SlowGuess/NAACL_2022_OCR huggingface dataset:
- OBJ1 refers to the options for objects. Similar to SUB, we only avail someone or something, indicating placeholders for objects.
- PREP refers to prepositions. We avail a short list of common prepositions: by, to, for, with, about, of, and from.
- OBJ2 refers to the additional options for objects. The complete list includes the following: someone, something, somewhere, do, doing, do something, and doing something.
B Additional Details on Generating Affirmative Interpretations from Questions and Answers
The process to generate affirmative interpretations from questions and answers is robust but not foolproof from a grammatical standpoint. Note that the semantics of the affirmative interpretation is dictated by the questions and answers, and our evaluation determined that only  $3\%$  are incorrect (Section 3.2). We manually validated the final affirmative interpretations for grammaticality and found that  $9\%$  have errors. For example, consider Most plastics do not form crystals. The questions and answers are as follows: What forms something? Plastic, What does something form? Crystals, and How many form? Few.<sup>3</sup> These result in the affirmative interpretation Plastic forms crystals few, which places few incorrectly. We manually fix all the grammatical issues we found in the affirmative interpretations. Table 10 provides additional examples (Similar to Table 3 in the paper).
C Additional Details on Corpus Analysis
Table 11 presents percentages of negated sentences and their affirmative interpretations in several length buckets. In the corpus, sentences with negation are fairly long, for example,  $29.76\%$  of them are longer than 29 tokens. The affirmative interpretations, however, are much shorter, with  $79.9\%$  being under 15 tokens.
In Table 12, we report the percentage of the argument questions that start with each wh-word (first column) and the percentage of negated verbs that contain a wh-word (second column). For example,  $52.61\%$  of all the argument questions start with the wh-word what, and  $92.27\%$  of all the negated verbs contains at least one question that starts with what.
D Training Procedure and Hyperparameters
D.1 Affirmative Interpretations and Natural Language Inference Classification
For all the experiments mentioned in Section 5.1 in the paper, we use Huggingface implementation (Wolf et al., 2019) of the transformer systems. In addition, we utilize the base architecture (12-layer, 768-hidden, 12-heads) of transformers and their pretrained weights. We accept the default setting for most of the hyperparameters, except a few carefully selected to fine-tune the systems. Table 13 shows the hyperparameters used to fine-tune RoBERTa (Liu et al., 2019) and XLNet (Yang et al., 2019) on the three NLI corpora. Our code is available at https://github.com/mosharafhossain/AFIN.
D.2 Generating Affirmative Interpretations
In order to generate affirmative interpretations for both input configurations (Section 5.2 in paper), we use the same set of hyperparameters discovered through cross-validation to tune the T5-Large system. Further, for the setup that adds the target verb with the sentence containing negation, we use two prefixes<sup>4</sup> (one for the target verb and another for the negated sentence) to create a single text before encoding it and passing to the T5 system. During the training process, we stop as soon as the loss (T5 uses cross-entropy) in the development split does not increase for 10 epochs. Thus, the final model is the one that produces the lowest loss in the development split. Table 14 provides the list of hyperparameters values in our experiments. In each run, the model requires approximately three hours to train on a single NVIDIA Tesla K80 GPU. The code is available at https://github.com/mosharafhossain/AFIN.
An alternative could be answering What forms something? with Few plastics (and skip the question starting with How many).
<sup>4</sup>https://huggingface.co/docs/transformers/model_doc/t5
WH	AUX	SUB	VERB	PREP	Answer	Affirmative Interpretation
(1)	What What	does	something	happens happen	with	? ?	Reflection Any type of waves	Reflection happens. Reflection happens with any type of waves.
(2)	What What	was was	something	made made	by by	? ?	It Inanimate organ-isms	It was made. It was made by inanimate or-organisms.
(3)	What What	has does	something something	have	? ?	Later life forms The ability to photo-synthesize	Later life forms have. Later life forms have the abl-ity to photosynthesize.
(4)	What When Where	does does	something something	rises rise rise	? ? ?	The Sun In all seasons In the sky	The Sun rises. The Sun rises in all seasons. The Sun rises in all seasons in the sky. The Sun rises in all seasons in the sky very low
How much	does	something	rise	?	Very low
(5)	Who When Where	did did	someone someone	returned return return	? ? ?	Locke After the Glorious Revolution Home	Locke returned. Locke returned after the Glori-ous Revolution. Locke returned after the Glori-ous Revolution home.
Table 10: Examples of questions and answers generated by annotators and the resulting affirmative interpretations. The sentences containing the negated predicates are (1) Reflection can happen with any type of waves, not just sound waves, (2) It was not made by living organisms, (3) The earliest life forms did not have the ability to photosynthesize, (4) Even in summer, the Sun never rises very high in the sky, and (5) Locke did not return home until after the Glorious Revolution. We do not show the OBJ1 and OBJ2 slots because they are empty for the questions in these examples.
Lengths	%Neg. Sentences	%Affirm. Interpretations
<10	4.10	43.12
10–14	13.93	36.79
15–19	21.09	13.53
20–24	19.06	4.30
25–29	12.06	1.53
>29	29.76	0.73
All	100	100
Table 11: Percentages of negated sentences and affirmative interpretations in different length buckets. Length is measured in tokens. The average length of a negated sentence and its affirmative interpretation is 25.8 and 11.2, respectively.
%	%verb with
What	52.61	92.27
Who	17.27	39.19
when	9.89	23.89
how	7.09	17.09
where	6.31	15.19
why	3.60	8.73
how much	1.65	4.00
how often	0.63	1.53
how many	0.51	1.23
how long	0.41	1.00
whom	0.03	0.07
Table 12: Percentages of argument questions starting with each wh-word and percentages of negated verbs containing questions that start with each wh-word.
Hyperparameter	RTE	SNLI	MNLI
RoBERTa	XLNet	RoBERTa	XLNet	RoBERTa	XLNet
Batch size	16	8	32	32	32	32
Learning rate	2e-5	2e-5	1e-5	1e-5	2e-5	2e-5
Epochs	10	50	3	3	3	3
Weight decay	0.0	0.0	0.1	0.1	0.0	0.0
Table 13: Hyperparameters for finetuning the transformer systems used in Section 5.1 in the paper.
Hyperparameter
Max Epochs	50
Batch Size	4
Sentence max length	128
Optimizer	Adafactor
Learning rate	1e-5
Weight decay	5e-6
Warmup epoch	5
Accumulate step	1
Grad_clipping	5.0
Top_k	50
Top_p	0.95
Repetition_penalty	2.5
Table 14: Hyperparameters for finetuning T5-Large on AFIN (Section 5.2 in paper).