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 NLI task -- which consists in choosing the more likely explanation for given observations. We train a specialized language model LMI 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 Abductive NLI task, which predicts a plausible explanation by a) considering different possible events emerging from candidate hypotheses -- events generated by LMI -- 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 fine-tuned on Abductive NLI. Our manual evaluation and analysis suggest that learning about possible next events from different hypothetical scenarios supports abductive inference.

Given a knowledge base and an observation as a set of facts, ABox abduction aims at computing a hypothesis that, when added to the knowledge base, is sufficient to entail the observation. In signature-based ABox abduction, the hypothesis is further required to use only names from a given set. This form of abduction has applications such as diagnosis, KB repair, or explaining missing entailments. It is possible that hypotheses for a given observation only exist if we admit the use of fresh individuals and/or complex concepts built from the given signature, something most approaches for ABox abduction so far do not support or only support with restrictions. In this paper, we investigate the computational complexity of this form of abduction -- allowing either fresh individuals, complex concepts, or both -- for various description logics, and give size bounds on the hypotheses if they exist.

Humans, on the other hand, need none of this. On the basis of very limited or incomplete data, we nonetheless come to the right conclusion about many things (yes, we are fallible, but the miracle is that we are right so often). Noam Chomsky's entire claim to fame in linguistics really amounts to exploring this underdetermination problem, which he referred to as "the poverty of the stimulus." Humans pick up language despite very varied experiences with other human language speakers. Babies born in abusive and sensory deprived environments pick up language.

In social settings, much of human behavior is governed by unspoken rules of conduct. For artificial systems to be fully integrated into social environments, adherence to such norms is a central prerequisite. We investigate whether contemporary NLG models can function as behavioral priors for systems deployed in social settings by generating action hypotheses that achieve predefined goals under moral constraints. Moreover, we examine if models can anticipate likely consequences of (im)moral actions, or explain why certain actions are preferable by generating relevant norms. For this purpose, we introduce 'Moral Stories', a crowd-sourced dataset of structured, branching narratives for the study of grounded, goal-oriented social reasoning. Finally, we propose decoding strategies that effectively combine multiple expert models to significantly improve the quality of generated actions, consequences, and norms compared to strong baselines, e.g. though abductive reasoning.

We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a matter of certainty, but is instead governed by a probability distribution. We then show that this framework gives a compelling account of several aspects of mathematical practice. These include: 1) the way in which mathematicians generate research programs, 2) the applicability of Bayesian models of mathematical heuristics, 3) the role of abductive reasoning in mathematics, 4) the way in which multiple proofs of a proposition can strengthen our degree of belief in that proposition, and 5) the nature of the hypothesis that there are multiple formal systems that are isomorphic to physically possible universes. Thus, by embracing a model of mathematics as not perfectly predictable, we generate a new and fruitful perspective on the epistemology and practice of mathematics.

We propose a novel approach for answering and explaining multiple-choice science questions by reasoning on grounding and abstract inference chains. This paper frames question answering as an abductive reasoning problem, constructing plausible explanations for each choice and then selecting the candidate with the best explanation as the final answer. Our system, ExplanationLP, elicits explanations by constructing a weighted graph of relevant facts for each candidate answer and extracting the facts that satisfy certain structural and semantic constraints. To extract the explanations, we employ a linear programming formalism designed to select the optimal subgraph. The graphs' weighting function is composed of a set of parameters, which we fine-tune to optimize answer selection performance. We carry out our experiments on the WorldTree and ARC-Challenge corpus to empirically demonstrate the following conclusions: (1) Grounding-Abstract inference chains provides the semantic control to perform explainable abductive reasoning (2) Efficiency and robustness in learning with a fewer number of parameters by outperforming contemporary explainable and transformer-based approaches in a similar setting (3) Generalisability by outperforming SOTA explainable approaches on general science question sets.

For many reasoning-heavy tasks, it is challenging to find an appropriate end-to-end differentiable approximation to domain-specific inference mechanisms. Neural-Symbolic (NeSy) AI divides the end-to-end pipeline into neural perception and symbolic reasoning, which can directly exploit general domain knowledge such as algorithms and logic rules. However, it suffers from the exponential computational complexity caused by the interface between the two components, where the neural model lacks direct supervision, and the symbolic model lacks accurate input facts. As a result, they usually focus on learning the neural model with a sound and complete symbolic knowledge base while avoiding a crucial problem: where does the knowledge come from? In this paper, we present Abductive Meta-Interpretive Learning ($Meta_{Abd}$), which unites abduction and induction to learn perceptual neural network and first-order logic theories simultaneously from raw data. Given the same amount of domain knowledge, we demonstrate that $Meta_{Abd}$ not only outperforms the compared end-to-end models in predictive accuracy and data efficiency but also induces logic programs that can be re-used as background knowledge in subsequent learning tasks. To the best of our knowledge, $Meta_{Abd}$ is the first system that can jointly learn neural networks and recursive first-order logic theories with predicate invention.

Current discussions of "Explainable AI" (XAI) do not much consider the role of abduction in explanatory reasoning (see Mueller, et al., 2018). It might be worthwhile to pursue this, to develop intelligent systems that allow for the observation and analysis of abductive reasoning and the assessment of abductive reasoning as a learnable skill. Abductive inference has been defined in many ways. For example, it has been defined as the achievement of insight. Most often abduction is taken as a single, punctuated act of syllogistic reasoning, like making a deductive or inductive inference from given premises. In contrast, the originator of the concept of abduction---the American scientist/philosopher Charles Sanders Peirce---regarded abduction as an exploratory activity. In this regard, Peirce's insights about reasoning align with conclusions from modern psychological research. Since abduction is often defined as "inferring the best explanation," the challenge of implementing abductive reasoning and the challenge of automating the explanation process are closely linked. We explore these linkages in this report. This analysis provides a theoretical framework for understanding what the XAI researchers are already doing, it explains why some XAI projects are succeeding (or might succeed), and it leads to design advice.

This paper presents an abductive framework for multi-hop and interpretable textual inference. The reasoning process is guided by the notions unification power and plausibility of an explanation, computed through the interaction of two major architectural components: (a) An analogical reasoning model that ranks explanatory facts by leveraging unification patterns in a corpus of explanations; (b) An abductive reasoning model that performs a search for the best explanation, which is realised via conceptual abstraction and subsequent unification. We demonstrate that the Step-wise Conceptual Unification can be effective for unsupervised question answering, and as an explanation extractor in combination with state-of-the-art Transformers. An empirical evaluation on the Worldtree corpus and the ARC Challenge resulted in the following conclusions: (1) The question answering model outperforms competitive neural and multi-hop baselines without requiring any explicit training on answer prediction; (2) When used as an explanation extractor, the proposed model significantly improves the performance of Transformers, leading to state-of-the-art results on the Worldtree corpus; (3) Analogical and abductive reasoning are highly complementary for achieving sound explanatory inference, a feature that demonstrates the impact of the unification patterns on performance and interpretability.

The requirement for artificial intelligence (AI) to provide explanations in making critical decision becomes increasingly important due to concerns of accountability, trust, as well as ethics. Such an explainable AI is expected to be capable of providing justifications that are human-understandable. A form of reasoning for providing explanations to an observation, known as abduction, has been well studied in AI, particularly in knowledge representation and reasoning. It extends to logic programming, dubbed abductive logic programming [3], and it has a wide variety of usage, e.g., in planning, scheduling, reasoning of rational agents, security protocols verification, biological systems, and machine ethics.