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A e-SNLI Explanations Templates
Below we present the list of templates that we manually found to match most of the e-SNLI explanations (Camburu et al., 2018). We recall that during the collection of the dataset Camburu et al. (2018) did not impose any template, they were a natural consequence of the task and SNLI dataset.
Here, "subphrase1/subphrase2/..." means that a separate template is to be considered for each of the subphrases. X and Y are the key elements that we want to identify and use in the other templates in order to create inconsistencies. "[...] is a placeholder for any string, and its value is not relevant. Subphrases placed between round parenthesis (for example, "(the)" or "(if)") are optional, and two distinct templates are formed one with and one without that subphrase.
Entailment Templates
X is/are a type of Y
X implies Y
- X is/are the same as Y
X is a rephrasing of Y
- X is a another form of Y
X is synonymous with Y
X and Y are synonyms/synonymous
- X and Y is/are the same thing
- (if)  $\mathrm{X}$ , then  $\mathrm{Y}$
X so Y
X must be Y
X has/have to be Y
X is/are Y
Neutral Templates
not all  $\mathbf{X}$  are Y
not every  $\mathbf{X}$  is Y
- just because X does not/n't mean/imply Y
X is/are not necessarily Y
X does not/n't have to be Y
- X does not/n't imply/mean Y
Contradiction Templates
- ([...]) cannot/can not/ca n't (be) X and Y at the same time/simultaneously
- ([...]) cannot/can not/ca n't (be) X and at the same time Y
X is/are not (the) same as Y
- ([...]) is/are either X or Y
X is/are not Y
X is/are the opposite of Y
- ([...]) cannot/can not/ca n't (be) X if (is/are) Y
X is/are different than Y
X and Y are different ([..])
A.1 Running Example for Creating Inconsistencies by Swapping between Templates of Explanations
Consider the explanation  $\mathbf{e} =$  "Dog is a type of animal." which may arise from a model explaining the instance  $\mathbf{x} =$  (premise: "A dog is in the park.", hypothesis: "An animal is in the park.). We identify that  $\mathbf{e}$  matches the template "X is/are a type of Y" with  $\mathrm{X} =$  "dog" (we convert to lowercase) and  $\mathrm{Y} =$  "animal". We generate the list  $\mathcal{I}_{\mathrm{e}}$  by replacing  $\mathrm{X}$  and  $\mathrm{Y}$  in each of the neutral and contradictory templates listed above with the exception of those that contain "[...] in order to avoid guessing the placeholder. We obtain  $\mathcal{I}_{\mathrm{e}}$  as:
not all dog are animal
not every dog is animal
- just because dog does not/n't mean/imply animal
- dog is/are not necessarily animal
dog does not/n't have to be animal
dog does not/n't imply/mean animal
- cannot/can not/ca n't (be) dog and animal at the same time/simultaneously
- cannot/can not/ca n't (be) dog and at the same time animal
- dog is/are not (the) same as animal
- is/are either dog or animal
dog is/are not animal
- dog is/are the opposite of animal
- cannot/can not/ca n't (be) dog if (is/are) animal
dog is/are different than animal
dog and animal are different
B More Examples of Detected Inconsistencies
In Table 2, we provide more examples of inconsistent explanations detected with our method.
C Manual Scanning
We performed three experiments of manually scanning. First, we manually analyzed the first 50 instances in the test set without finding any inconsistency. However, these examples were involving different concepts, thus decreasing the likelihood of finding inconsistencies. To account for this, in our second experiment, we constructed three groups around the concepts of woman, prisoner, and snowboarding, by simply selecting the explanations in the test set containing these words. We selected these concepts, because our framework detected inconsistencies about them — examples are listed in Table 1 and Table 2.
For woman, we obtained 1150 examples in the test set, and we looked at a random sample of 20, among which we did not find any inconsistency. For snowboarding, we found 16 examples in the test set and again no inconsistency among them. For prisoner, we only found one instance in the test set, so we had no way to find out that the model is inconsistent with respect to this concept simply by scanning the test set.
We only looked at the test set for a fair comparison with our method that was only applied on this set.
However, we highlight that, even if the manual scanning would have been successful, it should not be regarded as a proper baseline, since it does not bring the same benefits as our framework. Indeed, manual scanning requires considerable human effort to look over a large set of explanations in order to find if any two are inconsistent. Even a group of only 50 explanations required us a non-negligible
amount of time. Moreover, restricting ourselves to the instances in the original dataset would clearly be less effective than being able to generate new instances from the dataset's distribution. Our framework addresses these issues and directly provides pairs of inconsistent explanations. Nonetheless, we considered this experiment useful for illustrating that the explanation module does not provide inconsistent explanations in a frequent manner.
In our third experiment of manual scanning, we experimented with a few manually created hypotheses from Carmona et al. (2018), which had been shown to induce confusion at the label level. We were pleased to notice a good level of robustness against inconsistencies. For example, for the neutral pair (premise: "A bird is above water", hypothesis: "A swan is above water"), we get the explanation "Not all birds are a swan.", while when interchanging bird with swan, i.e., for the pair (premise: "A swan is above water", hypothesis: "A bird is above water"), ETPA generates the explanation "A swan is a bird.", showing a good understanding of the relationship between the entities "swan" and "bird". Similarly, interchanging "child" with "toddler" in (premise: "A small child watches the outside world through a window.", hypothesis: "A small toddler watches the outside world through a window.") does not confuse the model, which outputs "Not every child is a toddler." and "A toddler is a small child.", respectively. Further investigation on whether the model can be tricked on concepts where it seems to exhibit robustness, such as toddler or swan, are left for future work.
PREMISE: Biker riding through the forest.
ORIGINAL HYPOTHESIS: Man riding motorcycle on highway.	REVERSE HYPOTHESIS: A man rides his bike through the forest.
PREDICTED LABEL: contradiction	PREDICTED LABEL: entailment
ORIGINAL EXPLANATION: Biker and man are different.	REVERSE EXPLANATION: A biker is a man.
PREMISE: A hockey player in helmet.
ORIGINAL HYPOTHESIS: They are playing hockey	REVERSE HYPOTHESIS: A man is playing hockey.
PREDICTED LABEL: entailment	PREDICTED LABEL: neutral
ORIGINAL EXPLANATION: A hockey player in helmet is playing hockey.	REVERSE EXPLANATION: A hockey player in helmet doesn't imply playing hockey.
PREMISE: A blond woman speaks with a group of young dark-haired female students carrying pieces of paper.
ORIGINAL HYPOTHESIS: A blond speaks with a group of young dark-haired woman students carrying pieces of paper.	REVERSE HYPOTHESIS:The students are all female.
PREDICTED LABEL: entailment	PREDICTED LABEL: neutral
ORIGINAL EXPLANATION: A woman is a female.	REVERSE EXPLANATION: The woman is not necessarily female.
PREMISE: The sun breaks through the trees as a child rides a swing.
ORIGINAL HYPOTHESIS: A child rides a swing in the daytime.	REVERSE HYPOTHESIS: The sun is in the daytime.
PREDICTED LABEL: entailment	PREDICTED LABEL: neutral
ORIGINAL EXPLANATION: The sun is in the daytime.	REVERSE EXPLANATION: The sun is not necessarily in the daytime.
PREMISE: A family walking with a soldier.
ORIGINAL HYPOTHESIS: A group of people strolling.	REVERSE HYPOTHESIS: A group of people walking down a street.
PREDICTED LABEL: entailment	PREDICTED LABEL: contradiction
ORIGINAL EXPLANATION: A family is a group of people.	REVERSE EXPLANATION: A family is not a group of people.
Table 2: More examples of inconsistent explanations detected with our method.