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## Generating Hypothetical Events for Abductive Inference Debjit Paul Research Training Group AIPHES Institute for Computational Linguistics Heidelberg University paul@cl.uni-heidelberg.de ## Abstract Abductive reasoning starts from some observations and aims at finding the most plausible explanation for these observations. To perform abduction, humans often make use of temporal and causal inferences, and knowledge about how some hypothetical situation can result in different outcomes. This work offers the first study of how such knowledge impacts the Abductive α NLI task - which consists in choosing the more likely explanation for given observations. We train a specialized language model LM I that is tasked to generate what could happen next from a hypothetical scenario that evolves from a given event. We then propose a multi-task model MTL to solve the α NLI task , which predicts a plausible explanation by a) considering different possible events emerging from candidate hypotheses events generated by LM I - and b) selecting the one that is most similar to the observed outcome. We show that our MTL model improves over prior vanilla pre-trained LMs finetuned on α NLI. Our manual evaluation and analysis suggest that learning about possible next events from different hypothetical scenarios supports abductive inference. ## 1 Introduction Abductive reasoning (AR) is inference to the best explanation. It typically starts from an incomplete set of observations about everyday situations and comes up with what can be considered the most likely possible explanation given these observations (Pople, 1973; Douven, 2017). One of the key characteristics that make abductive reasoning more challenging and distinct from other types of reasoning is its non-monotonic character (Strasser and Antonelli, 2019) i.e., even the most likely explanations are not necessarily correct. For example, in Figure 1, the most likely explanation for Observation 1: 'wet grass outside my house' is that 'it has been Anette Frank Research Training Group AIPHES Institute for Computational Linguistics Heidelberg University frank@cl.uni-heidelberg.de Observation 1 : The grass outside my house is wet Observation 2 : The sprinkler outside was switched on Figure 1: Motivational example illustrating Abductive Reasoning and its non-monotonic character. <details> <summary>Image 1 Details</summary>  ### Visual Description ## Plausible Explanation ### Overview The image presents a simple diagram with two clouds, each containing a statement. The top cloud is labeled "It rained last night" and the bottom cloud is labeled "Sprinkler made the grass wet." ### Components/Axes - **Labels**: "It rained last night" and "Sprinkler made the grass wet" - **Clouds**: Two distinct clouds, one blue and one green ### Detailed Analysis or ### Content Details - The blue cloud represents the event of rain, which is a natural occurrence. - The green cloud represents the action of a sprinkler, which is a human-made device used to water plants. - The statement "Sprinkler made the grass wet" suggests that the sprinkler's action directly caused the grass to become wet. ### Key Observations - The diagram is straightforward and does not contain any additional elements or complexity. - The relationship between the rain and the sprinkler is clear: the sprinkler's action led to the grass being wet. ### Interpretation The data in the image suggests that the sprinkler's action was responsible for the grass becoming wet. This is a plausible explanation because it is common for sprinklers to be used to water plants, and it is reasonable to assume that the sprinkler's action would cause the grass to become wet. The diagram effectively communicates this relationship in a simple and clear manner. </details> raining' . However, when a new piece of information (observation or evidence) becomes available, the explanation must possibly be retracted, showing the defeasible character of abduction . With the new observation ( 'the sprinkler was switched on ') the most plausible explanation changes to 'Sprinkler caused the grass to be wet' . Humans, in such situations, could induce or validate such abductive inferences by performing hypothetical reasoning (such as 'What would happen if the sprinkler was switched on?' ) to arrive at a plausible explanation for 'wet grass outside my house' . In this work, we focus on the α NLI task (Bhagavatula et al., 2020), where given two observations ( O 1 at time t 1 , O 2 at time t 2 , with t 1 < t 2 ) as an incomplete context, the task is to predict which of two given hypothesized events ( H 1 or H 2 ) is more plausible to have happened between O 1 and O 2 . Figure 2 illustrates this with an example: given observations O 1 :'Priya decided to try a new restaurant. ' and O 2 : 'Priya thought her food was delicious. ' , the task is to predict whether H 1 or H 2 is the more plausible explanation given observations O 1 and O 2 . Both H 1 and H 2 are different plausible hypothetical situations that can evolve from the same observation (premise) O 1 . In this paper, we hypothesize that learning how different hypothetical scenarios ( H 1 and H 2 ) can result in different outcomes (e.g., O H j 2 , Fig. 2) can help in performing abductive inference. In order to decide which H i , is more plausible given observa- Figure 2: Motivational example for α NLI : The top box (red) shows the observations and two callout clouds (green) contain the hypotheses. The implications ( O H i i ) - generated by the LM conditioned on each hypothesis and the observations - are given in pink colored boxes. <details> <summary>Image 2 Details</summary>  ### Visual Description ## Hypothesis Testing Diagram ### Overview The diagram illustrates a hypothesis testing scenario involving a person named Priya. It presents two hypotheses (H1 and H2) and two observations (O1 and O2) to determine which hypothesis is more likely to be true. ### Components/Axes - **Hypothesis (H1)**: Priya ordered two shrimp dishes. - **Hypothesis (H2)**: Priya ordered microwaved and precooked food. - **Observation (O1)**: Priya decided to try a new restaurant. - **Observation (O2)**: Priya thought her food was delicious. - **What if**: This is a placeholder for the decision-making process. - **LM**: This could represent a logical model or a decision-making framework. - **Hypothesis (H2)**: Priya was disappointed in the quality of the food. ### Detailed Analysis or ### Content Details - **Hypothesis (H1)**: Priya ordered two shrimp dishes. - **Hypothesis (H2)**: Priya ordered microwaved and precooked food. - **Observation (O1)**: Priya decided to try a new restaurant. - **Observation (O2)**: Priya thought her food was delicious. - **What if**: This is a placeholder for the decision-making process. - **LM**: This could represent a logical model or a decision-making framework. - **Hypothesis (H2)**: Priya was disappointed in the quality of the food. ### Key Observations - **O1**: Priya decided to try a new restaurant. - **O2**: Priya thought her food was delicious. - **H2**: Priya was disappointed in the quality of the food. ### Interpretation The diagram suggests that Priya's decision to try a new restaurant and her positive feedback about her food (O1 and O2) are more consistent with the hypothesis that she ordered microwaved and precooked food (H2) rather than shrimp dishes (H1). The disappointment in the quality of the food (H2) is less likely to be explained by the positive feedback about her food. Therefore, the logical model (LM) suggests that Priya was more likely to have ordered microwaved and precooked food. </details> tions, we assume each H i to be true and generate a possible next event O H i 2 for each of them independently (e.g.: What will happen if Priya's ordered food was microwaved and precooked? ). We then compare the generated sentences ( O H 1 2 , O H 2 2 in Fig. 2) to what has been observed ( O 2 ) and choose as most plausible hypothesis the one whose implication is closest to observation O 2 . We design a language model ( LM I ) which, given observations and a hypothesis, generates a possible event that could happen next, given one hypothesis. In order to train this language model, we use the TIMETRAVEL (TT) corpus (Qin et al., 2019) (a subpart of the ROCStories corpus 1 ). We utilize the LM I model to generate a possible next event for each hypothesis, given the observations. We then propose a multi-task learning model MTL that jointly chooses from the generated possible next events ( O H 1 2 or O H 2 2 ) the one most similar to the observation O 2 and predicts the most plausible hypothesis ( H 1 or H 2 ). Our contributions are: i) To our best knowledge, we are the first to demonstrate that a model that learns to perform hypothetical reasoning can support and improve abductive tasks such as α NLI. We show that ii) for α NLI our multi-task model outperforms a strong BERT baseline (Bhagavatula et al., 2020). Our code is made publicly available. 2 ## 2 Learning about Counterfactual Scenarios The main idea is to learn to generate assumptions, in a given situation, about 'What could have hap- 1 We ensure that α NLI testing instances are held out. 2 https://github.com/Heidelberg-NLP/ HYPEVENTS <details> <summary>Image 3 Details</summary>  ### Visual Description ## Diagram Type: Flowcharts ### Overview The image displays two flowcharts, labeled (a) and (b), which illustrate different concepts related to time travel and counterfactual reasoning. ### Components/Axes - **Nodes**: Represent states or events, labeled as \( O_1 \), \( H_i \), \( O_2 \), \( s_1 \), \( s_2 \), \( s_3 \), \( s'_1 \), \( s'_2 \), \( s'_3 \), \( H_1 \), \( H_2 \), \( O_{H_1} \), \( O_{H_2} \). - **Arrows**: Indicate the flow or relationship between nodes. - **Legend**: Contains color-coded labels for different types of nodes or events. - **Axes**: Not explicitly labeled, but likely represent time or different states. ### Detailed Analysis or ### Content Details - **Flowchart (a)**: Shows a linear progression from \( O_1 \) to \( H_i \) to \( O_2 \). The arrow from \( O_1 \) to \( H_i \) is labeled with \( \alpha \text{NLI} \), suggesting a non-linear interaction or relationship. - **Flowchart (b)**: Illustrates a more complex scenario with multiple paths. \( s_1 \) leads to \( s_2 \) and \( s_3 \), with a counterfactual arrow indicating a hypothetical alternative path. \( s'_1 \) leads to \( s'_2 \) and \( s'_3 \), also with a counterfactual arrow. The arrows from \( H_1 \) and \( H_2 \) lead to \( O_{H_1} \) and \( O_{H_2} \), respectively, suggesting a branching or diverging path. ### Key Observations - **Counterfactual Reasoning**: Both flowcharts mention counterfactual reasoning, indicating a focus on hypothetical scenarios or alternative outcomes. - **Time Travel**: The presence of \( s_1 \), \( s_2 \), \( s_3 \), \( s'_1 \), \( s'_2 \), \( s'_3 \), and \( H_1 \), \( H_2 \) suggests a concept of time travel or temporal manipulation. - **Complexity**: Flowchart (b) is more complex, indicating a deeper exploration of time travel and counterfactual reasoning. ### Interpretation The flowcharts appear to be illustrating the concept of counterfactual reasoning in the context of time travel. Flowchart (a) suggests a linear progression with a specific interaction labeled \( \alpha \text{NLI} \), while Flowchart (b) shows a more complex scenario with multiple paths and counterfactual arrows, indicating a deeper exploration of hypothetical scenarios and alternative outcomes. The use of color-coding in the legend helps to differentiate between different types of nodes or events, aiding in the understanding of the flowcharts. </details> (c) Learning to generate possible future event for each hypothesis Figure 3: Different reasoning schemes and settings for our task and approach. The arrows denote the direction (temporal flow) of the reasoning chain. The dotted arrow in (b) denotes the derivation of a counterfactual situation s ′ 2 from a factual s 2 . In (c), the dotted arrows denote the learned inference; the dotted lines indicate the similarity between O 2 and O H i 2 . pened (next) if we had done X?' or 'What could happen (next) if we do X?' (Bhatt and Flanagan, 2010). Figure 3(a) depicts the α NLI task framework. We hypothesize that getting to know what will happen (next) if any of two hypotheses occurs , will help us verifying which of them is more plausible (see Fig. 3(c)). Therefore, we encourage the model to learn how different hypothetical events (including counterfactual events) evolving from the same premise ( s 1 ) can lead to different or similar outcomes (see Fig. 3(b)). Accordingly, we teach a pre-trained GPT-2 (Radford et al., 2019) language model how to generate a sequence of possible subsequent events given different hypothetical situations in a narrative setting. Training such a model on narrative texts encourages it to learn causal and temporal relations between events. We train a conditional language model, LM I , which generates a possible event that could happen next, given some counterfactual scenarios for a given story. We train this model on the TIMETRAVEL (TT) dataset (Qin et al., 2019), by fine-tuning GPT-2 to learn about possible next events emerging from a situation in a story, given some alternative, counterfactual event. The TT dataset consists of fivesentence instances S =( s 1 , s 2 ,.., s 5 ) 3 from the ROCStories corpus 1 plus additional crowd-sourced sen- 3 s 1 = premise , s 2 = initial context , s 3:5 = original ending O 1 : Dotty was being very grumpy. 2 : She felt much better afterwards. 1 : Dotty ate something bad. 2 Dotty call some close friends to chat. H 2 : She started to feel sick. : They all tried to make her happy. O H H : O 1 O H 2 2 Table 1: Example of generated possible next events O H j 2 using the LM I model. Bold hypothesis ( H 2 ) is more plausible. tences s ′ 2:5 , where s ′ 2 is counterfactual 4 to s 2 from the original story 5 . There are two reasons for using the TT dataset for our purposes: a) the domains on which GPT-2 was pretrained are broad 6 and different from the domain of ROCStories, b) the model can see how alternative situations can occur starting from the same premise s 1 , resulting in similar or different outcomes. Note that, although intermediate situations may be counterfactual to each other, the future outcome can still be similar to the original ending due to causal invariance 7 . Concretely, the language model LM I reads the premise ( s 1 ) and the alternative event(s) ( s 2 or s ′ 2 ), the masked token (serving as a placeholder for the missing possible next event(s) ( s 3: i or s ′ 3: i ), then the rest of the story ( s i +1:5 or s ′ i +1:5 ) and again the premise ( s 1 ). We train the model to maximize the log-likelihood of the missing ground-truth sentence(s) ( s 3: i ). $$\mathcal { L } ^ { L M _ { \mathcal { I } } } ( \beta ) = \begin{array} { r l } & { t h e o u n d B E R T a t e o u n d e v e n s h o u l } \\ \log _ { p _ { \beta } } ( s _ { 3 ; i } | [ S ] s _ { 1 } , [ M ] , s _ { i + 1 ; 5 } , [ E ] , [ S ] , s _ { 1 } , s _ { 2 } ) & ( 1 ) } \end{array}$$ where i ∈ [3 , 4] , s i = { w s i 1 , .., w s i n } a sequence of tokens, [ S ] =start-of-sentence token, [ E ] =end-ofsentence token, [ M ] =mask token. ## 3 Generating Hypothetical Events to support the α NLI task In this paper, we aim to investigate whether models perform better on the α NLI task when explicitly learning about events that could follow other events in a hypothetical scenario. We do so by introducing two methods LM I + BERTScore and LM I + 4 a counterfactual s ′ states something that is contrary to s During our experiments we treat them as two separate S s S s s ′ 5 instances: 1 =( 1:5 ) and 2 = ( 1 , 2:5 ). 6 GPT-2 was trained on the WebText Corpus. 7 the future events that are invariant under the counterfactual conditions (Qin et al., 2019) MTL for unsupervised and supervised settings, respectively. We first apply the trained model LM I on the α NLI task, where the given observations O 1 and O 2 , and alternative hypotheses H j are fed as shown in (2) below. 8 $$\begin{array} { r l } { v e n t s } & O _ { 2 } ^ { H _ { j } } = \beta ( [ S ] , O _ { 1 } , [ M ] , O _ { 2 } , [ E ] , [ S ] , O _ { 1 } , H _ { j } ) \quad ( 2 ) } \end{array}$$ We generate a possible next event for each hypothetical event H j , i.e., O H 1 2 and O H 2 2 (or: what will happen if some hypothesis H j occurs given the observations), where j ∈ [1 , 2] . Table 1 illustrates an example where different O H j 2 are generated using LM I . One of the challenges when generating subsequent events given a hypothetical situation is that there can be infinite numbers of possible next events. Therefore, to constrain this range, we chose to give future events ( O 2 ) as input, such that the model can generate subsequent events in a constrained context. ## 3.1 Unsupervised Setting In this setting, we do not train any supervised model to explicitly predict which hypothesis is more plausible given the observations. Instead, we apply the fine-tuned LM I model to the α NLI data, generate possible next events O H j 2 given O 1 and H j , as described above, and measure the similarity between such possible next events ( O H j 2 ) and the observation ( O 2 ) in an unsupervised way, using BERTScore (BS) (Zhang et al., 2020) 9 . We evaluate our hypothesis that the generated possible next event O H j 2 given the more plausible hypothesis H j should be more similar to observation O 2 . Table 1 illustrates an example where H 2 is the more plausible hypothesis. We impose the constraint that for a correctly predicted instance BS( O 2 H + , O 2 ) > BS( O 2 H -, O 2 ) should hold, where H + , H -are the more plausible vs. implausible hypothesis, respectively. ## 3.2 Supervised Setting In this setting, displayed in Figure 4, we explore the benefits of training a multi-task MTL model that predicts i) the most plausible hypothesis and ii) which possible next event ( O H j 2 ) is more similar 8 For definition of placeholders see (1). 9 BERTScore is an automatic evaluation metric for text generation that leverages the pre-trained contextual embeddings from BERT and matches words in candidate and reference sentences by cosine similarity. Figure 4: Overview of our LM I + MTL model for α NLI: (a) language model LM I takes the input in a particular format to generate different possible next events, (b) the MTL model learns to predict the best explanation ( H j ) and possible next events ( O H j 2 ) at the same time to perform the α NLI task. <details> <summary>Image 4 Details</summary>  ### Visual Description ## Diagram Type: Flowchart ### Overview The image is a flowchart that illustrates the process of similarity measurement in a machine learning model. It shows the relationship between different components of the model and how they interact to determine similarity. ### Components/Axes - **αNLI**: A parameter that represents the similarity between two entities. - **H1 or H2**: Two entities being compared. - **O1, O2**: Output values for the two entities. - **Linear Layer**: A layer in the model that processes the input data. - **Shared Layers**: Layers that are shared between the two entities. - **BERT (MTL)**: A model that uses multiple tasks to learn from the data. - **GPT-2 (LM1)**: A model that uses language modeling to learn from the data. ### Detailed Analysis or ### Content Details The flowchart shows that the similarity between two entities is determined by the output values (O1, O2) and the shared layers in the model. The linear layer processes the input data and the shared layers learn from the data to determine the similarity. The BERT and GPT-2 models are used to learn from the data and determine the similarity. ### Key Observations - The similarity between two entities is determined by the output values and the shared layers in the model. - The linear layer processes the input data and the shared layers learn from the data to determine the similarity. - The BERT and GPT-2 models are used to learn from the data and determine the similarity. ### Interpretation The data suggests that the similarity between two entities is determined by the output values and the shared layers in the model. The linear layer processes the input data and the shared layers learn from the data to determine the similarity. The BERT and GPT-2 models are used to learn from the data and determine the similarity. This suggests that the model is able to learn from the data and determine the similarity between two entities. </details> to the observation ( O 2 ). Multi-task learning aims to improve the performance of a model for a task by utilizing the knowledge acquired by learning related tasks (Ruder, 2019). We hypothesize that a) the possible next event O H j 2 of the more plausible hypothesis H j should be most similar to observation O 2 , and that b) learning which possible next event is more similar supports the model in the α NLI task ( inductive transfer ). The architecture of LM I + MTL model is shown in Figure 4. The model marked (a) in Figure 4 depicts the LM I model as described in §3. The outputs of the LM I model, which we get from Eq. (2) for both hypotheses are incorporated as an input to the MTL model. Concretely, we feed the MTL classifier a sequence of tokens as stated in part (b) of Figure 4, and aim to compute their contextualized representations using pre-trained BERT. The input format is described in Table 3. Similar to (Devlin et al., 2019), two additional tokens are added [CLS] at the start of each sequence input and [SEP] at the end of each sentence. In the shared layers (see Fig 4(b)), the model first transform the input sequence to a sequence of embedding vectors. Then it applies an attention mechanism that learns contextual relations between words (or sub-words) in the input sequence. For each instance we get four [CLS] embeddings ( CLS H j , CLS O Hj 2 ; j ∈ [1 , 2] ) which are then passed through two linear layers, one for the α NLI (main task) and another for predicting the Table 2: Dataset Statistics: nb. of instances | Task | Train | Dev | Test | |------------------|---------|-------|--------| | α NLI | 169654 | 1532 | 3059 | | TimeTravel (NLG) | 53806 | 2998 | - | Table 3: Input and output format for the α NLI task: [CLS] is a special token used for classification, [SEP] a delimiter. | Input Format | Output | |-----------------------------------------|--------------------| | [CLS] O 1 [SEP] H i [SEP] O 2 [SEP] | H 1 or H 2 | | [CLS] H i [SEP] O H i 2 [SEP] O 2 [SEP] | O H 1 2 or O H 2 2 | similarity (auxiliary task) between O H j 2 and O 2 . We compute the joint loss function L = L αNLI + w ∗ L similarity ; where w is a trainable parameter, L αNLI and L similarity are the loss function for the αNLI task and auxiliary task, respectively. ## 4 Experimental Setup Data. We conduct experiments on the ART (Bhagavatula et al., 2020) dataset. Data statistics are given in Table 2. For evaluation, we measure accuracy for α NLI. Hyperparameters. To train the LM I model we use learning rate of 5 e -05 . We decay the learning rate linearly until the end of training; batch size: 12. In the supervised setting for the α NLI task , we use the following set of hyperparameters for our MTL model with integrated LM I model ( LM I + MTL ): batch size: { 8 , 16 } ; epochs: { 3 , 5 } ; learning rate: { 2 e -5 , 5 e -6 } . For evaluation, we measure accuracy. We use Adam Optimizer, and dropout rate = 0 . 1 . We experimented on GPU size of 11 GB and 24 GB. Training is performed using cross-entropy loss. The loss function is L αNLI + w ∗ L similarity , where w is a trainable parameter. During our experiment we initialize w = 1 . The input format is depicted in Table 3. We report performance by averaging results along with the variance obtained for 5 different seeds. Baselines. We compare to the following baseline models that we apply to the α NLI task, training them on the training portion of the ART dataset (cf. Table 2). - ESIM + ELMo is based on the ESIM model previously used for NLI (Chen et al., 2017). We use (a) ELMo to encode the observations and hypothesis, followed by (b) an attention Table 4: Results on α NLI task , : as in Bhagavatula et al. (2020) (no unpublished leaderboard results). For each row, the best results are in bold, and performance of our models are in blue. | Model | Dev Acc.(%) Test Acc.(%) | Dev Acc.(%) Test Acc.(%) | |----------------------------------------------|----------------------------|----------------------------| | Majority ( from dev set ) | - | 50.8 | | LM I + BERTScore | 62.27 | 60.08 | | Infersent | 50.9 | 50.8 | | ESIM + ELMo | 58.2 | 58.8 | | BERT Large | 69.1 | 68.9 ± 0 . 5 | | GPT-2 + MTL | 68.9 ± 0 . 3 | 68.8 ± 0 . 3 | | COMET + MTL | 69.4 ± 0 . 4 | 69.1 ± 0 . 5 | | LM I + MTL | 72.9 ± 0 . 5 | 72.2 ± 0 . 6 | | Human Performance | - | 91.4 | layer, (c) a local inference layer, and (d) another bi-directional LSTM inference composition layer, and (e) a pooling operation, - Infersent (Conneau et al., 2017) uses sentence encoding based on a bi-directional LSTM architecture with max pooling. - BERT (Devlin et al., 2019) is a LM trained with a masked-language modeling (MLM) and next sentence prediction objective. As baselines for using the MTL model, we replace LM I with alternative generative LMs: - GPT-2 + MTL . In this setup, we directly use the pretrained GPT-2 model and task it to generate a next sentence conditioned on each hypothesis ( O H i 2 ) without finetuning it on the TIMETRAVEL data. We then use the supervised MTL model to predict the most plausible hypothesis and which of the generated observations is more similar to O 2 . - COMET + MTL . In this setting, we make use of inferential if-then knowledge from ATOMIC (Sap et al., 2019a) as background knowledge. Specifically, we use COMET to generate objects with Effect 10 relations for each hypothesis as a textual phrase. ## 5 Results In Table 4, we compare our models LM I + BERTScore and LM I + MTL against the models proposed in Bhagavatula et al. (2020): a majority baseline, supervised models ( Infersent and 10 as a result PersonX feels; as a result PersonX wants; PersonX then ESIM+ELMo ), as well as BERT Large . Bhagavatula et al. (2020) re-train the ESIM+ELMo and Infersent models on the ART dataset and fine-tuned the BERT model on the α NLI task and report the results. We find that our unsupervised model with BERTScore ( LM I + BERTScore) outperforms (by +9 . 28 pp. and +1 . 28 pp.) strong ESIM+ELMo and Infersent baseline models. Table 5 shows some examples of our generation model LM I along with the obtained BERTScores. Unlike the unsupervised LM I + BERTScore, our supervised LM I + MTL model also improves over the BERT Large baseline, by +3 . 3 pp. We can attribute the improvement to the model having been jointly trained to assess the similarity and dissimilarity of possible next events O H j 2 and observations ( O 2 ) along with the α NLI task. One of the advantages of training our proposed multitask learning ( MTL ) model, instead of directly feeding the possible next events O H j 2 as knowledge inputs is that it adds an explainable component to the model. One can view the generated next events O H j 2 as natural language rationales and our multitask model explicitly chooses one of them. Hence, the multi-task framework makes the model more expressive. Finally, we compare, for the MTL model, our embedded generation model LM I to pre-trained GPT-2 and COMET. Table 4 shows that LM I + MTL yields better performance compared to both COMET + MTL ( +3 . 1 pp.) and GPT-2 + MTL ( +3 . 4 pp.) - the intuitive reason being that the next events generated by LM I are more helpful than events generated using pretrained GPT-2 and objects generated by COMET. Table 5 illustrates some examples where our MTL model not only chooses the correct hypothesis, but also a likely possible next event that is similar to the observation O 2 . Interestingly, during training of MTL we initialize w = 1, and after training the model we found the w value had been adjusted to a range between 0 . 85 and 0 . 75 , which intuitively shows both the effectiveness of our LM I -generated possible next events, and their similarity to the given observations O 2 . ## 5.1 Case Study Table 5 displays possible next events, generated by our LM I model - along with the BERTscore measured between the possible next events O H j 2 and observation O 2 . We see two different scenarios: Table 5: Examples of generated possible next events for solving α NLI using our LM I model. Column 3: Hypothesis and possible next events chosen by our LM I + MTL model; Column 4: Reasoning type between the hypothesis H j and O 2 ; Column 5: BERTScore between the O H j 2 and O 2 ; Column5: Human evaluation of the possible next events with respect the observation O 2 . | Observation ( O ) | Given Hypotheses ( H j ) | What if H j happens? Generated possible next events O H j 2 | MTL | Reasoning Type | BERT Score | Human Evalua- tion | |-------------------------------------------------------------------|--------------------------------------------------------------------|---------------------------------------------------------------------|---------------|------------------|--------------|----------------------| | a. O 1 : Jim got ready for his first date. | H 1 : Jim's date wasn't at- tracted to him. | O H 2 1 : He tried to get her num- ber. She never responded to him. | H 1 , O H 1 2 | Reaction | 47.34 | Non- Contradiction | | O 2 : Since then, she has ig- nored all of Jim's text mes- sages. | H 2 : Jim went on the date and said he didn't like the girl. | O H 2 2 : He told her that he didn't want to date her. | | | 44.19 | Contradiction | | b. O 1 : Nate had the summer off before college. | H 1 : Nate spent the summer traveling and partying. | O H 1 2 : Nate had a lot of fun. | H 1 , O H 1 2 | Motivation | 49.02 | Non- Contradiction | | O 2 : Nate's last summer before college was a total blast! | H 2 :Nate decided to spend the entire summer working in the Mines. | O H 2 2 : Nate spent the summer working in the mines. | | | 44.34 | Redundancy | | c. O 1 : Dotty was being very grumpy. | H 1 : Dotty ate something bad. | O H 1 2 : She started to feel sick. | H 2 , O H 2 2 | Emotional Effect | 0.604 | Contradiction | | O 2 : She felt much better afterwards | H 2 : Dotty call some close friends to chat. | O H 2 2 : They all tried to make her happy. | | | 0.405 | Non- Contradiction | | d. O 1 : Cay had a crush on a boy in her class. | H 1 : Cay sent a love note to the boy. | O H 1 2 : The boy responded and said he liked Cay. | H 1 , O H 1 2 | Emotional Effect | 0.509 | Non- Contradiction | | O 2 : He smiled at her after and said he liked her too! | H 2 : She told him she did not like him. | O H 2 2 : The boy was very sad about it. | | | 0.423 | Contradiction | (i) examples (a), (b) and (d) depicting the scenario where possible next events and observation pairs correctly achieve higher BERTscores 11 , (ii) example (c) depicting the scenario where an incorrect possible next event and observation pair achieves higher BERTscores than the correct one. Intuitive reasons for these scenarios are, for example, for (a): there is a higher word overlap and semantic similarity between a correct next event and observation O 2 , for example (b): there is higher semantic similarity; whereas for example (c): although there is a higher semantic dissimilarity, the word overlap between the wrong possible next event ( 'She started to feel sick. ' ) and the observation ( 'She felt much better afterwards. ' ) is much higher. ## 6 Manual Evaluation Since the automatic scores only account for wordlevel similarity between observations and generated possible next events, we conduct a manual evaluation study, to assess the quality of sentences generated by our LM I model. Annotation Study on LM I generations. The annotation was performed by three annotators with computational linguistic background. We provide each of the three annotators with observations, hypotheses and sentences, as produced by our LM I 11 BERTscore matches words in candidate and reference sentences by cosine similarity. model, for 50 randomly chosen instances from the α NLI task. They obtain i) generated sentences for a next possible event for the correct and incorrect hypothesis , as well as ii) the sentence stating observation O 2 . We ask each annotator to rate the sentences according to four quality aspects as stated below. Grammaticality: the sentence is i) grammatical, ii) not entirely grammatical but understandable, or iii) completely not understandable; Redundancy: the sentence contains redundant or repeated information; Contradiction: the sentence contains any pieces of information that are contradicting the given observation O 2 or not; Relevance: the possible next event is i) relevant, ii) partially relevant, or iii) not relevant. For each aspect, they are asked to judge the sentence generated for the correct hypothesis 12 . Only for Contradiction , they are asked to judge both sentences, for correct and the incorrect hypotheses. Results and Discussion. Figures 5, 7, and 6 present the results of manual evaluations of the generation quality, according to the different criteria described above. 12 The correct hypothesis was marked for the annotation. Figure 5: Human evaluation of the grammaticality of generated sentences: ratio of i) grammatical, ii) not entirely grammatical but understandable, iii) completely not understandable sentences. <details> <summary>Image 5 Details</summary>  ### Visual Description ## Pie Chart: Language Proficiency ### Overview The pie chart illustrates the percentage of individuals who are proficient in three different languages: grammatical, understandable, and gibberish. The chart shows that the majority of individuals are proficient in grammatical language, followed by understandable language, and a small percentage in gibberish. ### Components/Axes - **Labels**: Grammatical, Understandable, Gibberish - **Scales**: Percentage - **Legends**: Color-coded to match the labels - **Axis Markers**: None ### Detailed Analysis or ### Content Details - **Grammatical Language**: 84.0% - **Understandable Language**: 12.0% - **Gibberish Language**: 4.0% ### Key Observations The chart indicates that the majority of individuals are proficient in grammatical language, suggesting that grammatical language is the most widely understood and used language among the three. The small percentage in gibberish language suggests that individuals who are not proficient in grammatical language may have difficulty understanding or communicating in this language. ### Interpretation The data suggests that grammatical language is the most widely understood and used language among the three. This could be due to the fact that grammatical language is the most commonly taught and used language in most countries. The small percentage in gibberish language suggests that individuals who are not proficient in grammatical language may have difficulty understanding or communicating in this language. This could be due to a variety of factors, including language barriers, cultural differences, or lack of exposure to the language. Overall, the data suggests that grammatical language is the most widely understood and used language among the three, while gibberish language is the least understood and used language. </details> Figure 6: Human evaluation of the Relevance of generated sentences for possible next events. <details> <summary>Image 6 Details</summary>  ### Visual Description ## Pie Chart: Data Relevance ### Overview The pie chart displays the percentage of data that is considered relevant, partially relevant, or irrelevant. The chart is divided into three segments, each representing a different category of relevance. ### Components/Axes - **Legend**: The legend is located at the top right of the chart and provides a color-coded key for the three categories of relevance. - **Axes**: There are no axes visible in the chart, as it is a pie chart and does not require axis labels. ### Detailed Analysis or ### Content Details - **Relevant**: 46.0% of the data is considered relevant. - **Partially Relevant**: 24.0% of the data is considered partially relevant. - **Irrelevant**: 30.0% of the data is considered irrelevant. ### Key Observations The chart shows that the majority of the data (46%) is considered relevant, followed by partially relevant data (24%), and the least amount of data (30%) is considered irrelevant. This suggests that the majority of the data is relevant to the context being analyzed. ### Interpretation The data suggests that the majority of the data is relevant to the context being analyzed. This could indicate that the data is useful for making informed decisions or that the context being analyzed is important. The partially relevant data could indicate that the data is useful in certain situations, but not in others. The irrelevant data could indicate that the data is not useful for the context being analyzed or that the context being analyzed is not important. </details> For measuring inter-annotator agreement, we computed Krippendorff's α (Hayes and Krippendorff, 2007) for Grammaticality and Relevance , as it is suited for ordinal values, and Cohen's Kappa κ for Redundancy and Contradiction . We found α values are 0 . 587 and 0 . 462 for Grammaticality and Relevance , respectively (moderate agreement) and κ values 0 . 61 and 0 . 74 for Redundancy and Contradiction (substantial agreement). We aggregated the annotations from the three annotators using majority vote. Figure 5 shows that the majority of sentences ( 96 %) are grammatical or understandable. Figure 7 shows that most sentences for correct labels are non-redundant ( 84 %) and noncontradictory ( 88 %), whereas for incorrect labels 39 instances are found to be contradictory with the observation O 2 ( 78 %). The manual evaluation supports our hypothesis that the generated sentences for correct labels should be more similar (less contradictory) compared to the sentences generated for incorrect labels. Figure 6 shows the ratio of sentences considered by humans as relevant, partially relevant, and irrelevant. The results show that 46 % of cases are relevant (based on majority agreement) and 24 %of cases are partially relevant. This yields that the generated sentences are (partially) relevant Figure 7: Human evaluation of Redundancy and Contradiction of generations for possible next events. <details> <summary>Image 7 Details</summary>  ### Visual Description ## Bar Chart: Number of Instances ### Overview The bar chart displays the number of instances of three different categories: Correct Label, Non-Redundancy, Non-Contradiction, and Incorrect Label. The categories are represented by two bars each, one for "Yes" and one for "No". ### Components/Axes - **Y-axis**: Number of Instances - **X-axis**: Categories (Correct Label, Non-Redundancy, Non-Contradiction, Incorrect Label) - **Legend**: Two bars for "Yes" and "No" in green and purple, respectively. ### Detailed Analysis or ### Content Details - **Correct Label**: The bar for "Yes" is significantly higher than the "No" bar, indicating a higher number of instances with the correct label. - **Non-Redundancy**: The "Yes" bar is slightly higher than the "No" bar, suggesting a higher number of instances with non-redundant labels. - **Non-Contradiction**: The "Yes" bar is the highest, indicating the most instances with non-contradictory labels. - **Incorrect Label**: The "No" bar is the highest, suggesting the most instances with incorrect labels. ### Key Observations - The "Correct Label" category has the highest number of instances, followed by "Non-Contradiction". - The "Non-Redundancy" category has the second highest number of instances. - The "Incorrect Label" category has the lowest number of instances. ### Interpretation The data suggests that the majority of instances are correctly labeled, with non-contradictory labels being the most common. The number of instances with non-redundant labels is slightly higher than those with incorrect labels. This could indicate that the labeling process is generally accurate, but there may be some instances where the labels are not as precise as desired. </details> in most cases and thus should support abduction for both unsupervised ( LM I + BERTScore) and supervised ( LM I + MTL ) models. Impact of Reasoning types. Finally, to better assess the performance of our model, we determine what types of reasoning underly the abductive reasoning tasks in our data, and examine to what extent our models capture or not these reasoning types. We consider again the 50 instances that were annotated by our previous annotators and manually classify them into different reasoning types. We broadly divided the data into 6 categories: (i) Motivation, (ii) Spatial-Temporal, (iii) Emotional, (iv) Negation, (v) Reaction, (vi) Situational fact. The most frequent type was Emotional (10), most infrequent was Spatial (7). We ask a new annotator to annotate the reasoning types for these 50 instances. Considering the relevance and contradiction categories from the previous annotations we determine that for Negation ( 8 ), Emotional ( 10 ), and Reaction ( 8 ) all generated events for correct labels are partially or fully relevant and non-contradictory . An intuitive reason can be that we train our LM I model to learn how different counterfactual hypothetical events emerging from a single premise can lead to the same or different outcomes through a series of events. Some counterfactual events ( s ′ 2 ) are negations of the original event ( s 2 ) in the TIMETRAVEL dataset. This may support the reasoning class Negation. For the other categories: Motivation, Spatial-temporal, and Situational fact, we detect errors regarding (missing) Relevance in 21 %, 14 %and 28 %of cases, respectively. Table 6 illustrates an example from the class Situational Fact, where our generated next event is irrelevant and redundant . - O 1 : Jenna hit the weight hard in the gym. O 2 : She took a cold bath in order to alleviate her pain. - H 1 : Her neck pain stopped because of this. H 2 : Jenna pulled a muscle lifting weights. O 1 2 : She decided to take a break . H O H 2 2 : Jenna lost weight in the gym. Table 6: Error Analysis: An example of generated possible next event O H j 2 from Situational Fact category. ## 7 Related Work Commonsense Reasoning. There is growing interest in this research field, which led to the creation of several new resources on commonsense reasoning, in form of both datasets , such as SocialIQA (Sap et al., 2019b), CommonsenseQA (Talmor et al., 2019), CosmosQA (Huang et al., 2019) and knowledge bases , e.g. ConceptNet (Speer et al., 2017), ATOMIC (Sap et al., 2019a), or Event2Mind (Rashkin et al., 2018). Recently, many works proposed to utilize external static knowledge graphs (KGs) to address the bottleneck of obtaining relevant commonsense knowledge. Lin et al. (2019) proposed to utilize knowledge graph embeddings to rank and select relevant knowledge triples or paths. Paul and Frank (2019) proposed to extract subgraphs from KGs using graph-based ranking methods and further Paul et al. (2020) adopted the graph-based ranking method and proposed to dynamically extend the KG to combat sparsity. In concurrent work, Paul and Frank (2021) introduced a method to dynamically generate contextually relevant knowledge that guides a model while performing the narrative story completion task. Both hypothetical reasoning and abductive reasoning are understudied problems in NLP. Recently, Tandon et al. (2019) proposed a first large-scale dataset of 'What if... ' questions over procedural text. They introduced the dataset to study the effect of perturbations in procedural text. Related to our work, Qin et al. (2019) investigated the capabilities of state-of-the-art LMs to rewrite stories with counterfactual reasoning. In our work we utilize this dataset to model how to generate possible next events emerging from different hypothetical and counterfactual events. Mostafazadeh et al. (2016) designed the narrative cloze task, a task to choose the correct ending of a story. 13 Conversely, Bhagavatula et al. (2020) proposed a task that requires 13 Their dataset, ROCStories, was later extended in Qin et al. (2019) and Bhagavatula et al. (2020). reasoning about plausible explanations for narrative omissions. Our research touches on the issue of hypothetical reasoning about alternative situations. We found that making language models learn how different hypothetical events can evolve from a premise and result in similar or different future events forming from a premise and how these events can result in similar or different future events helps models to perform better in abduction. Explainability. Despite the success of large pretrained language models, recent studies have raised some critical points such as: high accuracy scores do not necessarily reflect understanding (Min et al., 2019), large pretrained models may exploit superficial clues and annotation artifacts (Gururangan et al., 2018; Kavumba et al., 2019). Therefore, the ability of models to generate explanations has become desirable, as this enhances interpretability. Recently, there has been substantial effort to build datasets with natural language explanations (Camburu et al., 2018; Park et al., 2018; Thayaparan et al., 2020). There have also been numerous research works proposing models that are interpretable or explainable (Rajani et al., 2019; Atanasova et al., 2020; Latcinnik and Berant, 2020; Wiegreffe and Marasovi´ c, 2021). Our work sheds light in this direction, as our MTL model not only predicts the plausible hypothesis H j but also generates possible next events O H j 2 and chooses the one that is closer to the given context, thereby making our model more expressive. Abductive Reasoning. There has been longstanding work on theories of abductive reasoning (Peirce, 1903, 1965a,b; Kuipers, 1992, 2013). Researchers have applied various frameworks, some focused on pure logical frameworks (Pople, 1973; Kakas et al., 1992), some on probabilistic frameworks (Pearl, 1988), and others on Markov Logics (Singla and Mooney, 2011). Recently, moving away from logic-based abductive reasoning, Bhagavatula et al. (2020) proposed to study languagebased abductive reasoning. They introduced two tasks: Abductive Natural Language Inference ( α NLI) and Generation ( α NLG) . They establish baseline performance based on state-of-the-art language models and make use of inferential structured knowledge from ATOMIC (Sap et al., 2019a) as background knowledge. Zhu et al. (2020) proposed to use a learning-to-rank framework to address the abductive reasoning task. Ji et al. (2020) proposed a model GRF that enables pre-trained models (GPT-2) with dynamic multi-hop reasoning on multi-relational paths extracted from the external ConceptNet commonsense knowledge graph for the α NLG task. Paul and Frank (2020) have proposed a multi-head knowledge attention method to incorporate commonsense knowledge to tackle the α NLI task. Unlike our previous work in Paul and Frank (2020), which focused on leveraging structured knowledge, in this work, we focus on learning about what will happen next from different counterfactual situations in a story context through language model fine-tuning. Specifically, we study the impact of such forward inference on the α NLI task in a multi-task learning framework and show how it can improve performance over a strong BERT model. ## 8 Conclusion We have introduced a novel method for addressing the abductive reasoning task by explicitly learning what events could follow other events in a hypothetical scenario, and learning to generate such events, conditioned on a premise or hypothesis. We show how a language model - fine-tuned for this capability on a suitable narrative dataset - can be leveraged to support abductive reasoning in the α NLI tasks, in two settings: an unsupervised setting in combination with BertScore , to select the proper hypothesis, and a supervised setting in a MTL setting. The relatively strong performance of our proposed models demonstrates that learning to choose from generated hypothetical next events the one that is most similar to the observation, supports the prediction of the most plausible hypothesis. Our experiments show that our unsupervised LM I + BERTScore model outperforms some of the strong supervised baseline systems on α NLI. 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