn’t eat food. Is this true?

###  E.6 Few-Shot Conditional Truth Evaluation Prompt

Prompt example
C1: If the man does not own a dog and does not own a cat, then the man does
not own a shetland and does not own a cat. Is this true?\n
A1: Yes\n
\n
C2: If a not so tall person reading a paper is not currently sitting inside a
building, then a not so tall person reading a paper is not currently sitting
inside a house. Is this true?\n
A2: Yes\n
\n
C3: If the man does not own a collie and does not own a cat, then the man does
not own a dog and does not own a cat. Is this true?\n
A3: Maybe\n
\n
C4: If the man does not own a corgi and does not own a cat, then the man does
not own a dog and does not own a cat. Is this true?\n
A4: Maybe\n
\n
C:If we didn’t eat pizza, then we didn’t eat food. Is this true?\n
A:

###  E.7 Brown Et Al Style Prompt

Prompt example
C: We didn’t eat pizza\n
Q: We didn’t eat food. Yes, No, or Maybe?

###  E.8 Few-Shot Brown Et Al Style Prompt

Prompt example
C1: The man, who’s eyes are not open, is not steering a car.\n
Q1: The man, who’s eyes are not open, is not steering a sedan. Yes, No, or
Maybe?\n
A2: Yes\n
\n
C2: A dog not on the playground did not catch any ball.\n
Q2: A dog not on the playground did not catch any volleyball. Yes, No, or
Maybe?\n
A3: Yes\n
\n
C3: the man does not own a collie and does not own a cat.\n
Q3: the man does not own a dog and does not own a cat. Yes, No, or Maybe?\n
A4: Maybe\n
\n
C4: A not so tall person reading a paper is not currently sitting inside a
inn.\n
Q4: A not so tall person reading a paper is not currently sitting inside a
building. Yes, No, or Maybe?\n
A5: Maybe\n
\n
C: We didn’t eat pizza\n
Q: We didn’t eat food. Yes, No, or Maybe?\n
A:

###  E.9 Structured Prompt

Prompt example
P: We didn’t eat pizza\n
H: We didn’t eat food\n
L:

###  E.10 Few-Shot Structured Prompt

Prompt example
P1: The players who did not score did not have a ball.\n
H1: The players who did not score did not have a baseball.\n
L1: entailment\n
\n
P2: the man does not own a dog and does not own a cat.\n
H2: the man does not own a poodle and does not own a cat.\n
L2: entailment\n
\n
P3: the man does not own a terrier and does not own a cat.\n
H3: the man does not own a dog and does not own a cat.\n
L3: neutral\n
\n
P4: the man does not own a husky and does not own a cat.\n
H4: the man does not own a dog and does not own a cat.\n
L4: neutral\n
\n
P: We didn’t eat pizza\n
H: We didn’t eat food\n
L:

###  E.11 Reasoning Prompt

Prompt example
Logical and commonsense reasoning exam.\n
\n
Explain your reasoning in detail, then answer with Yes or No. Your answers
should follow this 4-line format:\n
\n
Premise: <a tricky logical statement about the world>.\n
Question: <question requiring logical deduction>.\n
Reasoning: <an explanation of what you understand about the possible
scenarios>.\n
Answer: <Yes or No>.\n
\n
Premise: we didn’t eat pizza\n
Question: Can we logically conclude for sure that we didn’t eat food?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that

###  E.12 Few-shot Reasoning Prompt

For this prompt, we insert two demonstrations right before the test example.
These are of the correct type for the test example, and they exemplify each of
the two labels. The demonstrations are from a fixed set of examples, which we
include here:

####  E.12.1 No Negation

Prompt example
Here are some examples of the kind of reasoning you should do:\n
\n
Premise: The students ate pizza\n
Question: Can we logically conclude for sure that the students ate food?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students ate
pizza entails that the students ate food.\n
Answer: Yes\n
\n
Premise: The students ate food\n
Question: Can we logically conclude for sure that the students ate pizza?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students ate
food does not allow us to conclude that the students ate pizza. They might
have eaten something else.\n
Answer: No\n
\n

####  E.12.2 One Scoped

Prompt example
Here are some examples of the kind of reasoning you should do:\n
\n
Premise: The students didn’t eat any pizza\n
Question: Can we logically conclude for sure that the students didn’t eat any
food?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students didn’t
eat any pizza does not allow us to conclude that the students didn’t eat any
food. They might have eaten something else.\n
Answer: No\n
\n
Premise: The students didn’t eat any food\n
Question: Can we logically conclude for sure that the students didn’t eat any
pizza?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students didn’t
eat any food entails that the students didn’t eat any pizza.\n
Answer: Yes\n
\n

####  E.12.3 One Not Scoped

Prompt example
Here are some examples of the kind of reasoning you should do:\n
\n
Premise: The students who weren’t in class ate pizza\n
Question: Can we logically conclude for sure that the students who weren’t in
class ate food?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students who
weren’t in class ate pizza entails that the students who weren’t in class ate
food.\n
Answer: Yes\n
\n
Premise: The students who weren’t in class ate food\n
Question: Can we logically conclude for sure that the students who weren’t in
class ate pizza?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students who
weren’t in class ate food does not allow us to conclude that the students who
weren’t in class ate pizza. They might have eaten something else.\n
Answer: No\n
\n

####  E.12.4 One Scoped, One Not Scoped

Prompt example
Here are some examples of the kind of reasoning you should do:\n
\n
Premise: The students who weren’t in class didn’t eat any pizza\n
Question: Can we logically conclude for sure that the students who weren’t in
class didn’t eat any food?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students who
weren’t in class didn’t eat any pizza does not allow us to conclude that the
students who weren’t in class didn’t eat any food. They might have eaten
something else.\n
Answer: No\n
\n
Premise: The students who weren’t in class didn’t eat any food\n
Question: Can we logically conclude for sure that the students who weren’t in
class didn’t eat any pizza?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students who
weren’t in class didn’t eat any food entails that the students who weren’t in
class didn’t eat any pizza.\n
Answer: Yes\n
\n

####  E.12.5 Two Not Scoped

Prompt example
Here are some examples of the kind of reasoning you should do:\n
\n
Premise: The students who weren’t in class ate pizza that wasn’t hot\n
Question: Can we logically conclude for sure that the students who weren’t in
class ate food that wasn’t hot?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students who
weren’t in class ate pizza that wasn’t hot entails that the students who
weren’t in class ate food that wasn’t hot.\n
Answer: Yes\n
\n
Premise: The students who weren’t in class ate food that wasn’t hot\n
Question: Can we logically conclude for sure that the students who weren’t in
class ate pizza that wasn’t hot?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that the students who
weren’t in class ate food that wasn’t hot does not allow us to conclude that
the students who weren’t in class ate pizza that wasn’t hot. They might have
eaten something else.\n
Answer: No\n
\n

####  E.12.6 Two Scoped

Prompt example
Here are some examples of the kind of reasoning you should do:\n
\n
Premise: It is not the case that the students didn’t eat any pizza\n
Question: Can we logically conclude for sure that it is not the case that the
students didn’t eat any food?\n
Reasoning: Let’s think logically step by step. The premise basically tells us
that pizza is a type of food. Therefore, the premise that it is not the case
that the students didn’t eat any pizza entails that it is not the case that
the students didn’t eat any food.\n
Answer: Yes\n
\n
Premise: It is not the case that the students didn’t eat any food\n
Question: Can we logically conclude for sure that it is not the case that the
students didn’t eat any pizza? Reasoning: Let’s think logically step by step.
The premise basically tells us that pizza is a type of food. Therefore, the
premise that it is not the case that the students didn’t eat any food does not
allow us to conclude that it is not the case that the students didn’t eat any
pizza. They might have eaten something else.\n
Answer: No\n
\n

###  E.13 ScoNe-NLG Prompts

In the zero-shot condition, models are simply prompted with the ScoNe-NLG
examples. In the few-shot condition, the test is example is proceeded with a
fixed set of four demonstrations, separated by double newlines. The examples
are as follows:

Prompt example
Glen is not a fan of learning math. When he sees that his new high school
requires that he take a geometry course, he is not pleased.\n
\n
I saw John take his BMW to the store the other day, so when Suzy asked me if
John owns a car, I said yes.\n
\n
I’ve seen John with a dog that isn’t very cute, so when Suzy asked me if John
owns a pet, I said yes.\n
\n
I recently confirmed that John is not allergic to any shellfish. So it makes
sense that when we served shrimp

##  Appendix F In-Context Learning Results for davinci-002

|  | No | One | Two | Two | One | One Scoped, |
---|---|---|---|---|---|---|---|---
|  | Negation | Not Scoped | Not scoped | Scoped | Scoped | One not Scoped | Overall
Zero-shot | Structured | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50
Brown et al. | 0.69 | 0.60 | 0.59 | 0.55 | 0.50 | 0.48 | 0.57
Conditional Q | 0.76 | 0.55 | 0.65 | 0.50 | 0.50 | 0.50 | 0.58
Conditional Truth | 0.76 | 0.64 | 0.66 | 0.60 | 0.50 | 0.57 | 0.62
Hypothesis Q | 0.80 | 0.83 | 0.86 | 0.62 | 0.45 | 0.40 | 0.66
Reasoning | 0.85 | 0.70 | 0.68 | 0.62 | 0.57 | 0.56 | 0.66
Few-shot | Structured | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50
Brown et al. | 0.82 | 0.75 | 0.78 | 0.72 | 0.35 | 0.29 | 0.62
Conditional Q | 0.92 | 0.82 | 0.78 | 0.52 | 0.36 | 0.32 | 0.62
Conditional Truth | 0.92 | 0.89 | 0.88 | 0.59 | 0.36 | 0.37 | 0.67
Hypothesis Q | 0.99 | 0.91 | 0.92 | 0.68 | 0.38 | 0.40 | 0.72
Reasoning | 0.73 | 0.85 | 0.78 | 0.62 | 0.74 | 0.54 | 0.71
Table 7: In-context learning results for GPT-3 (davinci-002 engine).


# Discovery of a large-scale bent radio jet in the merging cluster Abell 514

Wonki Lee  Yonsei University, Department of Astronomy, Seoul, Republic of
Korea  Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge,
MA 02138, USA  John ZuHone  Harvard-Smithsonian Center for Astrophysics, 60
Garden St., Cambridge, MA 02138, USA  M. James Jee  Yonsei University,
Department of Astronomy, Seoul, Republic of Korea  Department of Physics,
University of California, Davis, One Shields Avenue, Davis, CA 95616, USA M.
James Jee<EMAIL_ADDRESS><EMAIL_ADDRESS>Kim HyeongHan  Yonsei
University, Department of Astronomy, Seoul, Republic of Korea  Ruta Kale
National Centre for Radio Astrophysics–Tata Institute of Fundamental Research,
Ganeshkhind, Pune, Maharashtra, INDIA  Eunmo Ahn  Yonsei University,
Department of Astronomy, Seoul, Republic of Korea

###### Abstract

We report a discovery of a large-scale bent radio jet in the merging galaxy
cluster Abell 514 ($z=0.071$). The radio emission originates from the two
radio lobes of the AGN located near the center of the southern subcluster and
extends towards the southern outskirts with multiple bends. Its peculiar
morphology is characterized by a $400$-kpc “bridge”, a $300$-kpc “arc”, and a
$400$-kpc “tail”, which together contribute to its largest linear size of
$\raise 0.81805pt\hbox{$\scriptstyle\sim$}0.7$ Mpc. We find that both the flux
and spectral features of the emission change with the distance from the AGN.
Also, the “bridge” presents a $60\%$ polarized radio emission, which coincided
with an X-ray cold front. Based on our multi-wavelength observations, we
propose that A514 presents a clear case for the redistribution of an old AGN
plasma due to merger-driven gas motions. We support our interpretation with
idealized cluster merger simulations employing a passive tracer field to
represent cosmic-ray electrons and find that merger-driven motions can
efficiently create a cloud of these particles in the cluster outskirts, which
later can be re-accelerated by the cluster merger shock and produce radio
relics.

Galaxy clusters (584) — Abell clusters (9) — Radio jets (1347)

##  1 Introduction

Many radio jets in merging galaxy clusters present a characteristic bent radio
morphology (e.g., Burns et al., 1994). This bent morphology is believed to be
the result of interactions with the ambient intracluster medium (ICM, Owen &
Rudnick, 1976; Burns, 1998), which can bend (e.g., Pfrommer & Jones, 2011;
Nolting et al., 2019a, b) or stretch the radio jets (e.g., Chibueze et al.,
2021; ZuHone et al., 2021b, hereafter Z21). As the jets diffuse into the ICM,
the non-thermal plasma loses its energy via synchrotron radiation and inverse-
Compton scattering (Kardashev, 1962). Although these energy losses remove the
high-energy ($\gamma\sim 10^{4}$, where $\gamma$ is the Lorentz factor) cosmic
ray electrons (CRe), the jets are still rich in low-energy ($\gamma\lesssim
10^{3}$) CRe. This population of old, low-energy plasma, called fossil CRe,
has been hypothesized as the source of diffuse cluster radio emission through
various energization processes (van Weeren et al., 2019). For example, if a
cluster merger shock passes the cloud of fossil CRe that resides in the
cluster outskirts, the diffusive shock acceleration creates a radio relic, an
elongated arc-shaped radio emission feature found in the cluster periphery
(e.g., Kang & Ryu, 2016).

Recently, the unprecedented sensitivity at low-frequencies enabled by LOFAR
(van Haarlem et al., 2013), uGMRT (Gupta et al., 2017) and MWA (Tingay et al.,
2013), started to directly probe the fossil CRe content injected by the radio
jets (e.g., de Gasperin et al., 2017; Hodgson et al., 2021; Brienza et al.,
2021). Nevertheless, the long-term spatial evolution of these jets and their
contribution to the diffuse cluster radio emissions still remain unclear
(e.g., Vazza et al., 2023).

Figure 1: Multi-wavelength view of Abell 514. uGMRT radio maps (green),
adaptively smoothed XMM-Newton X-ray (red), and the red sequence number
density contours are overlaid on the Magellan/Megacam optical color composite
image. The radio map at a lower frequency is described with a darker green
color scale. The number density contours mark the level of 1.7, 2.3, and
$3.0\rm~{}galaxy~{}arcmin^{-2}$. The elongated X-ray and the two red sequence
number density peaks suggest the collision between the northwest and the
southeast clusters, while the southern AGN shows a large-scale bent radio jet
with the largest linear size $\raise
0.81805pt\hbox{$\scriptstyle\sim$}0.7\rm~{}Mpc$. The inset figure shows the
point-source subtracted X-ray map around the radio features of the southern
AGN. The green $410\rm~{}MHz$ radio contours start from $5\sigma$ and are
spaced by a factor of 2. The cyan arc marks the X-ray surface brightness
discontinuity, which we interpret as a cold front (§3.2).

In this letter, we report a discovery of a large-scale bent radio jet in the
merging cluster Abell 514 (hereafter A514). A514 is a massive ($M_{500}\sim
3\times 10^{14}M_{\odot}$111Derived with
$L_{X,\,[0.1,2.4]\rm~{}keV}=1.44\times 10^{44}~{}\rm erg\,s^{-1}$ (Ebeling et
al., 1996) and the X-ray luminosity-mass relation of Pratt et al. (2009).),
low-redshift cluster merger at $z=0.0714$ (Fadda et al., 1996). Burns et al.
(1994) reported the presence of three radio tails inside extended X-ray
emission. Weratschnig et al. (2008) claimed the detection of an X-ray
discontinuity and suggested an ongoing collision in the NW-SE direction. In
this study, we performed deep low-frequency radio observations using uGMRT and
discovered a large-scale bent radio jet of A514. Based on our multi-wavelength
data and simulations, we suggest that the observed radio feature represents
old AGN plasma that has been redistributed by the merger-driven gas motions
and evolved into a cloud of fossil CRe located in the outskirts of the
cluster.

This letter is organized as follows. We outline the reduction process of the
data in §2 and present the radio features and their multi-wavelength
properties in §3. We describe the numerical simulations of A514 in §4 before
we summarize our findings in §5. We adopt a $\Lambda$CDM cosmology with
$H_{0}=70$ km s-1Mpc-1, $\Omega_{m}=0.3$, and $\Omega_{\Lambda}=0.7$. The
angular size of $1\arcmin$ corresponds to a length scale of $\raise
0.81805pt\hbox{$\scriptstyle\sim$}80$ kpc at the cluster redshift $z=0.0714$.

##  2 Data & Reduction

###  2.1 Radio: uGMRT

We observed A514 using uGMRT Band 2 ($125-250\rm\,MHz$), Band 3
($250-500\rm\,MHz$), and Band 4 ($550-850\rm\,MHz$) with on-source integration
times of $3.5$, $3.7$, and $4.3$ hours, respectively222Program code: $\rm
38\\_124$, $\rm 41\\_076$. We used 3C147 as the amplitude calibrator in all
observations and selected 0447-220 (Band 2), 0521-207 (Band 3), and 0409-179
(Band 4) for the phase calibration. We processed our uGMRT data with CASA
v6.5.3333http://casa.nrao.edu and the latest CAPTURE pipeline (Kale & Ishwara-
Chandra, 2021). To briefly summarize, we self-calibrated the image using
tclean, implementing the multi-scale multi-frequency synthesis (MS-MFS, Rau &
Cornwell, 2011) and W-Projection (Cornwell et al., 2008). We employed the
auto-multithresh algorithm (Kepley et al., 2020) to define the mask regions
and the wbpbgmrt module 444https://github.com/ruta-k/uGMRTprimarybeam to
correct the primary beam. We refer readers to Kale & Ishwara-Chandra (2021)
for the detailed reduction steps.

Figure 2: Radio maps of PKS 0446-20 at $740\rm~{}MHz$ (Band 4,
$550-850\rm~{}MHz$, left) and smoothed radio maps with the beam size of
$35^{\prime\prime}$ at $410\rm~{}MHz$ (Band 3, $250-500\rm~{}MHz$, middle
left) and $190\rm~{}MHz$ (Band 2, $120-250\rm~{}MHz$, middle right). The right
panel depicts the spectral index map derived from the three frequency
channels. The radio maps are smoothed to match the beam size of
$35^{\prime\prime}$. The annotated ellipse in the bottom right corner
describes the synthesized beam size of each radio map. The overlaid contours
mark the $5\sigma$ detection in the $740\rm~{}MHz$ and $410\rm~{}MHz$ radio
maps and the $3\sigma$ detection in the $190\rm~{}MHz$ radio map. The contours
are spaced by a factor of 2. The radio emission gets fainter and presents a
steeper spectrum with increasing distance from the AGN.

We used the Briggs weighting scheme to create the radio map. After testing
different robust parameters, we set the robust parameter to 0 for Band 3 and 4
and 2 for Band2 in order to resolve both the substructures and the diffuse
radio emission effectively. The noise level of the resulting radio map is
$\sigma_{190\rm~{}MHz}\sim 3.0~{}\rm{mJy~{}b}^{-1}$
($b_{190\rm~{}MHz}=33^{\prime\prime}\times 21^{\prime\prime}$),
$\sigma_{400\rm~{}MHz}\sim 0.08~{}\rm{mJy~{}b}^{-1}$
($b_{400\rm~{}MHz}=12^{\prime\prime}\times 5^{\prime\prime}$), and
$\sigma_{740\rm~{}MHz}\sim 0.04~{}\rm{mJy~{}b}^{-1}$
($b_{740\rm~{}MHz}=5^{\prime\prime}\times 4^{\prime\prime}$) at Band 2, 3, and
4, respectively. We assume a flux calibration uncertainty of $10\%$ for Band 3
and 4 and $20\%$ for Band 2 (Chandra et al., 2004).

###  2.2 X-ray: XMM-Newton

We retrieved the archival XMM-Newton observations of A514 (ObsId: 0142240101,
0142240201, and 0300920101), and performed standard calibration based on the
XMM-Newton Cookbook555http://heasarc.gsfc.nasa.gov/docs/xmm/esas/cookbook/
using the XMM-Newton Extended Source Analysis Software (XMM-ESAS; SAS version
18.0.0; Gabriel et al., 2004). After filtering and removing flaring events,
the total clean exposure times of MOS1, MOS2, and PN are 14.8, 16.4, and 7.1
ks, respectively. We extracted a soft-band (0.5-2 keV) image and masked the
point sources detected by wavdetect (Freeman et al., 2002) to obtain the
surface brightness profile. It was rebinned to have a minimum S/N $>5$, using
the PROFFIT v1.5 package (Eckert et al., 2011) for the analysis.

###  2.3 Optical: Magellan/Megacam

We investigated the cluster galaxy distributions using optical data from the
Magellan/Megacam $g$ and $r$-filter observations (PI: W. Lee). The CCD level
processing including overscan correction, trimming, and bad pixel removal was
carried out at the Smithsonian Astrophysical Observatory (SAO) Telescope Data
Center using the SAO Megacam reduction pipeline. We created sky flats using
the same A514 observation consisting of multiple dithers and rotations.
Astrometric corrections were obtained with the SCAMP software (Bertin, 2006).
The final mosaic images were created with the SWARP package (Bertin et al.,
2002). We ran SExtractor (Bertin & Arnouts, 1996) in dual image mode using the
$r$-band mosaic as the detection image to identify sources and obtain
photometry. We calibrated the zero points using the PanSTARRS catalogs
covering our field.

##  3 A large-scale bent radio jet in Abell 514

Figure 1 presents the multi-wavelength view of A514. The presence of the two
galaxy number density peaks and the elongated X-ray morphology between them
strongly suggest that A514 is currently undergoing a binary merger in the NW-
SE direction. Previous observations have reported three head-tail radio
galaxies in A514 (Burns et al., 1994; Bliton et al., 1998; Govoni et al.,
2001), which are all classified as spectroscopic members (Owen et al., 1995;
Katgert et al., 1998). With our new uGMRT radio observations, we revealed the
bent morphology in these three radio galaxies. The two radio galaxies in the
northern subcluster extend by $\raise
0.81805pt\hbox{$\scriptstyle\sim$}300\rm~{}kpc$, before they bend at the
position of the northern X-ray discontinuity reported by Weratschnig et al.
(2008). Thus, they might present the case for jet bending caused by
discontinuous ICM velocity across the front (e.g., Pfrommer & Jones, 2011).

In this letter, we focus on the southern radio emission originating from the
AGN PKS 0446-20 (hereafter A514S), which exhibits a remarkably peculiar
morphology. Govoni et al. (2001) have reported two radio lobes with a hint of
extended radio emission towards the south. We found that this radio feature
extends much longer than what has been reported. The two radio lobes are
connected to the $\raise 0.81805pt\hbox{$\scriptstyle\sim$}400$-kpc long N-S
structure that we refer to as “bridge”. The southern end of the bridge meets
the $\raise 0.81805pt\hbox{$\scriptstyle\sim$}300$-kpc long “arc”, which is
concave toward the cluster center. Finally, the eastern end of the arc touches
the northern end of the $\raise 0.81805pt\hbox{$\scriptstyle\sim$}400$-kpc
long tail. The largest projected linear size of the combination of the three
radio segments is $\raise 0.81805pt\hbox{$\scriptstyle\sim$}0.7~{}$Mpc. Note
that the aforementioned radio features, albeit in low resolution, can also be
identified in the archival low-frequency radio survey data from TGSS (Intema
et al., 2017) and GLEAM (e.g., Wayth et al., 2015).

Figure 2 depicts the details of the radio emission in A514S at different
frequencies. In the $740\rm~{}MHz$ radio map, the bridge is resolved into two
filamentary substructures, whose surface brightness decreases rapidly toward
the south. On the other hand, the surface brightness level is elevated at the
intersection of the bridge and the arc in the $410\rm~{}MHz$ and
$190\rm~{}MHz$ radio maps. The arc is only marginally detected in the
$740\rm~{}MHz$ radio map while its presence is clear in the $410\rm~{}MHz$ and
$190\rm~{}MHz$ radio maps. The current data do not hint at any filamentary
substructure within the arc. Similarly, the tail presents a low surface
brightness in the low-frequency radio maps. The tail extends along the
hypothesized merger axis of A514.

Table 1: Radio properties of the substructures in the southern bent jet Name | $S_{740\rm~{}MHz}$ | $S_{400\rm~{}MHz}$ | $S_{190\rm~{}MHz}$ | $\alpha^{740\rm~{}MHz}_{190\rm~{}MHz}$ | $\alpha^{400\rm~{}MHz}_{190\rm~{}MHz}$
---|---|---|---|---|---
| $\rm Jy$ | $\rm Jy$ | $\rm Jy$ |  |
bridge | $0.39\pm 0.04$ | $0.84\pm 0.08$ | $2.1\pm 0.4$ | $-1.3\pm 0.03$ | $-1.2\pm 0.3$
arc | $0.021\pm 0.007$ | $0.10\pm 0.01$ | $0.46\pm 0.11$ | $-2.6\pm 0.1$ | $-1.9\pm 0.3$
tail | $-$ | $0.035\pm 0.006$ | $0.26\pm 0.08$ | $-$ | $-2.6\pm 0.5$

###  3.1 AGN Activity or Radio Relics?

Table LABEL:tab:flux summarizes the radio properties of the substructures in
the southern bent jet. The integrated flux gradually decreases with distance
from A514S in the order of the bridge, the arc, and the tail. We estimate the
spectral slopes by fitting a power-law spectrum ($S\propto\nu^{\alpha}$) on
the smoothed radio maps with the matched beam size of $35^{\prime\prime}$. The
resulting spectral map in the right panel of Figure 2 clearly shows that the
radio spectrum steepens with the distance from A514S. Moreover, the spectrum
of the arc is curved
($\alpha^{740\rm~{}MHz}_{190\rm~{}MHz}<\alpha^{400\rm~{}MHz}_{190\rm~{}MHz}$),
whereas the bridge presents a flat spectrum
($\alpha^{740\rm~{}MHz}_{190\rm~{}MHz}\sim\alpha^{400\rm~{}MHz}_{190\rm~{}MHz}$).
These patterns of changes in the flux and spectral slope are anticipated due
to the aging of the CRe originating from the radio lobes through synchrotron
and inverse-Compton energy losses (e.g., Kardashev, 1962; Jaffe & Perola,
1973).

Based on its morphology, orientation, and location, one may identify the arc
as a possible radio relic. Also, when we estimate its $1.4\rm~{}GHz$
luminosity assuming a power-law spectrum, we find that the value is in line
with the expectation from the typical size-luminosity relation of radio relics
(Feretti et al., 2012). However, the steep and curved radio spectrum of the
arc is different from the feature of typical radio relics, which are well-
described with a single power-law description. A radio relic can feature a
curved spectrum if a shock illuminates a cloud of fossil CRe that has been re-
accelerated $>100\rm~{}Myrs$ ago (e.g., Kang & Ryu, 2016). Nevertheless, we
believe that this scenario does not apply to the current case, where we expect
the shock that re-accelerated the arc to propagate and re-accelerate the tail
as well, because the tail extends along the collision axis. As the spectral
slope of the tail is steep, we conclude that the arc is not a relic-type
source.

The aforementioned features of the AGN radio jet have been reported in other
clusters. A perpendicular reorientation of the radio jets similar to the
bridge-arc intersection has been observed in the Coma cluster (Lal, 2020),
A3560 (Venturi et al., 2013), A3376 (Chibueze et al., 2021), and A3528 (Di
Gennaro et al., 2018). As in the bridge of A514, filamentary substructures
associated with the cluster AGN has been discovered in A4038 (Kale et al.,
2018), A85 (Rahaman et al., 2022), A194 (Rudnick et al., 2022), and A3562
(Giacintucci et al., 2022). These examples demonstrate that the plasma ejected
through AGN jets can undergo redistribution and evolve into peculiar radio
morphologies, as observed in A514.

###  3.2 Jet Redistribution by merger-driven gas motions?

If the extended radio emission of A514 indeed originated from AGN activity,
the AGN plasma must have been transported from the injection point at the AGN
to the observed locations. One possible source of jet redistribution is the
motion of the host galaxy A514S. If the host galaxy falls into the cluster
with a high velocity, its jet will lag behind it. Also, the interaction with
ICM can further warp the AGN jet distribution (e.g., Pfrommer & Jones, 2011).
Another possible scenario is the redistribution of the jet material due to
merger-driven gas motions (Z21). As described earlier, the rotational motion
of the ICM can stretch the AGN bubble along a cold front given the fast
motions underneath the front.

Guided by the prediction of Z21, we assess the presence of a cold front by
examining the X-ray surface brightness profile. Figure 3 presents an X-ray
surface brightness discontinuity, where the surface brightness jump coincides
with the radio emission from the bridge. We find that a broken power-law model
($\chi_{\rm red}^{2}\sim 0.8$) is preferred over a single power-law model
($\chi_{\rm red}^{2}\sim 1.6$). The fitted broken power-law model gives a
compression ratio $C\sim 1.75\pm 0.25$.

This X-ray discontinuity can either be a cold front or a shock with
$\mathcal{M}\sim 1.5\pm 0.2$ based on the Rankine-Hugoniot conditions based on
the density jump alone. The current X-ray data cannot constrain the
temperature of the western side (it corresponds to the upstream if the
discontinuity is a shock) because of insufficient photon statistics. Still,
since the discontinuity is found near the southern X-ray core, we believe that
a cold front is more plausible than a merger shock that is launched ahead of
the X-ray cores (e.g., Markevitch et al., 2000). Also, if the discontinuity
originates from a shock, its shock propagation direction is in tension with
the hypothesized merger axis deduced from the elongation of the ICM and galaxy
distribution. The possibility of an equatorial shock is ruled out because it
is expected to be found in the cluster periphery (e.g., Ha et al., 2018).

Z21 argued that the AGN jet redistributed by sloshing would provide a highly
polarized radio emission due to the aligned and amplified intracluster
magnetic fields along the cold front (e.g., ZuHone et al., 2011). We examined
if the bridge is polarized with the NVSS data (Condon et al., 1998).
Interestingly, we find that the emission in the bridge remains highly
polarized ($\lesssim 60\%$) despite the depolarization due to the large beam
of NVSS ($45^{\prime\prime}$). Based on these signatures, we suggest that the
bridge traces the older material redistributed from the AGN jet along the cold
front by the sloshing motion (Z21).

One can interpret the high polarization fraction and the filamentary
substructures as originating from the magnetic flux bundles in the ICM, which
may present extended radio features with the CRe diffusion along the magnetic
fields (e.g., Rudnick et al., 2022). The direct comparison between the
magnetic fields and the radio features is difficult with the current data, and
we plan to address this in the follow-up project with MeerKAT L-band
polarization observations.

Figure 3: X-ray surface brightness profile (black) over the bridge. The X-ray
surface brightness profile is well-described with a broken-power law (red)
with a compression ratio $C\sim 1.75\pm 0.25$. The radio surface brightness
profile (green) presents a peak at the X-ray surface brightness jump.

##  4 Formation scenario of the bent radio jet

We perform magnetohydrodynamics simulations of a binary cluster merger to test
our scenario in explaining the observed radio morphology. We set up the
initial conditions of the simulations using the cluster_generator
package666https://github.com/jzuhone/cluster_generator. We place the two
clusters inside a $15~{}$Mpc closed box, with each cluster composed of a dark
halo modelled by an NFW profile(Navarro et al., 1996) and the ICM modelled by
a modified beta profile ICM (Vikhlinin et al., 2006). We set a turbulent
magnetic field and normalize its strength so that the ICM has an average ratio
between the thermal and the magnetic pressure of $\raise
0.81805pt\hbox{$\scriptstyle\sim$}100$. We guide the readers to Brzycki &
ZuHone (2019) for more details on the initial setups.

We perform the merger simulations with GAMER-2 (Schive et al., 2018), a GPU-
accelerated Adaptive MEsh Refinement code. The code refines the patch down to
$\raise 0.81805pt\hbox{$\scriptstyle\sim$}8~{}$kpc based on the number of dark
matter particles. In a suite of simulations with different collision
parameters, we create a mock X-ray map using the yt(Turk et al., 2011) and
pyXSIM packages (ZuHone & Hallman, 2016) and determine the viewing angle that
can reproduce the observed X-ray core separation of $\raise
0.81805pt\hbox{$\scriptstyle\sim$}0.7\rm~{}Mpc$. We find that an off-axis
collision between two clusters with masses of $2$ and $1\times
10^{14}~{}M_{\odot}$ clusters can reproduce the overall X-ray features of A514
(top panel of Figure 4). This collision started with a relative infall
velocity of $900\rm~{}km~{}s^{-1}$, an initial separation of $3\rm~{}Mpc$, and
an initial impact parameter of $600\rm~{}kpc$. The snapshot and viewing angle
which best match the features of A514 are $\raise
0.81805pt\hbox{$\scriptstyle\sim$}0.5$ Gyr after the first core passage and a
line-of-sight angle of $\raise 0.81805pt\hbox{$\scriptstyle\sim$}70\deg$777We
define the viewing angle of plane of sky merger as $90\deg$.. We note that the
northern X-ray core in A514 is the less-massive cluster in this scenario.

In this collision, we use a passive scalar to track gas sampled inside a
randomly-placed $50$ kpc sphere before the first closest passage. We use this
bubble gas to describe the redistribution of fossil CRe injected by a cluster
AGN. This passive tracer is a simple model, which does not include a physical
model that can modify the substructures of the bubble or the ICM itself (e.g.,
ZuHone et al., 2021a). However, we assume the spatial extent of the
redistributed bubble can roughly describe the extent of the redistributed non-
thermal plasma as the non-thermal plasma is known to follow the ICM gas flows
after it has become mixed with the thermal plasma (e.g., Botteon et al.,
2023).

Fiugre 4 demonstrates that the bubble redistributes along the cold front
formed ahead of the infalling main cluster, where the cluster core stretches
the bubble perpendicular to its motion. This infalling motion stretches the
bubble by $\raise 0.81805pt\hbox{$\scriptstyle\sim$}400~{}$kpc in the north-
south direction with a curved morphology, like the bridge in A514, which
supports our scenario for the jet redistribution by the merger-driven gas
motions.

Figure 4:  Mock X-ray surface brightness map of the simulations overlaid with
scalar field density map (green), which is normalized with the injected
density. The scalar field contours (white) start at $10^{-5}$ and are spaced
equally by a factor of 2. The cyan arcs mark the temperature discontinuity,
which shows the shock fronts. At $\raise
0.81805pt\hbox{$\scriptstyle\sim$}0.5\rm~{}Gyr$ after the first closest
passage (top panel), the bubble extends by $\raise
0.81805pt\hbox{$\scriptstyle\sim$}0.4$ Mpc in a direction similar to Abell
514. At $\raise 0.81805pt\hbox{$\scriptstyle\sim$}1.0\rm~{}Gyr$ after the
second closest passage ($\raise
0.81805pt\hbox{$\scriptstyle\sim$}4.5\rm~{}Gyr$ after the first closest
passage, bottom panel), the bubble stretches along the merger shock in the
cluster outskirts.

###  4.1 Injection of Fossil CRe in the Cluster Outskirts

The diffuse radio emission of A514 extends towards the cluster periphery,
which implies that the AGN plasma will distribute in the cluster outskirts and
possibly seed radio relics. To check the long-term evolution of AGN plasma, we
further perform the simulation until the second closest passage.

The bottom panel of Figure 4 presents the simulated merger $\raise
0.81805pt\hbox{$\scriptstyle\sim$}1.0\rm~{}Gyr$ after the second closest
passage (i.e., $\raise 0.81805pt\hbox{$\scriptstyle\sim$}4.5\rm~{}Gyr$ after
the first closest passage). At this late merger phase, the bubble plasma has
reached the cluster outskirts, stretched by $\raise
0.81805pt\hbox{$\scriptstyle\sim$}1$ Mpc, and extends tangentially with
respect to the cluster center. These characteristics of the redistributed
bubble plasma are not surprising as the cold front, which was the primary
source of the jet redistribution, is known to create an arc-shape gas tail
that overruns its parent cluster’s dark matter during an off-axis cluster
merger (e.g., Sheardown et al., 2019; Lee et al., 2020). As a result, we find
that the merger shock from the second closest passage aligns with the
redistributed bubble plasma (see the cyan arc in Figure 4). Under this
condition, we expect this bubble to be re-accelerated and present a radio
relic-like emission.

The fossil CRe injection presented in Figure 4 is similar to the scenario
described in Z21. Our results suggest that the redistribution process can be
efficient. Specifically, our simulation shows that the AGN plasma injected
before the first closest passage can be transformed into a fossil CRe cloud
before the merger shock from the second closest passage reaches the plasma.

Accurate modeling of the CRe is required to predict the characteristics of the
radio relics created under this scenario, which is beyond the scope of this
work. Instead, we qualitatively discuss the observable signatures of the radio
relics formed under this scenario. One possible signature is a steep radio
halo. The turbulence generated from the cluster merger can re-accelerate the
non-thermal plasma inside the ICM and present a radio halo (Brunetti et al.,
2001). As the bubble plasma redistributes 1 Gyr after the second closest
passage, we expect the radio halo would have a steep radio spectrum (e.g.,
Donnert et al., 2013). Another possible feature is the inhomogeneous surface
brightness of the radio relic. The rotational motion that redistributes the
bubble plasma is tangential to the cluster center, aligning the bubble with
the merger shock. However, the merger shock does not need to pass the center
of the redistributed bubble plasma. As a result, the re-accelerated radio
relic will produce an inhomogeneous surface brightness feature with the
brightest emission produced where the fossil CRe exist.

##  5 Summary

We have reported the discovery of a large-scale bent radio jet in the merging
cluster A514. The radio emission originates from the two radio lobes of the
AGN located in the central region of the southern cluster and extends towards
the southern periphery. The entirety of the radio feature is believed to be
traced back to the AGN because both its flux and spectral slope decrease as
the distance from the AGN increases. We have detected both a discontinuity in
X-ray surface brightness and high polarization at the location of the extended
radio emission. We interpret these features as a result of the jet plasma
redistribution along the cold front of the recent cluster merger.

To assess the viability of our scenario, we conducted cluster merger
simulations using a toy model. The simulations show that a passive plasma
bubble, injected during an off-axis cluster merger, can undergo stretching
along the cold front of the infalling cluster. This stretching process results
in an extended radio emission that resembles the observation in A514. At the
late merger phase, the bubble redistributes at the cluster outskirt with its
elongation aligned tangential to the cluster. Based on these findings, we
propose that A514 shows the early stage of fossil CRe injection, where the
redistributed fossil CRe in the cluster outskirts can help boost the
acceleration efficiency of the merger shocks.

M. J. Jee acknowledges support for the current research from the National
Research Foundation (NRF) of Korea under the programs 2022R1A2C1003130 and
RS-2023-00219959. RK acknowledges the support of the Department of Atomic
Energy, Government of India, under project no. 12-R&D-TFR-5.02-0700.

## References

  * Bertin (2006) Bertin, E. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 112
  * Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164
  * Bertin et al. (2002) Bertin, E., Mellier, Y., Radovich, M., et al. 2002, in Astronomical Society of the Pacific Conference Series, Vol. 281, Astronomical Data Analysis Software and Systems XI, ed. D. A. Bohlender, D. Durand, & T. H. Handley, 228
  * Bliton et al. (1998) Bliton, M., Rizza, E., Burns, J. O., Owen, F. N., & Ledlow, M. J. 1998, MNRAS, 301, 609, doi: 10.1046/j.1365-8711.1998.01973.x
  * Botteon et al. (2023) Botteon, A., Markevitch, M., van Weeren, R. J., Brunetti, G., & Shimwell, T. W. 2023, arXiv e-prints, arXiv:2302.07881, doi: 10.48550/arXiv.2302.07881
  * Brienza et al. (2021) Brienza, M., Shimwell, T. W., de Gasperin, F., et al. 2021, Nature Astronomy, 5, 1261, doi: 10.1038/s41550-021-01491-0
  * Brunetti et al. (2001) Brunetti, G., Setti, G., Feretti, L., & Giovannini, G. 2001, MNRAS, 320, 365, doi: 10.1046/j.1365-8711.2001.03978.x
  * Brzycki & ZuHone (2019) Brzycki, B., & ZuHone, J. 2019, ApJ, 883, 118, doi: 10.3847/1538-4357/ab3983
  * Burns (1998) Burns, J. O. 1998, Science, 280, 400, doi: 10.1126/science.280.5362.400
  * Burns et al. (1994) Burns, J. O., Rhee, G., Owen, F. N., & Pinkney, J. 1994, ApJ, 423, 94, doi: 10.1086/173792
  * Chandra et al. (2004) Chandra, P., Ray, A., & Bhatnagar, S. 2004, ApJ, 612, 974, doi: 10.1086/422675
  * Chibueze et al. (2021) Chibueze, J. O., Sakemi, H., Ohmura, T., et al. 2021, Nature, 593, 47, doi: 10.1038/s41586-021-03434-1
  * Condon et al. (1998) Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693, doi: 10.1086/300337
  * Cornwell et al. (2008) Cornwell, T. J., Golap, K., & Bhatnagar, S. 2008, IEEE Journal of Selected Topics in Signal Processing, 2, 647, doi: 10.1109/JSTSP.2008.2005290
  * de Gasperin et al. (2017) de Gasperin, F., Intema, H. T., Shimwell, T. W., et al. 2017, Science Advances, 3, e1701634, doi: 10.1126/sciadv.1701634
  * Di Gennaro et al. (2018) Di Gennaro, G., Venturi, T., Dallacasa, D., et al. 2018, A&A, 620, A25, doi: 10.1051/0004-6361/201832801
  * Donnert et al. (2013) Donnert, J., Dolag, K., Brunetti, G., & Cassano, R. 2013, MNRAS, 429, 3564, doi: 10.1093/mnras/sts628
  * Ebeling et al. (1996) Ebeling, H., Voges, W., Bohringer, H., et al. 1996, MNRAS, 281, 799, doi: 10.1093/mnras/281.3.799
  * Eckert et al. (2011) Eckert, D., Molendi, S., & Paltani, S. 2011, A&A, 526, A79, doi: 10.1051/0004-6361/201015856
  * Fadda et al. (1996) Fadda, D., Girardi, M., Giuricin, G., Mardirossian, F., & Mezzetti, M. 1996, ApJ, 473, 670, doi: 10.1086/178180
  * Feretti et al. (2012) Feretti, L., Giovannini, G., Govoni, F., & Murgia, M. 2012, A&A Rev., 20, 54, doi: 10.1007/s00159-012-0054-z
  * Freeman et al. (2002) Freeman, P. E., Kashyap, V., Rosner, R., & Lamb, D. Q. 2002, ApJS, 138, 185, doi: 10.1086/324017
  * Gabriel et al. (2004) Gabriel, C., Denby, M., Fyfe, D. J., et al. 2004, in Astronomical Society of the Pacific Conference Series, Vol. 314, Astronomical Data Analysis Software and Systems (ADASS) XIII, ed. F. Ochsenbein, M. G. Allen, & D. Egret, 759
  * Giacintucci et al. (2022) Giacintucci, S., Venturi, T., Markevitch, M., et al. 2022, ApJ, 934, 49, doi: 10.3847/1538-4357/ac7805
  * Govoni et al. (2001) Govoni, F., Taylor, G. B., Dallacasa, D., Feretti, L., & Giovannini, G. 2001, A&A, 379, 807, doi: 10.1051/0004-6361:20011355
  * Gupta et al. (2017) Gupta, Y., Ajithkumar, B., Kale, H. S., et al. 2017, Current Science, 113, 707, doi: 10.18520/cs/v113/i04/707-714
  * Ha et al. (2018) Ha, J.-H., Ryu, D., & Kang, H. 2018, ApJ, 857, 26, doi: 10.3847/1538-4357/aab4a2
  * Hodgson et al. (2021) Hodgson, T., Bartalucci, I., Johnston-Hollitt, M., et al. 2021, ApJ, 909, 198, doi: 10.3847/1538-4357/abe384
  * Intema et al. (2017) Intema, H. T., Jagannathan, P., Mooley, K. P., & Frail, D. A. 2017, A&A, 598, A78, doi: 10.1051/0004-6361/201628536
  * Jaffe & Perola (1973) Jaffe, W. J., & Perola, G. C. 1973, A&A, 26, 423
  * Kale & Ishwara-Chandra (2021) Kale, R., & Ishwara-Chandra, C. H. 2021, Experimental Astronomy, 51, 95, doi: 10.1007/s10686-020-09677-6
  * Kale et al. (2018) Kale, R., Parekh, V., & Dwarakanath, K. S. 2018, MNRAS, 480, 5352, doi: 10.1093/mnras/sty2227
  * Kang & Ryu (2016) Kang, H., & Ryu, D. 2016, ApJ, 823, 13, doi: 10.3847/0004-637X/823/1/13
  * Kardashev (1962) Kardashev, N. S. 1962, Soviet Ast., 6, 317
  * Katgert et al. (1998) Katgert, P., Mazure, A., den Hartog, R., et al. 1998, A&AS, 129, 399, doi: 10.1051/aas:1998399
  * Kepley et al. (2020) Kepley, A. A., Tsutsumi, T., Brogan, C. L., et al. 2020, PASP, 132, 024505, doi: 10.1088/1538-3873/ab5e14
  * Lal (2020) Lal, D. V. 2020, AJ, 160, 161, doi: 10.3847/1538-3881/abacd1
  * Lee et al. (2020) Lee, W., Jee, M. J., Kang, H., et al. 2020, ApJ, 894, 60, doi: 10.3847/1538-4357/ab855f
  * Markevitch et al. (2000) Markevitch, M., Ponman, T. J., Nulsen, P. E. J., et al. 2000, ApJ, 541, 542, doi: 10.1086/309470
  * Navarro et al. (1996) Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563, doi: 10.1086/177173
  * Nolting et al. (2019a) Nolting, C., Jones, T. W., O’Neill, B. J., & Mendygral, P. J. 2019a, ApJ, 876, 154, doi: 10.3847/1538-4357/ab16d6
  * Nolting et al. (2019b) —. 2019b, ApJ, 885, 80, doi: 10.3847/1538-4357/ab4650
  * Owen et al. (1995) Owen, F. N., Ledlow, M. J., & Keel, W. C. 1995, AJ, 109, 14, doi: 10.1086/117252
  * Owen & Rudnick (1976) Owen, F. N., & Rudnick, L. 1976, ApJ, 205, L1, doi: 10.1086/182077
  * Pfrommer & Jones (2011) Pfrommer, C., & Jones, T. W. 2011, ApJ, 730, 22, doi: 10.1088/0004-637X/730/1/22
  * Pratt et al. (2009) Pratt, G. W., Croston, J. H., Arnaud, M., & Böhringer, H. 2009, A&A, 498, 361, doi: 10.1051/0004-6361/200810994
  * Rahaman et al. (2022) Rahaman, M., Raja, R., Datta, A., Burns, J. O., & Rapetti, D. 2022, MNRAS, 515, 2245, doi: 10.1093/mnras/stac1892
  * Rau & Cornwell (2011) Rau, U., & Cornwell, T. J. 2011, A&A, 532, A71, doi: 10.1051/0004-6361/201117104
  * Rudnick et al. (2022) Rudnick, L., Brüggen, M., Brunetti, G., et al. 2022, ApJ, 935, 168, doi: 10.3847/1538-4357/ac7c76
  * Schive et al. (2018) Schive, H.-Y., ZuHone, J. A., Goldbaum, N. J., et al. 2018, MNRAS, 481, 4815, doi: 10.1093/mnras/sty2586
  * Sheardown et al. (2019) Sheardown, A., Fish, T. M., Roediger, E., et al. 2019, ApJ, 874, 112, doi: 10.3847/1538-4357/ab0c06
  * Tingay et al. (2013) Tingay, S. J., Goeke, R., Bowman, J. D., et al. 2013, PASA, 30, e007, doi: 10.1017/pasa.2012.007
  * Turk et al. (2011) Turk, M. J., Smith, B. D., Oishi, J. S., et al. 2011, The Astrophysical Journal Supplement Series, 192, 9, doi: 10.1088/0067-0049/192/1/9
  * van Haarlem et al. (2013) van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2, doi: 10.1051/0004-6361/201220873
  * van Weeren et al. (2019) van Weeren, R. J., de Gasperin, F., Akamatsu, H., et al. 2019, Space Sci. Rev., 215, 16, doi: 10.1007/s11214-019-0584-z
  * Vazza et al. (2023) Vazza, F., Wittor, D., Brüggen, M., & Brunetti, G. 2023, Galaxies, 11, 45, doi: 10.3390/galaxies11020045
  * Venturi et al. (2013) Venturi, T., Rossetti, M., Bardelli, S., et al. 2013, A&A, 558, A146, doi: 10.1051/0004-6361/201322023
  * Vikhlinin et al. (2006) Vikhlinin, A., Kravtsov, A., Forman, W., et al. 2006, ApJ, 640, 691, doi: 10.1086/500288
  * Wayth et al. (2015) Wayth, R. B., Lenc, E., Bell, M. E., et al. 2015, PASA, 32, e025, doi: 10.1017/pasa.2015.26
  * Weratschnig et al. (2008) Weratschnig, J., Gitti, M., Schindler, S., & Dolag, K. 2008, A&A, 490, 537, doi: 10.1051/0004-6361:20079289
  * ZuHone et al. (2021a) ZuHone, J., Ehlert, K., Weinberger, R., & Pfrommer, C. 2021a, Galaxies, 9, 91, doi: 10.3390/galaxies9040091
  * ZuHone & Hallman (2016) ZuHone, J. A., & Hallman, E. J. 2016, pyXSIM: Synthetic X-ray observations generator, Astrophysics Source Code Library, record ascl:1608.002.  http://ascl.net/1608.002
  * ZuHone et al. (2011) ZuHone, J. A., Markevitch, M., & Lee, D. 2011, ApJ, 743, 16, doi: 10.1088/0004-637X/743/1/16
  * ZuHone et al. (2021b) ZuHone, J. A., Markevitch, M., Weinberger, R., Nulsen, P., & Ehlert, K. 2021b, ApJ, 914, 73, doi: 10.3847/1538-4357/abf7bc