# ENTRUST: Argument Reframing with
Language Models and Entailment

Tuhin Chakrabarty1, Christopher Hidey 3 Smaranda Muresan1,2
Department of Computer Science, Columbia University 1
Data Science Institute, Columbia University 2
Google 3
{tuhin.chakr<EMAIL_ADDRESS>
<EMAIL_ADDRESS>The work is not affiliated to Google and was conducted
independently outside of the organization

###### Abstract

Framing involves the positive or negative presentation of an argument or issue
depending on the audience and goal of the speaker Entman (1983). Differences
in lexical framing, the focus of our work, can have large effects on peoples’
opinions and beliefs. To make progress towards reframing arguments for
positive effects, we create a dataset and method for this task. We use a
lexical resource for connotations to create a parallel corpus and propose a
method for argument reframing that combines controllable text generation
(positive connotation) with a postdecoding entailment component (same
denotation). Our results show that our method is effective compared to strong
baselines along the dimensions of fluency, meaning, and
trustworthiness/reduction of fear.

##  1 Introduction

Public opinion has been shown to be significantly influenced by framing
effects. Framing refers to the presentation of an issue, where even small
changes may have outsized effects on beliefs Chong and Druckman (2007). For
example, when asked about “welfare,” the American public is largely against
increasing spending (with only 20% in favor), but when asked about “assistance
to the poor,” 65% believe that the government is not spending enough Rasinski
(1989).

While other research has focused on syntactic framing Greene and Resnik (2009)
or issue framing Hartmann (2019), we focus specifically on lexical framing,
distinguishing sentences by their connotative meaning even where they have the
same denotative meaning. According to Frege (1892), two sentences with the
same truth conditions may refer to the same entities or state of affairs
(“reference,” also known as denotation) but be presented differently (“sense”
or connotation). For example, “undocumented workers” and “illegal aliens” have
the same denotation but different connotations Webson et al. (2020).

Arg1 |  | Alabama’s Supreme Court Chief Justice was
---
suspended… for ordering state probate
judges not to grant marriage licenses to gay
couples…
| Rf
---
Arg1
| Alabama’s Supreme Court Chief Justice was
---
suspended… for ordering state probate
judges not to grant legal marriage equality
to gay couples…
Arg2 |  | Every nation with territorial claims in the
---
arctic is a member of NATO, except Russia.
| Rf
---
Arg2
| Every nation with sovereign competence in the
---
arctic is a member of NATO, except Russia.
Arg3 |  | At this dire moment , we all need to amplify our
---
voices in defense of free speech .
| Rf
---
Arg3
| At this crucial moment , we all need to amplify
---
our voices in support of free speech.
Arg4 |  | It is difficult to think of any single act that
---
would do more to restore America’s soft power
than the election of Obama to the presidency
| Rf
---
Arg4
| It is difficult to think of any single act that
---
would do more to restore America’s diplomatic
credibility than the election of Obama to the
presidency
Table 1: Examples of arguments (Arg1, Arg2) with high partisan skew
collocations (in red) Webson et al. (2020) as well as appeal to fear or
prejudice argument fallacies (Arg3, Arg4) Da San Martino et al. (2019), along
with reframed arguments as an attempt by our model ENTRUST to improve
trustworthiness.

The examples in Table 1 are instances of lexical framing, where word choice
determines the difference in presentation Mccombs and Ghanem (2001). For
example, Arg1 and Arg2 contain collocations (in red) that have a high partisan
skew Webson et al. (2020), while Arg 3 and Arg 4 are examples of appeal to
fear or prejudice argument fallacies from propagandist news articles Da San
Martino et al. (2019). The goal is to reframe such arguments to be more
trustworthy (e.g., less partisan, no appeal to fear fallacy).

Connotations may be distinguished along the dimensions of politeness,
sentiment, or tangibility, among others Allaway and McKeown (2020), but in our
work we consider emotional association such as fear and trust. Appeal to fear
is considered an argumentative fallacy Walton (2006); Thierer (2012) and
appears prominently in manipulative text such as propaganda Da San Martino et
al. (2019). On the other hand, arguments with trusted language align with the
Aristotelian modes of persuasion, specifically ethos Aristotle and Bartlett
(2019).

In our work, we leverage such a lexical resource for connotations Allaway and
McKeown (2020) to reframe arguments to be more trustworthy (e.g., less
partisan, no appeal to fear fallacy), while maintaining the same denotative
meaning. While retrieve-and-replace methods perform well on other attribute
transfer tasks such as sentiment Li et al. (2018a); Sudhakar et al. (2019a),
our task is more dependent on broader context within a sentence even though we
are performing localized replacement. Thus, there are two main challenges we
need to address: 1) the lack of a parallel dataset of negatively and
positively framed arguments (naturally-occurring); and 2) a generation
approach that can not only change the connotative meaning but also keep the
same denotative meaning of the input argument.

We introduce our approach called ENTRUST : ArgumENT Reframing with langUage
modelS and enTailment, with the following contributions: 1) A Connotation-
guided Masked Language Model approach to generate a parallel dataset of
naturally occuring arguments and their reframings (Section 2); 2) A method for
argument reframing that combines controllable text generation (connotative
meaning associated with trust) and entailment (same denotative meaning)
(Section 3); 3) An evaluation on two different tasks — reframing partisan
arguments and appeal to fear/prejudice fallacies — showing that our method is
preferred over a strong retrieval-based baseline Sudhakar et al. (2019a) and
state-of-the-art pretrained language model Lewis et al. (2019), and it is
close to human performance on several evaluation criteria such as fluency,
meaning, trustworthiness/reduction in fear. Code, data, and models available
at https://github.com/tuhinjubcse/ArgReframingNAACL2021

##  2 Automatic Parallel Data Creation

To facilitate the reframing of arguments, we require a large-scale parallel
corpora of sentences with the same denotation but different connotative
meaning.

#### Selection of naturally-occurring arguments.

Since our goal is to re-write arguments, it is essential to identify an
abundant source of naturally-occurring arguments. The Change My View
subreddit, an argumentative discussion forum intended for persuasion on
diverse topics, has been used extensively in computational argumentation
research Tan et al. (2016); Wei et al. (2016); Musi et al. (2018); Chakrabarty
et al. (2019a, b); Hidey et al. (2017). We collect sentences from the same
source and classify them as claim, premise, or non-argument using the fine-
tuned BERT model released by Chakrabarty et al. (2019b). This results in
301,166 arguments labeled as premises. We consider only premises to create our
parallel data because argumentative appeals occur within justifications
(premises) for or against the speaker’s claim.

#### Connotation-guided Masked Language Model.

Allaway and McKeown (2020) provide a resource with words labeled for lexical
connotations, using the aspects of Social Value, Politeness, Impact,
Factuality, Sentiment, Emotional Association. For our work we only consider
Emotional Association, although in future work our methods could be applied
for other aspects. To create a parallel corpus, we use this lexical resource
and the 301,166 automatically identified premises from Change My View to
obtain candidate words within those premises for replacement. We match words
from the premises to those that have entries in the dictionary with emotional
connotations such as fear, trust, anticipation, and joy. To generate
replacements for these words, we need to find substitutions that maintain
denotative meaning while changing connotative meaning. We use the connotation
dictionary to address the latter. However, to address the former, we need to
provide only paraphrases that consider the context in which these words occur.
We thus use a masked language model (MLM).

Figure 1:  A schematic illustration of our system ENTRUST, where the top block
shows our training process where we use MLM along with connotation resource to
transform an original argument to an argument bearing different emotional
connotation and use them to fine-tune BART. The block below shows the
inference step (test time) where we use fine-tuned BART to reframe the
argument containing partisan collocation along with a NLI component to ensure
the same denotation with the input argument.

Masked language modeling approaches like BERT Devlin et al. (2018) and RoBERTa
Liu et al. (2019) can be considered cloze or “fill-in-the-blank” tasks, where
the model uses the context surrounding a masked-out token to try to predict
what the masked word should be. We borrow this framework (RoBERTa-large, in
particular) to mask the candidate words we identified via the connotation
lexicon. However, the rank of a predicted token from an MLM is based on the
language model probability – it provides no information about lexical
connotations. A premise re-written from MLM replacements may thus have the
same connotative meaning. To avoid this scenario, we restrict the MLM
replacements to be words with different connotations than the original masked
word (i.e., different Emotional Association).

Our data creation process is depicted in Figure 1. In example 2, the word
“resources” has the connotations joy;trust in our dictionary. The MLM
generates the replacement “tools,” which we verify has a different connotation
(emotionally neutral). For example 1, the words "prepare," "real," and
"defense" have the emotional connotations anticipation, trust, and
anticipation;anger;fear respectively. These words are replaced with plan,
your, and safety, using our MLM.

We treat the original premises as the “target” and the connotation-guided MLM
generated premises as the “source" for our method of argument reframing
detailed in the next section (Figure 1). While this process provides us with a
parallel dataset for reframing, we enhance the source-side of the data to
provide additional control during generation. Motivated by the work of
Schiller et al. (2020), which used aspect as a “control code” Keskar et al.
(2019) for argument generation, we also prepend the emotional associations of
the replaced words. Using the connotations from the lexical resource, we add
all listed emotions as control codes by separating them with a special token
(“[DELIM]”) (the top right block of Figure 1). During inference, we thus have
more control over the emotion of the words we are generating (in our case we
specifically use trust as the control code). For additional control, we also
insert demarcator tokens (“[SEP]”) at the boundary of the words we aim to
replace to provide our generative model with a better signal on what to
replace or rewrite. While the downside is that we need to identify spans for
replacement at test/inference time, our experiments will show that using
collocations or fear words makes it unnecessary.

By using the lexical connotation resource we do not have to rely on a separate
module/tagger based approach like that of Pryzant et al. (2020) to find biased
or problematic words that may introduce additional noise during training. Our
parallel data has 271,022 pairs for training and 30,114 for validation on
which perplexity is evaluated.

##  3 Method for Argument Reframing

As our goal is to change connotation while maintaining denotation, we divide
our approach to re-writing arguments into two primary tasks: 1) generating the
appropriate lexical substitutions while being pertinent to the context; 2)
ensuring that re-written arguments reflect the desired emotional association
while maintaining the same denotative meaning as the input.

###  3.1 Controllable Text Generation

BART Lewis et al. (2019) is a pre-trained model combining bidirectional and
auto-regressive transformers that achieves state-of-the-art results in several
text generation tasks. It is implemented as a sequence-to-sequence model with
a bidirectional encoder over corrupted text and a left-to-right auto-
regressive decoder. In principle, the pre-training procedure has two stages:
(1) text is corrupted with an arbitrary noising function, and (2) a
transformer-to-transformer model is learned to reconstruct the original text.
Because BART has an auto-regressive decoder, it can be directly fine-tuned for
most sequence generation tasks. Here, the encoder input is a sequence of
words, and the decoder generates outputs auto-regressively. We refer the
reader to Lewis et al. (2019) for further details.

For our task, we fine-tune BART on our parallel data, where the reframed
argument using MLM & connotation dictionary is the encoder source and the
original argument is the decoder target (Figure 1). The emotional connotations
added to the source via the special token DELIM (see Section 2) act as a
“control code” for generation. Moreover, for lexical framing, subtle
differences in word choices matter the most. By explicitly using special
tokens ([SEP]) in our parallel data during fine-tuning, the BART model learns
what to edit, instead of editing random words in the sentence, a common issue
often found in attribute transfer models Li et al. (2018a); Sudhakar et al.
(2019a). At test time, therefore, we can ensure the model reframes a desired
content span. All hyper-parameters are mentioned in the Appendix A.

Post fine-tuning at the decoding step, we use a top-k sampling strategy Fan et
al. (2018) to reframe arguments conditioned on a input argument and a target
emotion.

Source |  | trust <V>I suppose we could argue that they’re
---
much better at soft power than Nazi Germany
or the USSR, but come on
BART |  | I suppose we could argue that they’re much
---
better at military strength than ……….
| BART
---
\+ NLI
| I suppose we could argue that they’re much
---
better at diplomatic communication than ……
Table 2: Generation from fine-tuned BART without control for entailment can
sometime contradict the input thereby failing to maintain the same denotative
meaning

###  3.2 Post-decoding NLI

Our task is challenging in comparison to traditional text attribute transfer
tasks as we need to maintain the same denotative meaning as the input. While
in most cases BART is able to generate content which is semantically similar
to the input, it sometimes contradicts the input. For example, Table 2 shows
that BART changes soft power to military strength. Here the denotative meaning
changes. To control for this, we introduce an additional post-processing step.

We generate multiple outputs by varying the value of k (between 5 and 50)
while conducting top-k sampling. We then calculate the entailment scores of
these outputs with the input argument respectively using a RoBERTa Liu et al.
(2019) model fine-tuned on the Multi-NLI dataset Williams et al. (2018) and
then select the output having the best entailment score. We also experimented
with other methods for incorporating entailment during decoding based on prior
work (Section 8), but found these techniques to be less effective than our
method. As pre-trained sequence-to-sequence language models are good at
copying input and generating natural-sounding output, we hypothesize that our
approach will better allow us to change connotative meaning without affecting
fluency and denotation. In contrast, approaches such as “vocab boosting” Ghosh
et al. (2017) increase the logits of key connotative words, which would
necessarily decrease the probabilities of functional words and words necessary
for maintaining denotative meaning. Other approaches such as reinforcement
learning Pasunuru and Bansal (2017) may further decrease these desired
qualities, while trying to maximize another objective.

##  4 Evaluation Tasks and Test Data

To evaluate our methods for argument reframing we need to look beyond our
automatically labeled data. We consider two tasks: 1) reframing an argument
that contains partisan language to a less partisan argument; and 2) reframing
an appeal to fear or prejudice fallacy to an argument without this fallacy.

Recently Webson et al. (2020), proposed resources and methods to disentangle
denotation and connotation in vector spaces. They evaluate their methods on a
sample of around 300 collocations from vocabulary of Congressional records
Gentzkow et al. (2019) and Hyper-partisan News Kiesel et al. (2019) that occur
at least 100 times and have high partisan skew. We use these words to filter
arguments from the subreddits ChangeMyView and Politics. Some of these
collocations include phrases such as abortion providers, investment vehicles,
broken system, soft power, and territorial claims. We randomly sample 100 such
arguments to benchmark the performance of our model and further use towards
human evaluation.

In addition, we test our models on propaganda techniques employed in news
articles with an Appeal to Fear or Prejudice Da San Martino et al. (2019).
There are a total of 182 sentence-level text fragments labeled as Appeal to
Fear or Prejudice in the dataset released by Da San Martino et al. (2019). We
classify these 182 fragments as claims/premises/non-argument and randomly
sample 50 premises. Our goal is to reduce the fallacious nature of the
argument without changing the denotative meaning.

As our training distribution is different from these two datasets, these tasks
and test sets allow us to better test the generalization capabilities of our
models. Furthermore, almost none of the collocations introduced by Webson et
al. (2020) appear in the connotation dictionary of Allaway and McKeown (2020),
which helps us avoid the risk of mimicking replacements from our training
data.

INP1 |  | It would be dangerous , suicidal folly for
---
infidels to pretend that ramadan is not the
month of jihad
HUM1 |  | It would be counterproductive and
---
unreasonable for infidels to …….. jihad
INP2 |  | Trump backs away from further
---
military confrontation with Iran
HUM2 |  | Trump backs away from further
---
military engagement with Iran
Table 3: INP1 and INP2 are test data instances where INP1 is a Appeal to Fear
example while INP2 is an argument containing partisan collocation

For both of these tasks, we ask humans to generate reframings based on our
input test data for comparison and benchmark. We recruit two experts with
argumentation and journalism background (not authors of this paper) to reframe
arguments. For Appeal to Fear the instructions given were to make it less
fallacious by reducing the fear and rephrasing the argument (HUM1 in Table 3),
while for arguments with partisan collocation the human was instructed to
change the collocation so as to make it trustworthy (HUM2 in Table 3).

##  5 Experimental Setup

To compare the quality of the reframed arguments, we benchmark our ENTRUST
model against human performance and four baseline systems described below. For
the data containing collocations from Webson et al. (2020), because we know
they represent partisan language the ideal goal is to reframe them. For Appeal
to Fear or Prejudice data we reframe words which portray an emotion of fear
based on the popular NRC Emotion Lexicon Mohammad and Turney (2013).

###  5.1 Baseline Systems

As argument reframing is a new task, we adapt several baselines that have been
used for other generation tasks and also compare with human-generated
reframings.

####  Bart wIthout Demarcator and ENtailment (BART${}^{w/o}_{D+EN}$):

This is the pre-trained BART model fine-tuned on our parallel data without
explicitly adding signals on what to edit or reframe and without post-
processing based on entailment scores. This experiment helps us understand if
BART learns to adapt to the emotional connotations and can automatically edit
partisan collocations or words inducing fear without control.

####  Bart without EnTAilment (BART${}^{w/o}_{EN}$):

This is the pre-trained BART model fine-tuned on our parallel data with
explicit signals ([SEP] token) but without the NLI component as a post-
processing tool. This experiment helps us understand how well BART learns to
adapt to the emotional connotations without altering the denotative meaning
once guided with what to reframe.

####  Lexical Replacement (LEXREP):

We use a similar method employed for our parallel data creation. We rely on
Masked Language Models for lexical substitutions. Because our goal is to
reframe arguments to be trustworthy we prefer substitutions which have a
connotation of trust in the resource by Allaway and McKeown (2020). In case we
cannot find the substitution in the connotation dictionary we honor default
MLM predicted infilling.

####  Generative Style Transformer (GST):

We use the state of art for text style transfer by Sudhakar et al. (2019a),
which is a part of a larger “Delete Retrieve Generate" framework Li et al.
(2018a). To maintain parity with other baselines, instead of letting the model
delete attribute keywords we delete the partisan collocations or fear related
words from the arguments as the first step, followed by the usual retrieve and
generate steps. Our training data for this method includes only arguments
labeled with their attribute (e.g., positive or negative). Arguments
containing lexical connotations catering to trust are positive, while those
not catering to trust are negative.

System | Partisan Task | Appeal to Fear Task
---|---|---
BART${}^{w/o}_{D+EN}$ | 64.1 | 38.5
BART${}^{w/o}_{EN}$ | 91.9 | 43.1
GST | 86.4 | 38.3
LEXREP | 92.4 | 44.3
ENTRUST | 92.9 | 44.5
HUMAN | 93.9 | 41.6 *
Table 4: Semantic Similarity of reframed arguments with input arguments. (*) Here human did not restrict themselves to just lexical framing, so automated metrics might penalize them for more reframing. System |  Fluency |  Meaning | Trust $\uparrow$ | Fear$\downarrow$
---|---|---|---|---
INPUT |  - |  - | 3.24 | 3.36
BART${}^{w/o}_{D+EN}$ |  2.78 |  2.56 | 2.60 | 3.01
BART${}^{w/o}_{EN}$ |  3.39 |  3.00 | 3.13 | 2.58
LEXREP |  3.38 |  3.00 | 3.08 | 2.54
GST |  2.14 |  1.81 | 2.01 | 2.44
ENTRUST |  3.51 |  3.30 | 3.52 | 2.39
HUMAN |  3.72 |  3.63 | 3.71 | 2.59
Table 5: Fluency and Meaning Preservation scores given by human judges on a
scale of (1-5) for reframed arguments with respect to input arguments. Fluency
and Meaning Preservation ratings are for all arguments in test set, while
Trust ratings are for arguments with Partisan collocation (higher scores
better), and Fear ratings for Appeal To Fear or Prejudice ones only (lower
scores better).

###  5.2 Evaluation Criteria

#### Automatic evaluation.

One important criterion is to measure if the reframed arguments are faithful
to the input. Even though we are changing the argument for connotations, it
should still maintain the same denotative meaning as the input. To this end we
calculate Semantic Similarity with our input using SENTENCE BERT(SBERT)
Reimers and Gurevych (2019).

#### Human evaluation.

We use Amazon Mechanical Turk to evaluate on a total of 900 utterances, 750
generated from 5 systems and 150 utterances generated by humans. We proposed a
set of 3 criteria to evaluate the generated output: (1) Fluency (F) (“How
fluent and grammatical are the utterances?”), (2) Meaning Preservation (M)
(“How well does the reframed argument capture the same denotative meaning as
the input argument?”), (3) Trustworthiness/Presence of Fear(T/PF). For the 100
input arguments reflecting partisan view we ask Turkers to rate reframed
arguments based on trustworthiness with respect to the input. For the 50
Appeal to Fear or Prejudice fallacies we ask Turkers to rate reframed
arguments based on presence of fear (the intention behind this being that we
want to rank systems which portray the least amount of fear). In both of these
ratings we still ask Turkers to keep into account the denotative meaning
(i.e., making it trustworthy or less fallacious at the expense of meaning
alterations should be scored lower). We hired 40, 25, 39 (23 and 16) Turkers
for the three separate tasks respectively. The computed IAA using
Krippendorff’s alpha for Fluency, Meaning Preservation , Trust-Worthiness and
Presence of Fear is 0.62, 0.65, 0.51, 0.46, respectively.

Original Argument | System |  reframed Argument | F | M | T$\uparrow$/PF$\downarrow$
---|---|---|---|---|---
It is difficult to think of any single act that would do more to restore America’s soft power than the election of Obama to the presidency | BART${}^{w/o}_{D+EN}$ |  It is difficult to think of any single act that would do more to restore America’s soft power than the election of Obama to the presidency | 3.7 | 2.3 | 3.3
BART${}^{w/o}_{EN}$ |  It is difficult to think of any single act that would do more to restore America’s moral authority than the election of Obama to the presidency | 3.7 | 3.3 | 3.0
LEXREP |  It is difficult to think of any single act that would do more to restore America’s moral standing than the election of Obama to the presidency | 3.7 | 3.3 | 2.7
GST |  Hated it is difficult to think of any single act that would do more to restore America’s economy than the election of Obama to the presidency | 1.7 | 1.7 | 2.7
ENTRUST |  It is difficult to think of any single act that would do more to restore America’s diplomatic credibility than the election of Obama to the presidency | 4.3 | 3.7 | 5.0
HUMAN |  It is difficult to think of any single act that would do more to restore America’s political and economic influence than the election of Obama to the presidency | 4.0 | 3.3 | 4.0
Or he can seize this opportunity and use his government’s diplomatic influence to defend the life of an australian citizen , whose courageous public service is recognised by countless people across the world | BART${}^{w/o}_{D+EN}$ |  Or he can seize this opportunity and use his governments’s diplomatic influence to defend the life of an australian citizen , whose courageous  military service is recognised by countless people across the world | 2.7 | 3.0 | 2.3
BART${}^{w/o}_{EN}$ |  Or he can honor this opportunity and use his nation’s diplomatic resources to honor the life of an australian citizen , whose  unwavering public service is recognised by countless people across the world | 4.0 | 4.7 | 1.3
LEXREP |  Or he can take this opportunity and use his nations’s diplomatic resources to defend the life of an australian citizen , whose courageous  military service is recognised by countless people across the world | 4.7 | 4.0 | 2.0
GST |  Or he can do this opportunity and use his diplomatic expertise to change the life of an australian citizen , whose public service is recognised by countless people across the world | 1.7 | 2.0 | 2.0
ENTRUST |  Or he can honor this opportunity and use his nation’s diplomatic resources to vindicate the life of an australian citizen , whose unwavering public service is recognised by countless people across the world | 4.7 | 4.7 | 1.3
HUMAN |  Or he can pick up this opportunity and use his government’s diplomatic influence to defend the life of an Australian citizen, whose actions have been publicly recognized as highly relevant at an international level. | 3.7 | 4.0 | 2.3
Table 6: Examples of generated outputs from different systems (with human
reframed argument as references) for arguments containing partisan
collocations and appeal to fear, respectively. We show average scores (over
three annotators) on a 1-5 scale with 1 denotes the worst and 5 be the best.
More examples in Appendix

##  6 Results

#### Automatic Evaluation.

As can be seen in Table 4 our model ENTRUST maintains the denotative meaning
with the input better than other systems ($p<.001$ using approximate
randomization tests) and only marginally behind humans when it comes to
arguments with partisan collocations. For Appeal to Fear or Prejudice our
system maintains better denotative meaning than all systems except LEXREP
($p<.001$). The automatic metric somewhat penalizes humans for changing more
content than just targeted words; this unreliability is a known issue with
automated metrics Novikova et al. (2017) and strongly implies a need for human
evaluation.

#### Human Evaluation.

Table 5 shows the results of our human-based evaluations. For fluency, meaning
preservation, trustworthiness, and reduction of fear the ENTRUST model is
better than all the baselines ($p<.001$ using approximate randomization
tests). It is further encouraging to see that the entailment step helps us
maintain better denotative meaning (See Table 5 Col3: Row 4 vs Row 7). For
Presence of Fear, Turkers often rate our ENTRUST model to be the least
fearful, including slightly when compared to reframings of an expert. We
hypothesize this is because the human judges found it difficult to completely
remove fear while keeping the denotative meaning (indeed the humans scores
slightly better on meaning comparing with our system ENTRUST). Sometimes, an
ungrammatical generation or a reframing which change the meaning will contain
less fear (rating 1 meaning no fear at all). However, to avoid this we
explicitly asked Turkers to rate those samples as moderate so as to not bias
the overall results.

##  7 Analysis and Discussion

As can be seen in Table 6, the ENTRUST model accurately captures diplomatic
credibility as an alternate for soft power which is encouraging as soft power
is measured through culture, diplomacy, education, business/innovation, and
government.111https://en.wikipedia.org/wiki/Soft_power The
BART${}^{w/o}_{D+EN}$ model often fails to reframe anything, which shows the
importance of adding [SEP] tokens as explicit supervision so that the model
knows what to edit. The GST model fails at both grammaticality and meaning
preservation, which makes it harder to judge its trustworthiness and ability
to ameliorate fearful appeal. Finally, ENTRUST reframings are not static.
Table 8 shows that for the same collocation of targeted killing, the
reframings are different, contingent on the context. This goes on to prove
that our model not only generalizes to unseen test data, but can produce
novel, grammatical and meaningful edits based on context.

| An Iranian government official seemed to suggest that
---
President Trump’s properties could be potential targets
in retaliation for the US targeted killing of Iranian
general Qassem Soleimani.
| An Iranian government official seemed to …. suggest that
---
President Trump’s properties …. in retaliation for the US
involvement in the execution of Iranian …..
| A federal appeals court ordered the U.S. Department of
---
Justice to turn over key portions of a memorandum
justifying the government’s targeted killing of people
linked to terrorism, including Americans
| A federal appeals court ordered the U.S. Department of
---
Justice to turn ……… justifying the government’s
extrajudicial execution of people … terrorism, ………
Table 7: Different reframed arguments by ENTRUST model based on same
collocation

##  8 Related Work

The effects of lexical framing have been studied for social and political
issues, although our work is the first to use lexical framing in generation
for positive framing effects (less partisan, no appeal to fear fallacy).
Demszky et al. (2019) and Tyagi et al. (2020) study political polarization and
how this manifests in differences in word choice among different groups;
KhudaBukhsh et al. (2020) provide an interpretable framework using machine
translation between groups to generate differences. While these works
encourage computational approaches to reframe arguments for better lexical
choice, these approaches do not control for denotation or connotation and thus
may cause differences in word choice to result in a change in meaning. The
most similar work to ours is that of Pryzant et al. (2020), who use a corpus
of Wikipedia edits to train a model for debiasing, which includes framing.
However, in their work communicative intent is left implicit; the corpus is
only labeled for types of debiasing, which includes framing at a high level
and not the connotations involved. Thus, their model only learns lexical
differences, whereas our model is controllable.

While our focus is on lexical framing, other work has investigated the
identification of other types of frames and their effects. Greene and Resnik
(2009) studied syntactic framing, finding a link between implicit sentiment
and syntactic packagings. Previous studies have also involved emphasis framing
– Ding and Pan (2016) find that emphasizing aspects of products given personal
information is more effective for content selection in advertisements. Other
research has involved issue framing – Ajjour et al. (2019) and Hartmann et al.
(2019) study how arguments are framed in debates (e.g., in terms of economics
or safety). Nguyen (2013) and Field et al. (2018) study “agenda-setting” for
news and congressional debates and August et al. (2018) for study recruitment.
Cano-Basave and He (2016) and Musi and Aakhus (2019) leverage semantic frames
for distant labeling and analysis of arguments in political debates,
respectively, and find, for example, that evidence and reasoning are among the
most common. However, these approaches have focused on identification rather
than generation.

Finally, our work is also related to style transfer and controllable
generation. Much of the work in “style transfer” has referred to changing the
sentiment of a statement, which changes the truth condition and thus the
denotative meaning. Sentiment is often explicitly marked and thus approaches
such as deleting and replacing lexical markers are effective Li et al.
(2018b); Sudhakar et al. (2019b), although our experiments showed the
difficulty of applying these techniques to our task. To control text
generation by limiting contradictions, Pasunuru and Bansal (2017) use an
entailment score as a reward in Reinforcement Learning, ensuring that a
generated text is logically implied by the ground-truth text. Holtzman et al.
(2018) utilize a discriminative model trained on SNLI Bowman et al. (2015) to
complement an RNN generator and guide the decoding process to improve
contradictions in generation. Although we experimented with both of these
approaches, including the approach of Holtzman et al. (2018) with MNLI to
account for entailment in text generation, none of them yielded better results
than our method. Other approaches have explored “vocab boosting” Ghosh et al.
(2017) for tasks such as de-biasing Ma et al. (2020), which involves
increasing the values of certain words; however, as these values are on the
simplex, the softmax function necessarily decreases the values of other logits
which are key to fluency such as function words.

##  9 Conclusion

Our experiments showed that our approach is effective in reframing partisan
arguments and appeals to fear for increased trustworthiness. We provided a
method for creating a dataset using a lexical resource for connotations and
masked language modeling. We used this dataset to fine-tune a controllable
text generation model for the task of changing connotative meaning and used a
model trained for natural language inference to maintain the denotative
meaning. Our evaluations found that our approach generalized to two different
tasks and data sets. In future work, we plan to directly incorporate the role
of stance in framing (for arguments and counter-arguments). We also plan to
expand our work to generating concessions Musi (2018), where the goal is for
the speaker to portray some point of agreement in a positive light before
disagreeing.

##  10 Ethics

Our data is collected from Reddit and we understand and respect user privacy.
Our models are fine-tuned on sentence level data obtained from user posts.
These do not contain any explicit detail which leaks information about a users
name, health, negative financial status, racial or ethnic origin, religious or
philosophical affiliation or beliefs, sexual orientation, trade union
membership, alleged or actual commission of crime.

Second, although we use language models trained on data collected from the
Web, which have been shown to have issues with bias and abusive language Sheng
et al. (2019); Wallace et al. (2019), the inductive bias of our models should
limit inadvertent negative impacts. Unlike model variants such as GPT, BART is
a conditional language model, which provides more control of the generated
output. We have two levels of control on our generation approach: lexical
replacements via connotations associated with trust and an entailment method
that aims to keep the same denotation of the original argument. While dual-use
concerns are certainly possible here, we think that open-sourcing this
technology will help to generate arguments with more balanced and trusted
language that are less targeted towards partisanship or appeals to fear.

Finally, while there may be concerns about building generative models for
persuasion, social scientists distinguish persuasion from manipulation based
on two aspects: dissimulation and constraint Nettel and Roque (2012).
Dissimulation involves concealing intention, which requires hiding
information, whereas constraint involves removing options from the audience
and forcing them to accept the conclusion. Our work on reframing arguments
does not aim to hide information about a topic or present it as the only
choice, but aims to provide the same argument using more balanced and trusted
language. We achieve this by two key components of our technology:
controllable text generation (connotation associated with trust) and
entailment model to ensure same denotation.

The technology should be used responsibly, particularly making sure the
generation is controllable for trust and positive emotion and that the
entailment component is used for ensuring the same denotation with the
original argument.

Finally we pay the Turkers at a rate of 15$/hour, complying with minimum wage
standards in most places.

## References

  * Ajjour et al. (2019) Yamen Ajjour, Milad Alshomary, Henning Wachsmuth, and Benno Stein. 2019.  Modeling frames in argumentation.  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 2922–2932, Hong Kong, China. Association for Computational Linguistics.
  * Allaway and McKeown (2020) Emily Allaway and Kathleen McKeown. 2020.  A unified feature representation for lexical connotations.
  * Aristotle and Bartlett (2019) Aristotle and R. Bartlett. 2019.  Aristotle’s "art of rhetoric".
  * August et al. (2018) Tal August, Nigini Oliveira, Chenhao Tan, Noah A. Smith, and Katharina Reinecke. 2018.  Framing effects: Choice of slogans used to advertise online experiments can boost recruitment and lead to sample biases.  _PACMHCI_ , 2(CSCW):22:1–22:19.
  * 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.  _arXiv preprint arXiv:1508.05326_.
  * Cano-Basave and He (2016) Amparo Elizabeth Cano-Basave and Yulan He. 2016.  A study of the impact of persuasive argumentation in political debates.  In _Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 1405–1413, San Diego, California. Association for Computational Linguistics.
  * Chakrabarty et al. (2019a) Tuhin Chakrabarty, Christopher Hidey, and Kathleen McKeown. 2019a.  Imho fine-tuning improves claim detection.  _arXiv preprint arXiv:1905.07000_.
  * Chakrabarty et al. (2019b) Tuhin Chakrabarty, Christopher Hidey, Smaranda Muresan, Kathleen McKeown, and Alyssa Hwang. 2019b.  Ampersand: Argument mining for persuasive online discussions.  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 2926–2936.
  * Chong and Druckman (2007) Dennis Lee Chong and James N. Druckman. 2007.  Framing theory.
  * Da San Martino et al. (2019) Giovanni Da San Martino, Seunghak Yu, Alberto Barrón-Cedeno, Rostislav Petrov, and Preslav Nakov. 2019.  Fine-grained analysis of propaganda in news article.  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 5640–5650.
  * Demszky et al. (2019) Dorottya Demszky, Nikhil Garg, Rob Voigt, James Zou, Matthew Gentzkow, Jesse Shapiro, and Dan Jurafsky. 2019.  Analyzing polarization in social media: Method and application to tweets on 21 mass shootings.  _arXiv preprint arXiv:1904.01596_.
  * Devlin et al. (2018) Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2018.  Bert: Pre-training of deep bidirectional transformers for language understanding.  _arXiv preprint arXiv:1810.04805_.
  * Ding and Pan (2016) Tao Ding and Shimei Pan. 2016.  Personalized emphasis framing for persuasive message generation.  In _Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing_ , pages 1432–1441, Austin, Texas. Association for Computational Linguistics.
  * Entman (1983) R. Entman. 1983.  Framing: Toward clarification of a fractured paradigm.  _Journal of Communications_.
  * Fan et al. (2018) Angela Fan, Mike Lewis, and Yann Dauphin. 2018.  Hierarchical neural story generation.  _arXiv preprint arXiv:1805.04833_.
  * Field et al. (2018) Anjalie Field, Doron Kliger, Shuly Wintner, Jennifer Pan, Dan Jurafsky, and Yulia Tsvetkov. 2018.  Framing and agenda-setting in russian news: a computational analysis of intricate political strategies.  _arXiv preprint arXiv:1808.09386_.
  * Frege (1892) G. Frege. 1892.  Über sinn und bedeutung.  _Zeitschrift für Philosophie und philosophische Kritik_ , 100:25–50.
  * Gentzkow et al. (2019) Matthew Gentzkow, Jesse M Shapiro, and Matt Taddy. 2019.  Measuring group differences in high-dimensional choices: method and application to congressional speech.  _Econometrica_ , 87(4):1307–1340.
  * Ghosh et al. (2017) Sayan Ghosh, Mathieu Chollet, Eugene Laksana, Louis-Philippe Morency, and Stefan Scherer. 2017.  Affect-LM: A neural language model for customizable affective text generation.  In _Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 634–642, Vancouver, Canada. Association for Computational Linguistics.
  * Greene and Resnik (2009) Stephan Greene and Philip Resnik. 2009.  More than words: Syntactic packaging and implicit sentiment.  In _Proceedings of Human Language Technologies: The 2009 Annual Conference of the North American Chapter of the Association for Computational Linguistics_ , pages 503–511, Boulder, Colorado. Association for Computational Linguistics.
  * Hartmann (2019) Frederik Hartmann. 2019.  Predicting historical phonetic features using deep neural networks: A case study of the phonetic system of Proto-Indo-European.  In _Proceedings of the 1st International Workshop on Computational Approaches to Historical Language Change_ , pages 98–108, Florence, Italy. Association for Computational Linguistics.
  * Hartmann et al. (2019) Mareike Hartmann, Tallulah Jansen, Isabelle Augenstein, and Anders Søgaard. 2019\.  Issue framing in online discussion fora.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 1401–1407, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Hidey et al. (2017) Christopher Hidey, Elena Musi, Alyssa Hwang, Smaranda Muresan, and Kathleen McKeown. 2017.  Analyzing the semantic types of claims and premises in an online persuasive forum.  In _Proceedings of the 4th Workshop on Argument Mining_ , pages 11–21.
  * Holtzman et al. (2018) Ari Holtzman, Jan Buys, Maxwell Forbes, Antoine Bosselut, David Golub, and Yejin Choi. 2018.  Learning to write with cooperative discriminators.  _arXiv preprint arXiv:1805.06087_.
  * Keskar et al. (2019) Nitish Shirish Keskar, Bryan McCann, Lav R Varshney, Caiming Xiong, and Richard Socher. 2019.  Ctrl: A conditional transformer language model for controllable generation.  _arXiv preprint arXiv:1909.05858_.
  * KhudaBukhsh et al. (2020) Ashiqur R KhudaBukhsh, Rupak Sarkar, Mark S Kamlet, and Tom M Mitchell. 2020.  We don’t speak the same language: Interpreting polarization through machine translation.  _arXiv preprint arXiv:2010.02339_.
  * Kiesel et al. (2019) Johannes Kiesel, Maria Mestre, Rishabh Shukla, Emmanuel Vincent, Payam Adineh, David Corney, Benno Stein, and Martin Potthast. 2019.  SemEval-2019 task 4: Hyperpartisan news detection.  In _Proceedings of the 13th International Workshop on Semantic Evaluation_ , pages 829–839, Minneapolis, Minnesota, USA. Association for Computational Linguistics.
  * Lewis et al. (2019) Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Ves Stoyanov, and Luke Zettlemoyer. 2019.  Bart: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension.  _arXiv preprint arXiv:1910.13461_.
  * Li et al. (2018a) Juncen Li, Robin Jia, He He, and Percy Liang. 2018a.  Delete, retrieve, generate: A simple approach to sentiment and style transfer.  _arXiv preprint arXiv:1804.06437_.
  * Li et al. (2018b) Juncen Li, Robin Jia, He He, and Percy Liang. 2018b.  Delete, retrieve, generate: a simple approach to sentiment and style transfer.  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 1865–1874, New Orleans, Louisiana. Association for Computational Linguistics.
  * 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_.
  * Ma et al. (2020) Xinyao Ma, Maarten Sap, Hannah Rashkin, and Yejin Choi. 2020.  Powertransformer: Unsupervised controllable revision for biased language correction.  _arXiv preprint arXiv:2010.13816_.
  * Mccombs and Ghanem (2001) M. Mccombs and Salma I. Ghanem. 2001.  The convergence of agenda setting and framing.
  * Mohammad and Turney (2013) Saif M Mohammad and Peter D Turney. 2013.  Crowdsourcing a word–emotion association lexicon.  _Computational Intelligence_ , 29(3):436–465.
  * Musi (2018) Elena Musi. 2018.  How did you change my view? a corpus-based study of concessions’ argumentative role.  _Discourse Studies_ , 20:270 – 288.
  * Musi and Aakhus (2019) Elena Musi and Mark Aakhus. 2019.  Framing fracking: Semantic frames as meta-argumentative indicators for knowledge-driven argument mining of controversies.
  * Musi et al. (2018) Elena Musi, Debanjan Ghosh, and Smaranda Muresan. 2018.  Changemyview through concessions: Do concessions increase persuasion?  _arXiv preprint arXiv:1806.03223_.
  * Nettel and Roque (2012) Ana Laura Nettel and Georges Roque. 2012.  Persuasive argumentation versus manipulation.  _Argumentation_ , 26(1):55–69.
  * Nguyen (2013) Viet-An Nguyen. 2013.  Lexical and hierarchical topic regression.  In _NIPS 2013_.
  * Novikova et al. (2017) Jekaterina Novikova, Ondřej Dušek, Amanda Cercas Curry, and Verena Rieser. 2017.  Why we need new evaluation metrics for NLG.  In _Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing_ , pages 2241–2252, Copenhagen, Denmark. Association for Computational Linguistics.
  * Ott et al. (2019) Myle Ott, Sergey Edunov, Alexei Baevski, Angela Fan, Sam Gross, Nathan Ng, David Grangier, and Michael Auli. 2019.  fairseq: A fast, extensible toolkit for sequence modeling.  _arXiv preprint arXiv:1904.01038_.
  * Pasunuru and Bansal (2017) Ramakanth Pasunuru and Mohit Bansal. 2017.  Reinforced video captioning with entailment rewards.  _arXiv preprint arXiv:1708.02300_.
  * Pryzant et al. (2020) Reid Pryzant, Richard Diehl Martinez, Nathan Dass, Sadao Kurohashi, Dan Jurafsky, and Diyi Yang. 2020.  Automatically neutralizing subjective bias in text.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 34, pages 480–489.
  * Rasinski (1989) K. Rasinski. 1989.  The effect of question wording on public support for government spending.  _Public Opinion Quarterly_ , 53:388–394.
  * Reimers and Gurevych (2019) Nils Reimers and Iryna Gurevych. 2019.  Sentence-bert: Sentence embeddings using siamese bert-networks.  _arXiv preprint arXiv:1908.10084_.
  * Schiller et al. (2020) Benjamin Schiller, Johannes Daxenberger, and Iryna Gurevych. 2020.  Aspect-controlled neural argument generation.  _arXiv preprint arXiv:2005.00084_.
  * Sheng et al. (2019) Emily Sheng, Kai-Wei Chang, Premkumar Natarajan, and Nanyun Peng. 2019.  The woman worked as a babysitter: On biases in language generation.  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 3407–3412, Hong Kong, China. Association for Computational Linguistics.
  * Sudhakar et al. (2019a) Akhilesh Sudhakar, Bhargav Upadhyay, and Arjun Maheswaran. 2019a.  Transforming delete, retrieve, generate approach for controlled text style transfer.  _arXiv preprint arXiv:1908.09368_.
  * Sudhakar et al. (2019b) Akhilesh Sudhakar, Bhargav Upadhyay, and Arjun Maheswaran. 2019b.  “transforming” delete, retrieve, generate approach for controlled text style transfer.  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 3269–3279, Hong Kong, China. Association for Computational Linguistics.
  * Tan et al. (2016) Chenhao Tan, Vlad Niculae, Cristian Danescu-Niculescu-Mizil, and Lillian Lee. 2016\.  Winning arguments: Interaction dynamics and persuasion strategies in good-faith online discussions.  In _Proceedings of the 25th international conference on world wide web_ , pages 613–624.
  * Thierer (2012) Adam Thierer. 2012.  Technopanics, threat inflation, and the danger of an information technology precautionary principle.  _IO: Productivity_.
  * Tyagi et al. (2020) Aman Tyagi, Anjalie Field, Priyank Lathwal, Yulia Tsvetkov, and Kathleen M Carley. 2020.  A computational analysis of polarization on indian and pakistani social media.  _arXiv preprint arXiv:2005.09803_.
  * Wallace et al. (2019) Eric Wallace, Shi Feng, Nikhil Kandpal, Matt Gardner, and Sameer Singh. 2019.  Universal adversarial triggers for attacking and analyzing NLP.  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 2153–2162, Hong Kong, China. Association for Computational Linguistics.
  * Walton (2006) D. Walton. 2006.  Fundamentals of critical argumentation.  In _Critical reasoning and argumentation_.
  * Webson et al. (2020) Albert Webson, Zhizhong Chen, Carsten Eickhoff, and Ellie Pavlick. 2020.  Do “Undocumented Workers” == “Illegal Aliens”? Differentiating Denotation and Connotation in Vector Spaces.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 4090–4105, Online. Association for Computational Linguistics.
  * Wei et al. (2016) Zhongyu Wei, Yang Liu, and Yi Li. 2016.  Is this post persuasive? ranking argumentative comments in online forum.  In _Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)_ , pages 195–200.
  * 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. Association for Computational Linguistics.

##  Appendix A Hyper-Parameters and Other Experimental Settings

  1. 1.

No of Parameters: For Connotation guided MLM and Entailment we use RoBERTa
large model (355M). For generation we use the BART large checkpoint (400M
parameters) and use the implementation by FAIRSEQ Ott et al. (2019)
222https://github.com/pytorch/fairseq/tree/master/examples/bart.

  2. 2.

No of Epochs: We fine-tune pre-trained BART for 20 epochs for ENTRUST model
and save best model based on validation perplexity.

  3. 3.

Training Time: Our training time is 80 minutes for BART.

  4. 4.

Hardware Configuration: We use 4 RTX 2080 GPU

  5. 5.

Training Hyper parameters: We use the same parameters mentioned in the github
repo where BART was fine-tuned for CNN-DM summarization task with the
exception of MAX-TOKENS (size of each mini-batch, in terms of the number of
tokens.) being 1024 for us. For entailment we rely on AllenNLP roberta
checkpoint that is finetuned on MNLI 333urlhttps://demo.allennlp.org/textual-
entailment

  6. 6.

Decoding Strategy & Hyper Parameters:For decoding we reframe from our models
using a top-k random sampling scheme Fan et al. (2018). At each timestep, the
model generates the probability of each word in the vocabulary being the
likely next word. We randomly sample from the k = 5 to k=50 for most likely
candidates from this distribution and re-rank them based on entailment scores.

###  A.1 Role of Context in re-framing

As mentioned ENTRUST reframings are not static. Table 8 shows that for
multiple same collocations the reframings are different, contingent on the
context. This supports our claim that our model not only generalizes on unseen
test data, but can produce novel, grammatical and meaningful edits based on
context. We notice that for the first example, ENTRUST believes scientific
proof leads to be better credibility instead of using the broad umbrella term
experts. For the same collocation of leading expert we see that given the
premise talks about a neurological basis related to birth , ENTRUST reframes
it to reflect to leading medical fact as the term “expert" can be ambiguous,
while people are generally more likely to believe medical facts.

| Statistically based-wise though, the number of violent
---
crime is more prevalent in warm areas,leading experts
to believe a correlation between warm and people being
more aggressive.
| Statistically based-wise though, the number of violent
---
crime is more prevalent in warm areas,leading scientific
proof to believe a correlation between warm and people
being more aggressive.
| The leading experts all agree that there’s a neurological
---
basis & there is significant evidence showing it’s caused
during fetal neurological development
| The leading medical facts all agree that there’s a
---
neurological basis & there is significant evidence showing
it’s caused during fetal neurological development
| We need leaders who recognize our moral obligation
---
for health equality
| We need leaders who recognize our moral accountability
---
for health equality
| We all have a moral obligation to the next generation to
---
leave America’s natural resources in better condition than
when we inherited them
| We all have a personal oath to the next generation to
---
leave America’s natural resources in better condition than
when we inherited them
Table 8: Different reframed arguments by ENTRUST model based on same collocation Original Argument | System |  reframed Argument | F | M | T$\uparrow$/PF$\downarrow$
---|---|---|---|---|---
AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the U.S. said bilateral relations are in crisis | BART${}^{w/o}_{D+EN}$ |  AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the U.S. said bilateral relations are in fact stable | 3.7 | 2.0 | 2.3
BART${}^{w/o}_{EN}$ |  AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the U.S. said diplomatic relations are in crisis | 4.7 | 3.3 | 4.3
LEXREP |  AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the U.S. said that negotiations are in crisis | 4.0 | 2.3 | 3.0
GST |  AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the law said are in crisis | 1.3 | 1.3 | 1.3
ENTRUST |  AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the U.S. said diplomatic ties are in crisis | 5.0 | 4.7 | 4.7
HUMAN |  AIPAC called on the Obama administration to take steps to defuse tension with Israel, while Israel’s ambassador to the U.S. said relations are in crisis | 4.7 | 3.7 | 4.0
Kentucky Senate President Robert Stivers on Wednesday a federal judge to withhold action against Davis for her defiance of the ruling by denying marriage licenses to gay couples, until the Kentucky General Assembly can act | BART${}^{w/o}_{D+EN}$ |  Kentucky Senate President Robert Stivers on Wednesday asked a federal judge to withhold action against Davis for her defiance of the law ruling by denying  marriage licenses to gay couples, until the Kentucky General Assembly can act. | 4.3 | 3.7 | 3.0
BART${}^{w/o}_{EN}$ |  Kentucky Senate President Robert Stivers on Wednesday asked a federal judge to withhold action against Davis for her defiance of the ruling by denying legal marriage equality to gay couples, until the Kentucky General Assembly can act. | 4.7 | 4.0 | 4.0
LEXREP |  Kentucky Senate President Robert Stivers on Wednesday asked a federal judge to withhold action against Davis for her defiance of the ruling by denying wedding services to gay couples, until the Kentucky General Assembly can act. | 4.0 | 1.3 | 2.3
GST |  Kentucky Senate President Robert Stivers on Wednesday asked a federal judge to withhold action against Davis for her defiance of the ruling by denying the gay couples, until the Kentucky General Assembly can act. | 1.7 | 1.3 | 2.7
ENTRUST |  Kentucky Senate President Robert Stivers on Wednesday asked a federal judge to withhold action against Davis for her defiance of the ruling by denying legal marriage authorization to gay couples, until the Kentucky General Assembly can act. | 4.3 | 4.7 | 4.3
HUMAN |  Kentucky Senate President Robert Stivers on Wednesday asked a federal judge to withhold action against Davis for her defiance of the ruling by denying  marriage paperwork to gay couples, until the Kentucky General Assembly can act. | 4.7 | 3.0 | 3.7
A campaign of  hate laced with blatant anti-semitic overtones | BART${}^{w/o}_{D+EN}$ |  A campaign of  hate laced with  genuine anti-semitic overtones | 4.3 | 4.7 | 2.3
BART${}^{w/o}_{EN}$ |  A campaign of  trust laced with  obvious anti-semitic overtones | 2.0 | 1.7 | 2.0
LEXREP |  A campaign of intimidation laced with strong anti-semitic overtones | 3.3 | 3.0 | 3.0
GST |  A campaign of injuring rollercoaster laced with anti - semitic overtones | 2.3 | 1.0 | 3.0
ENTRUST |  A campaign of prejudice  laced with genuine anti - semitic overtones | 3.7 | 4.0 | 2.0
HUMAN |  A campaign with clear anti-semitic overtones which does not promote peace | 2.7 | 2.7 | 3.7
Table 9: Examples of generated outputs from different systems (with human
reframed argument as references) for arguments containing partisan
collocations and appeal to fear, respectively. We show average scores (over
three annotators) on a 1-5 scale with 1 denotes the worst and 5 be the best.


# Cassini, d’Ocagne, and Vajda identities for $n$-step Fibonacci numbers

Milan Janjić

###### Abstract.

Results of this paper concern $n$-determinants which we defined in the paper
[2]. In the paper [1], $2$-determinants are considered. In this paper, we
extend results from [1] on $n$-determinants by proving that Cassini, d’Ocagne,
Catalan and Vajda identities may be extended to hold for $n$-step Fibonacci
numbers.

Department for Mathematics and Informatics, University of Banja Luka

Republic of Srpska, Bosnia and Herzegovina

##  1\. Introduction

We restate a particular case of a result proved in [2]. Let $n$ and $r$ be
positive integers. We consider the following $n+r-1$ by $r$ matrix $P$:

$P=\begin{pmatrix}1&0&\cdots&0&0\\\ 1&1&\cdots&0&0\\\
\vdots&\vdots&\cdots&\vdots&\vdots\\\ 1&1&\cdots&1&0\\\ -1&1&\cdots&1&1\\\
0&-1&\cdots&1&1\\\ \vdots&\vdots&\cdots&\vdots&\vdots\\\ 0&0&\cdots&1&1\\\
0&0&\cdots&-1&1\end{pmatrix}.$

We note that in each column we have exactly $n$ ones. We connect the matrix
$P$ with recursively given sequence of vector-columns in the following way:
Let $A=(A_{1}|A_{2}|\ldots|A_{n})$ be a square matrix of order $n$, where
$A_{1},\ldots,A_{n}$ are columns of $A.$ We define a block matrix $A_{n+r}$ of
$n$ rows and $n+r$ columns in the following way: First $n$ columns of
$A_{n+r}$ are $A_{i},(1,2,\ldots,n)$, and

(1) $A_{n+j}=\sum_{i=j}^{n+j-1}A_{i},\;(j=1,2,\ldots,r).$

For a sequence $1\leq j_{1}<j_{2}<\cdots<j_{r}<n+r$ of positive integers we
let $M=M(\widehat{j_{1}},\widehat{j_{2}},\ldots,\widehat{j_{r}})$ denote the
minor of $A_{n+r}$ of order $n$, obtained by deleting columns
$j_{1},j_{2},\ldots,j_{r}$ of $A_{n+r}.$ Note that the last column of
$A_{n+r}$ can not be deleted. The sign of $M$ is defined as ${\rm
sgn}(M)=(-1)^{nr+j_{1}+j_{2}+\cdots+j_{r}+\frac{(r-1)r}{2}}.$ We let
$Q_{r}=Q_{r}(j_{1},\ldots,j_{r})$ denote the sub-matrix of order $r$, laying
in rows $j_{1},j_{2},\ldots,j_{r}$ of $P.$

Denote by $\\{i_{1},i_{2},\ldots,i_{n}\\}$ the numbers of columns of $B_{n+r}$
in which the minor $M$ lies. We have $i_{n}=r+n$, since the last column of
$A_{n,n+r}$ can not be deleted. We have
$\\{i_{1},i_{2},\ldots,i_{n-1}\\}\cup\\{j_{1},j_{2},\ldots,j_{r}\\}=\\{1,2,\ldots,n+r-1\\}.$
It follows that
$M=M(\widehat{j_{1}},\widehat{j_{2}},\ldots,\widehat{j_{r}})=M(i_{1},i_{2},\ldots,i_{n-1},n+r).$
and ${\rm sgn}(M)=(-1)^{\frac{n(n-1)}{2}+i_{1}+i_{2}+\ldots,i_{n-1}}$. In [2]
the following result is proved:

######  Proposition 1.

Let $1\leq j_{1}<\cdots<j_{r}<r+n$ be a sequence of positive integers. Then,

(2) $M({i_{1}},\ldots,i_{n-1},r+n)={\rm sgn}(M)\cdot\det
Q(j_{1},j_{2},\ldots,j_{r})\cdot\det A.$

We stress a particular case of this result, when $i_{k}=k,(k=1,2,\ldots,n-1)$.
In this case, we have $j_{1}=n,j_{2}=n+1,\ldots,j_{r}=n+r-1$, so that the
matrix $Q_{r}$ has the following form

$Q_{r}(n,\ldots,n+r-1)=\begin{vmatrix}1&1&\cdots&1&0&0&\cdots&0\\\
-1&1&\cdots&1&1&0&\cdots&0\\\ 0&-1&\cdots&1&1&1&\cdots&0\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots&\vdots&\vdots\\\
0&0&0&\cdots&0&-1&1&1\\\ 0&0&0&\cdots&0&0&-1&1\end{vmatrix}.$

For $r=1,2,\ldots$, we define $\det Q_{r}=F^{(n)}_{r}$. It follows that

$F^{(n)}_{1}=1,F^{(n)}_{2}=2,\ldots,F^{(n)}_{n}=2^{n-1},$

and $r>n$ we have

$F^{(n)}_{r}=F^{(n)}_{r-1}+F^{(n)}_{r-2}+\cdots+F^{(n)}_{r-n}.$

Hence, the sequence $\det Q_{1},\det Q_{2},\ldots$ consists of Fibonacci
$n$-step numbers. It is obvious that ${\rm sgn}(M)=1$. Using equation (2), we
obtain

######  Proposition 2.

[Generalized d’Ocagne identity] The following equation holds

$M(1,\ldots,n-1,r+n-1)=F^{(n)}_{r}\cdot\det A.$

We see that the expression $\frac{M(1,\ldots,n-1,r+n-1)}{\det A}$ does not
depend on the matrix $A$ with $\det A\not=0$. In other words, the following
result holds:

######  Proposition 3.

Assume that $A$ and $B$ are regular matrices of order $n$, and let $A_{n+r}$
and $B_{n+r}$ be formed according the same role described above. Let $M$ and
$N$ are corresponding minors. Then

$\frac{M(1,\ldots,n-1,r+n-1)}{\det A}=\frac{N(1,\ldots,n-1,r+n-1)}{\det B}.$

Our next goal is to extend Cassini identity of Fibonacci numbers on $n$-step
Fibonacci numbers.

##  2\. Cassini Identity for $n$-step Fibonacci numbers

We note that cases $n=2$ and $n=3$ are already considered in [2].

For the matrix $A$, we take the following upper triangular matrix:

$A=\begin{pmatrix}F^{(n)}_{1}&F^{(n)}_{2}&F^{(n)}_{3}&\cdots&F^{(n)}_{n-1}&F^{(n)}_{n}\\\
0&F^{(n)}_{1}&F^{(n)}_{2}&\cdots&F^{(n)}_{n-2}&F^{(n)}_{n-1}\\\
\vdots&\vdots&\vdots&\cdots&\vdots\\\
0&0&0&\cdots&0&F^{(n)}_{1}\end{pmatrix}.$

Hence, $\det A=1$. We next take $i_{k}=r+k,(i=1,2,\ldots,n-1)$. Since
$Q_{r}(1,2,\ldots,r)$ is a lower triangular matrix having ones on the main
diagonal, we have $\det Q_{r}=1$. Also, $M=M(r+1,r+2,\ldots,r+n)$, and ${\rm
sgn}M=(-1)^{(n-1)r}$. We thus obtain

######  Proposition 4 (Cassini identity for $n$-step Fibonacci numbers).

(3) $\begin{vmatrix}F^{(n)}_{r+1}&F^{(n)}_{r+2}&\cdots&F^{(n)}_{r+n}\\\
F^{(n)}_{r}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r+n-1}\\\
\vdots&\vdots&\cdots&\vdots\\\
F^{(n)}_{r-n+2}&F^{(n)}_{r-n+3}&\cdots&F^{(n)}_{r+1}\end{vmatrix}=(-1)^{(n-1)r}.$

######  Remark 1.

This result is known. It is obtained in [3] using induction. Also a number of
particular identities is given in this paper.

######  Corollary 1.

In the case $n=2$, equation (3) becomes Cassini identity for Fibonacci numbers

$\begin{vmatrix}F_{r+1}&F_{r+2}\\\ F_{r}&F_{r+1}\end{vmatrix}=(-1)^{r}.$

######  Corollary 2.

In the case $n=3$, we obtain Cassini identity for Tribonacci numbers
$T_{1}=1,T_{2}=1,T_{3}=2,\ldots$:

$\begin{vmatrix}T_{r+1}&T_{r+2}&T_{r+3}\\\ T_{r}&T_{r+1}&T_{r+2}\\\
T_{r-1}&T_{r}&T_{r+1}\end{vmatrix}=1.$

##  3\. d’Ocagne identity for $n$-step Fibonacci numbers

We next take that
$A=\begin{pmatrix}F^{(n)}_{r+1}&F^{(n)}_{r+2}&\cdots&F^{(n)}_{r+n}\\\
F^{(n)}_{r}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r+n-1}\\\
\vdots&\vdots&\cdots&\vdots\\\
F^{(n)}_{r-n+2}&F^{(n)}_{r-n+3}&\cdots&F^{(n)}_{r+1}\end{pmatrix}$. For $s>0$,
we form the matrix $A_{n+s}$, such that columns $n+i,(i=n+1,\ldots,s)$ are
sums of preceding $n$ columns. We calculate $M=M(1,2,\ldots,s-1,s+n)$. In this
case, we have ${\rm sgn}(M)=(-1)^{\frac{n(n-1)}{2}+1+2+\ldots+n-1}=1$. Using
Proposition 2, we obtain

######  Proposition 5 (D’Ocagne identity for $n$-step Fibonacci numbers).

The following formula holds

(4)
$\begin{vmatrix}F^{(n)}_{r+1}&F^{(n)}_{r+2}&\cdots&F^{(n)}_{r+n-1}&F^{(n)}_{r+n+s-1}\\\
F^{(n)}_{r}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r+n-2}&F^{(n)}_{r+n+s-2}\\\
\vdots&\vdots&\cdots&\vdots&\vdots\\\
F^{(n)}_{r-n+2}&F^{(n)}_{r-n+3}&\cdots&F^{(n)}_{r}&F^{(n)}_{r+s}\end{vmatrix}=(-1)^{(n-1)r}\cdot
F^{(n)}_{s}.$

######  Example 1.

For $n=2$, (4) becomes d’Ocagne identity for Fibonacci numbers:

$\begin{vmatrix}F_{r+1}&F_{r+s+1}\\\ F_{r}&F_{r+s}\end{vmatrix}=(-1)^{r}\cdot
F_{s}.$

######  Example 2.

For $n=3$, from (4) we obtain d’Ocagne identity for Tribonacci numbers:

$\begin{vmatrix}T_{r+1}&T_{r+2}&T_{r+s+2}\\\ T_{r}&T_{r+1}&T_{r+s+1}\\\
T_{r-1}&T_{r}&T_{r+s}\end{vmatrix}=T_{s}.$

##  4\. Vajda identity for $n$-step Fibonacci numbers

In the determinant on the right hand side of the equation (4) sums of elements
in rows are no more $n$-step Fibonacci numbers. But sums of element in columns
are. So we consider the following matrix

(5)
$B=\begin{pmatrix}F^{(n)}_{r+1}&F^{(n)}_{r}&\cdots&F^{(n)}_{r-n+3}&F^{(n)}_{r-n+2}\\\
F^{(n)}_{r+2}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r-n+4}&F^{(n)}_{r-n+3}\\\
\vdots&\vdots&\cdots&\vdots&\vdots\\\
F^{(n)}_{r+n-1}&F^{(n)}_{r+n-2}&\cdots&F^{(n)}_{r-1}&F^{(n)}_{r}\\\
F^{(n)}_{r+n+s-1}&F^{(n)}_{r+n+s-2}&\cdots&F^{(n)}_{r+s-1}&F^{(n)}_{r+s}\end{pmatrix},$

which is simple the transpose of $A$. Hence, $\det B=(-1)^{(n-1)r}\cdot
F^{(n)}_{s}$. Permuting columns $1$ and $n$, $2$ and $n-1$ and so on, the
matrix $B$ becomes

(6)
$C=\begin{pmatrix}F^{(n)}_{r-n+2}&F^{(n)}_{r-n+3}&\cdots&F^{(n)}_{r}&F^{(n)}_{r+1}\\\
F^{(n)}_{r-n+3}&F^{(n)}_{r-n+4}&\cdots&F^{(n)}_{r+1}&F^{(n)}_{r+2}\\\
\vdots&\vdots&\cdots&\vdots&\vdots\\\
F^{(n)}_{r}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r+n-2}&F^{(n)}_{r+n-1}\\\
F^{(n)}_{r+s}&F^{(n)}_{r+s+1}&\cdots&F^{(n)}_{r+n+s-2}&F^{(n)}_{r+n+s-1}\end{pmatrix}.$

For this we need $\lfloor\frac{n}{2}\rfloor$ permutation. It follows that

$\det C=(-1)^{\lfloor\frac{n}{2}\rfloor}\cdot\det B.$

Applying (4), we obtain

######  Proposition 6 (Vajda identity for $n$-step Fibonacci numbers).

The following formula holds

$\begin{vmatrix}F^{(n)}_{r-n+2}&F^{(n)}_{r-n+3}&\cdots&F^{(n)}_{r}&F^{(n)}_{p+r}\\\
F^{(n)}_{r-n+3}&F^{(n)}_{r-n+4}&\cdots&F^{(n)}_{r+1}&F^{(n)}_{p+r+1}\\\
\vdots&\vdots&\cdots&\vdots&\vdots\\\
F^{(n)}_{r}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r+n-2}&F^{(n)}_{p+r+n-2}\\\
F^{(n)}_{q+r}&F^{(n)}_{q+r+1}&\cdots&F^{(n)}_{q+r+n-2}&F^{(n)}_{p+q+r+n-2}\end{vmatrix}=(-1)^{(n-1)r+\lfloor\frac{n}{2}\rfloor}\cdot
F^{(n)}_{p}\cdot F^{(n)}_{q}$

As a particular case, for $p=q$, we obtain

######  Corollary 3 (Catalan identity for $n$-step Fibonacci numbers).

The following formula holds

$\begin{vmatrix}F^{(n)}_{r-n+2}&F^{(n)}_{r-n+3}&\cdots&F^{(n)}_{r}&F^{(n)}_{p+r}\\\
F^{(n)}_{r-n+3}&F^{(n)}_{r-n+4}&\cdots&F^{(n)}_{r+1}&F^{(n)}_{p+r+1}\\\
\vdots&\vdots&\cdots&\vdots&\vdots\\\
F^{(n)}_{r}&F^{(n)}_{r+1}&\cdots&F^{(n)}_{r+n-2}&F^{(n)}_{p+r+n-2}\\\
F^{(n)}_{r+p}&F^{(n)}_{r+p+1}&\cdots&F^{(n)}_{r+p+s-2}&F^{(n)}_{2p+r+n-2}\end{vmatrix}=(-1)^{(n-1)r+\lfloor\frac{n}{2}\rfloor}\cdot[F^{(n)}_{p}]^{2}.$

######  Example 3.

In the case $n=2$, we obtain the standard Vajda and Catalan identities for
Fibonacci numbers. We have

######  Identity 1 (Vajda identity).

The following formula holds

$\begin{vmatrix}F_{r}&F_{p+r}\\\
F_{r+q}&F_{p+r+q}\end{vmatrix}=(-1)^{r+1}\cdot F_{p}\cdot F_{q}.$

We also have

######  Identity 2 (Catalan identity).

The following formula holds

$\begin{vmatrix}F_{r-p}&F_{r}\\\ F_{r}&F_{p+r}\end{vmatrix}=(-1)^{r-p}\cdot
F_{p}^{2}.$

######  Example 4 (Tribonacci numbers).

In the case $n=3$, we obtain the following identities for Tribonacci numbers
$T_{1}=1,T_{2}=2,T_{3}=4,T_{5}=7,\ldots$

######  Identity 3 (Vajda identity for Tribonacci numbers).

The following formula holds

$\begin{vmatrix}T_{r-1}&T_{r}&T_{p+r}\\\ T_{r}&T_{r+1}&T_{p+r+1}\\\
T_{r+q}&T_{r+q+1}&T_{p+r+q+1}\end{vmatrix}=-T_{p}\cdot T_{q}.$

For $p=q$ we have

######  Identity 4 (Catalan identity for Tribonacci numbers).

We have

$\begin{vmatrix}T_{r-1}&T_{r}&T_{p+r}\\\ T_{r}&T_{r+1}&T_{p+r+1}\\\
T_{r+p}&T_{r+p+1}&T_{2p+r+1}\end{vmatrix}=-T_{p}^{2}.$

## References

  * [1] D. Bogdanić, M. Janjić, Arithmetic of some sequences via $2$-determinants, Bull. Int. Math. Virtual Inst.,11(3)(2021), 517-526.
  * [2] M, Janjic, Determinants and Recurrence Sequences, J. Integer Sequences, 15 (2012), Article 12.3.5.
  * [3] Yüksel Soykan, Simson Identity of Generalized $m$-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2) (2019) 45 – 56.