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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 \n ## Diagram: Plausible Explanations for Wet Grass ### Overview The image is a diagram illustrating two plausible explanations for why the grass is wet. It uses cloud-shaped bubbles to represent each explanation, connected by curved lines suggesting a causal relationship. The diagram is labeled with "Plausible Explanation" at the top and "Explanation" at the bottom-left. ### Components/Axes The diagram consists of: * **Title:** "Plausible Explanation" (top-center) * **Explanation 1:** "It rained last night" (within a light blue cloud bubble) * **Explanation 2:** "Sprinkler made the grass wet" (within a light green cloud bubble) * **Label:** "Explanation" (bottom-left) * **Connecting Lines:** Curved lines linking the title to the explanations. ### Detailed Analysis or Content Details The diagram presents two distinct, independent explanations: 1. **Explanation 1:** The text within the light blue cloud states, "It rained last night." 2. **Explanation 2:** The text within the light green cloud states, "Sprinkler made the grass wet." There are no numerical values or axes in this diagram. It is purely qualitative. ### Key Observations The diagram highlights two possible causes for the same effect (wet grass). The use of cloud shapes suggests these are potential, rather than definitive, explanations. The diagram does not prioritize one explanation over the other. ### Interpretation The diagram demonstrates a simple problem-solving approach: identifying multiple possible causes for an observed phenomenon. It illustrates that a single effect can have multiple explanations. The diagram is a visual aid for brainstorming or considering different hypotheses. It doesn't offer evidence to support either explanation, but simply presents them as possibilities. The diagram is a basic example of abductive reasoning – inferring the best explanation given the available evidence. </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 \n ## Diagram: Hypothesis Testing with Language Model ### Overview This diagram illustrates a hypothesis testing process involving a Language Model (LM) responding to initial observations. It depicts two competing hypotheses (H1 and H2) stemming from observations (O1 and O2), and how the LM generates subsequent observations (O1' and O2') based on evaluating these hypotheses. ### Components/Axes The diagram consists of the following components: * **Observations (O1, O2):** Located at the top-left, presented in a light pink box. * **Hypothesis (H1, H2):** Two cloud-shaped boxes, positioned on either side of the central LM. * **Language Model (LM):** A central rectangular box with a face, representing the core processing unit. * **Subsequent Observations (O1', O2'):** Located at the bottom, presented in a light purple box. * **Arrows:** Indicate the flow of information and influence between components. * **Text Labels:** Descriptive text associated with each component. ### Detailed Analysis or Content Details **Observations:** * O1: "Priya decided to try a new restaurant." * O2: "Priya thought her food was delicious." **Hypotheses:** * H1: "She ordered two shrimp dishes." (Located on the left) * H2: "The food that Priya ordered was microwaved and precooked." (Located on the right) **Language Model (LM):** * The LM is depicted as a grey box with a smiling face. * An arrow points from the observations (O1, O2) to the LM, labeled "What if". * Two arrows emanate from the LM, labeled H1 and H2, pointing towards the subsequent observations. **Subsequent Observations:** * O1': "She was excited to try them out." (Associated with H1) * O2': "Priya was disappointed in the quality of the food." (Associated with H2) ### Key Observations The diagram demonstrates a branching scenario where the LM evaluates two different hypotheses based on initial observations. Each hypothesis leads to a different subsequent observation, suggesting the LM can generate diverse outcomes based on its internal reasoning. The "What if" arrow indicates the LM is performing a counterfactual reasoning process. ### Interpretation This diagram illustrates a simplified model of how a language model might engage in hypothesis testing. The initial observations set the context, and the LM explores alternative explanations (hypotheses) for those observations. The LM then generates new observations based on each hypothesis, effectively simulating different possible scenarios. This process highlights the LM's ability to reason about cause and effect, and to generate plausible continuations of a given narrative. The diagram suggests that the LM doesn't simply recall information, but actively constructs explanations and explores possibilities. The contrasting outcomes (excitement vs. disappointment) demonstrate the LM's capacity for nuanced and context-dependent reasoning. The use of a smiling face on the LM box could be interpreted as anthropomorphizing the model, suggesting a degree of agency or intentionality. However, it's important to remember that the LM is ultimately a statistical model, and its outputs are based on patterns learned from data. </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 \n ## Diagram: Conceptual Models for Reasoning ### Overview The image presents four distinct diagrams illustrating conceptual models for different reasoning approaches. The diagrams utilize nodes and directed edges to represent relationships between entities. The top-left diagram represents αNLI, the top-right represents Counterfactual Reasoning from TimeTravel, and the bottom two diagrams represent a model with branching hypotheses. ### Components/Axes The diagrams consist of nodes (circles) and directed edges (arrows) connecting them. The nodes are filled with different colors: light orange, light green, and yellow. Each diagram is labeled with a letter and a descriptive title. The top diagrams are separated from the bottom diagrams by a dashed horizontal line. The top-right diagram includes the text "Counterfactual" along one of the edges. ### Detailed Analysis or Content Details **Diagram (a) - αNLI:** * Nodes: O1 (light orange), Hi (light green), O2 (light orange). * Edges: O1 -> Hi, Hi -> O2. * This diagram represents a sequential relationship between observations and a hypothesis. **Diagram (b) - Counterfactual Reasoning from TimeTravel:** * Nodes: S1 (light orange), S2 (light green), S3 (light orange), S2' (light green), S3' (light orange). * Edges: S1 -> S2, S1 -> S2', S2 -> S3, S2' -> S3'. * The edge between S1 and S2' is labeled "Counterfactual". * This diagram illustrates branching possibilities, representing a counterfactual scenario. **Diagram (c) - Branching Hypotheses (Top-Left of Bottom Section):** * Nodes: O1 (light orange), H1 (light green), O2 (light orange). * Edges: O1 -> H1, H1 -> O2. * This diagram represents a sequential relationship between observations and a hypothesis. **Diagram (d) - Branching Hypotheses (Top-Right of Bottom Section):** * Nodes: O1 (light orange), H2 (light green), H1 (light green), O2 (light orange), H2 (light green), O2 (yellow). * Edges: O1 -> H1, O1 -> H2, H1 -> O2, H2 -> O2. * This diagram represents branching hypotheses originating from a single observation. ### Key Observations * The diagrams utilize a consistent visual language of nodes and edges. * The color coding appears to represent different types of entities (observations, hypotheses). * Diagram (b) explicitly introduces the concept of "Counterfactual" reasoning. * The bottom diagrams demonstrate a more complex branching structure compared to the top diagrams. * The bottom diagrams have a dashed line connecting O2 and O2. ### Interpretation These diagrams likely represent different approaches to reasoning within a computational or philosophical framework. * **αNLI (Diagram a)** represents a simple inference process where an observation (O1) leads to a hypothesis (Hi), which in turn leads to another observation (O2). This is a straightforward chain of reasoning. * **Counterfactual Reasoning (Diagram b)** introduces the idea of alternative realities or "what if" scenarios. Starting from a state (S1), two possible paths are explored: a factual path (S2 -> S3) and a counterfactual path (S2' -> S3'). This is crucial for understanding causality and making decisions. * **Branching Hypotheses (Diagrams c & d)** illustrate how multiple hypotheses can be generated from a single observation. Diagram (d) shows how these hypotheses can lead to different observations, highlighting the importance of considering multiple possibilities. The use of color coding suggests that observations are represented by orange nodes, hypotheses by green nodes, and potentially outcomes or results by yellow nodes. The dashed line in the bottom diagrams might indicate a relationship or connection between the different branches of reasoning. These diagrams are likely used to illustrate the underlying logic of different reasoning systems or to compare and contrast their capabilities. They provide a visual representation of complex concepts, making them easier to understand and analyze. The diagrams are not presenting data, but rather a conceptual framework. </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 \n ## Diagram: Multi-Task Learning Architecture with BERT and GPT-2 ### Overview The image depicts a diagram illustrating a multi-task learning (MTL) architecture combining BERT and GPT-2 models. The diagram shows the flow of data through these models for two tasks: Natural Language Inference (NLI) and Similarity. It highlights shared layers between the models and the loss function used for multi-task learning. ### Components/Axes The diagram consists of the following components: * **BERT (MTL):** Represented by a large, light-orange rectangular block labeled "(b) BERT (MTL)". This block signifies the shared layers of the BERT model used for multi-task learning. * **GPT-2 (LM_T):** Represented by a large, light-red rectangular block labeled "(a) GPT-2 (LM_T)". This block signifies the GPT-2 model used for language modeling. * **Linear Layers:** Two green rectangular blocks labeled "Linear Layer" positioned above the BERT block. These layers are specific to each task. * **Tasks:** Two tasks are represented: * **nNLI:** Labeled "nNLI" in a light-blue rectangular block. * **Similarity:** Labeled "Similarity" in a light-blue rectangular block. * **Input Data:** Various input sequences are represented as: * O₁, H₁, O₂ * O₁, H₂, O₂ * H₁, O₂, O₂ * H₂, H₂, O₂ * O₁, [M], O₂, O₁ * **Loss Function:** A rectangular block labeled "Loss_MT = λ_NLI + W * L_similarity". * **Questions:** Two questions are written above the GPT-2 block: "What if H₁ happens?" and "What if H₂ happens?". ### Detailed Analysis or Content Details The diagram illustrates the following data flow: 1. **GPT-2 Branch:** * Input: O₁, [M], O₂, O₁ is fed into the GPT-2 model. * Output: H₁ and H₂ are generated. * Questions: The questions "What if H₁ happens?" and "What if H₂ happens?" are posed, suggesting conditional generation or reasoning. 2. **BERT Branch:** * Input: Four different input sequences are fed into the BERT model: O₁, H₁, O₂; O₁, H₂, O₂; H₁, O₂, O₂; H₂, H₂, O₂. * Shared Layers: These inputs pass through the shared layers of the BERT model. * Linear Layers: The outputs from the shared layers are then fed into two separate linear layers, one for each task. 3. **Tasks and Loss Function:** * nNLI: The output of the first linear layer is used for the nNLI task, taking input H₁ or H₂. * Similarity: The output of the second linear layer is used for the Similarity task, taking input H₂ or O₂. * Loss Function: The overall loss function (Loss_MT) is a weighted sum of the nNLI loss (λ_NLI) and the similarity loss (L_similarity), with 'W' being the weight for the similarity loss. ### Key Observations * The diagram emphasizes the sharing of layers between the BERT model for both tasks, which is a key characteristic of multi-task learning. * The GPT-2 model appears to be used for generating hypotheses (H₁ and H₂) which are then used as input to the BERT model for the nNLI and Similarity tasks. * The loss function explicitly shows the weighting between the two tasks, allowing for control over the relative importance of each task during training. ### Interpretation This diagram illustrates a sophisticated multi-task learning approach that leverages the strengths of both BERT and GPT-2. GPT-2 is used to generate potential hypotheses or contextual information, while BERT is used to perform downstream tasks like nNLI and similarity assessment. The shared layers in BERT allow for knowledge transfer between the two tasks, potentially improving performance on both. The weighted loss function provides a mechanism for balancing the contributions of each task to the overall learning process. The questions posed above the GPT-2 block suggest a focus on counterfactual reasoning or exploring different scenarios. This architecture is likely designed to improve the robustness and generalization ability of the model by training it on multiple related tasks simultaneously. The use of [M] in the GPT-2 input suggests a masking token, commonly used in language modeling to predict missing words or phrases. </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 \n ## Pie Chart: Text Quality Distribution ### Overview This image presents a pie chart illustrating the distribution of text quality categorized into three classes: Grammatical, Understandable, and Gibberish. The chart visually represents the percentage of text falling into each category. ### Components/Axes The chart is a standard pie chart with no explicit axes. The categories are defined by color and labeled in a legend positioned to the right of the chart. * **Categories:** * Grammatical * Understandable * Gibberish * **Legend:** * Green: Grammatical * Yellow: Understandable * Light Green: Gibberish ### Detailed Analysis The pie chart segments represent the following percentages: * **Grammatical (Green):** The largest segment, occupying approximately 84.0% of the pie. * **Understandable (Yellow):** A smaller segment, representing approximately 4.0% of the pie. * **Gibberish (Light Green):** The smallest segment, representing approximately 12.0% of the pie. The segments are arranged clockwise, starting with the largest (Grammatical) at the bottom and proceeding to Understandable and then Gibberish. ### Key Observations The overwhelming majority (84.0%) of the text is classified as "Grammatical". A small portion (4.0%) is "Understandable", and a moderate portion (12.0%) is categorized as "Gibberish". ### Interpretation The data suggests that the majority of the analyzed text is well-formed and grammatically correct. However, a non-negligible portion (12%) is unintelligible ("Gibberish"), and a small portion is only "Understandable" but not necessarily grammatically perfect. This could indicate a source of data with varying quality, potentially including machine-generated text, errors in transcription, or text from diverse sources with differing linguistic standards. The large proportion of "Grammatical" text suggests a relatively high overall quality of the source material. </details> Figure 6: Human evaluation of the Relevance of generated sentences for possible next events. <details> <summary>Image 6 Details</summary>  ### Visual Description \n ## Pie Chart: Relevance Assessment ### Overview The image is a pie chart illustrating the distribution of relevance across three categories: Relevant, Partially Relevant, and Irrelevant. The chart visually represents the percentage breakdown of each category. ### Components/Axes The chart consists of three slices, each representing a category. A legend is positioned to the right of the chart, associating colors with the categories. * **Categories:** Relevant, Partially Relevant, Irrelevant * **Colors:** * Relevant: Green * Partially Relevant: Orange/Yellow * Irrelevant: Red * **Percentages:** The chart displays percentages for each slice directly within the slices. ### Detailed Analysis The pie chart shows the following distribution: * **Relevant (Green):** The largest slice, occupying approximately 46.6% of the pie. * **Partially Relevant (Orange/Yellow):** The second largest slice, occupying approximately 24.0% of the pie. * **Irrelevant (Red):** The smallest slice, occupying approximately 30.0% of the pie. The slices are arranged clockwise, starting with the largest (Relevant) at the top and proceeding to Partially Relevant and then Irrelevant. ### Key Observations The "Relevant" category represents the largest proportion of the data, almost half of the total. The "Irrelevant" category is the second largest, representing nearly a third of the total. The "Partially Relevant" category is the smallest, representing just over a quarter of the total. ### Interpretation The data suggests that a significant portion of the assessed items are considered "Relevant" (46.6%), indicating a substantial degree of usefulness or applicability. However, a considerable portion (30.0%) is deemed "Irrelevant," suggesting a need to filter or exclude these items. The "Partially Relevant" category (24.0%) indicates that a moderate amount of the assessed items have some value, but may require further refinement or consideration. The chart likely represents an assessment of information, data, or items based on their relevance to a specific task, goal, or context. The distribution highlights the need for careful selection and prioritization of relevant information while discarding or re-evaluating irrelevant items. The presence of a "Partially Relevant" category suggests a nuanced evaluation process, acknowledging that some items may have limited or conditional value. </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 \n ## Bar Chart: Label Consistency Analysis ### Overview This is a bar chart comparing the number of instances of "Non-Redundancy", "Non-Contradiction", and "Non-Contradiction" across "Correct Label" and "Incorrect Label" categories. The chart uses green bars to represent "Yes" instances and purple bars to represent "No" instances. The y-axis represents the "Number of Instances", ranging from 0 to 50. The x-axis represents the categories being compared. ### Components/Axes * **X-axis:** Label Consistency - Categories: "Correct Label", "Correct Label", "Incorrect Label". Each category has two sub-categories: "Non-Redundancy", "Non-Contradiction", and "Non-Contradiction". * **Y-axis:** Number of Instances (Scale: 0 to 50, increments of 10). * **Legend:** * Green: Yes * Purple: No * **Chart Title:** (Not explicitly present, but implied to be related to label consistency) ### Detailed Analysis The chart consists of three sets of paired bars, one for each category on the x-axis. * **Correct Label - Non-Redundancy:** The green bar (Yes) reaches approximately 43 instances. The purple bar (No) reaches approximately 10 instances. The green bar is significantly taller than the purple bar. * **Correct Label - Non-Contradiction:** The green bar (Yes) reaches approximately 46 instances. The purple bar (No) reaches approximately 8 instances. The green bar is significantly taller than the purple bar. * **Incorrect Label - Non-Contradiction:** The green bar (Yes) reaches approximately 15 instances. The purple bar (No) reaches approximately 39 instances. The purple bar is significantly taller than the green bar. ### Key Observations * For both "Correct Label" categories ("Non-Redundancy" and "Non-Contradiction"), the number of "Yes" instances is substantially higher than the number of "No" instances. * For the "Incorrect Label" category ("Non-Contradiction"), the number of "No" instances is substantially higher than the number of "Yes" instances. * The difference between "Yes" and "No" instances is most pronounced in the "Incorrect Label" category. ### Interpretation The data suggests a strong correlation between label correctness and consistency. When labels are correct, instances of non-redundancy and non-contradiction are prevalent ("Yes" instances dominate). Conversely, when labels are incorrect, instances of non-contradiction are rare ("No" instances dominate). This indicates that incorrect labels are often associated with contradictory information. The chart demonstrates that label quality is a critical factor in maintaining data consistency. The large difference in the "Incorrect Label" category suggests that incorrect labels are a significant source of inconsistency. This could be due to errors in the labeling process or inherent ambiguity in the data itself. Further investigation into the reasons for incorrect labeling is warranted. </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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