Abductive Learning is a framework that combines machine learning with first-order logical reasoning. It allows machine learning models to exploit complex symbolic domain knowledge represented by first-order logic rules. However, it is challenging to obtain or express the ground-truth domain knowledge explicitly as first-order logic rules in many applications. The only accessible knowledge base is implicitly represented by groundings, i.e., propositions or atomic formulas without variables. This paper proposes Grounded Abductive Learning (GABL) to enhance machine learning models with abductive reasoning in a ground domain knowledge base, which offers inexact supervision through a set of logic propositions. We apply GABL on two weakly supervised learning problems and found that the model's initial accuracy plays a crucial role in learning. The results on a real-world OCR task show that GABL can significantly reduce the effort of data labeling than the compared methods.

Stroke evaluation is critical for coaches to evaluate players' performance in table tennis matches. However, current methods highly demand proficient knowledge in table tennis and are time-consuming. We collaborate with the Chinese national table tennis team and propose Tac-Valuer, an automatic stroke evaluation framework for analysts in table tennis teams. In particular, to integrate analysts' knowledge into the machine learning model, we employ the latest effective framework named abductive learning, showing promising performance. Based on abductive learning, Tac-Valuer combines the state-of-the-art computer vision algorithms to extract and embed stroke features for evaluation. We evaluate the design choices of the approach and present Tac-Valuer's usability through use cases that analyze the performance of the top table tennis players in world-class events.

To utilize the raw inputs and symbolic knowledge simultaneously, some recent neuro-symbolic learning methods use abduction, i.e., abductive reasoning, to integrate sub-symbolic perception and logical inference. While the perception model, e.g., a neural network, outputs some facts that are inconsistent with the symbolic background knowledge base, abduction can help revise the incorrect perceived facts by minimizing the inconsistency between them and the background knowledge. However, to enable effective abduction, previous approaches need an initialized perception model that discriminates the input raw instances. This limits the application of these methods, as the discrimination ability is usually acquired from a thorough pre-training when the raw inputs are difficult to classify. In this paper, we propose a novel abduction strategy, which leverages the similarity between samples, rather than the output information by the perceptual neural network, to guide the search in abduction. Based on this principle, we further present ABductive Learning with Similarity (ABLSim) and apply it to some difficult neuro-symbolic learning tasks. Experiments show that the efficiency of ABLSim is significantly higher than the state-of-the-art neuro-symbolic methods, allowing it to achieve better performance with less labeled data and weaker domain knowledge.

In many practical tasks, there are usually two kinds of common information: cheap unlabeled data and domain knowledge in the form of symbols. There are some attempts using one single information source, such as semi-supervised learning and abductive learning. However, there is little work to use these two kinds of information sources at the same time, because it is very difficult to combine symbolic logical representation and numerical model optimization effectively. The learning becomes even more challenging when the domain knowledge is insufficient. In this paper, we present an attempt-Semi-Supervised ABductive Learning (SS-ABL) framework. In this framework, semi-supervised learning is trained via pseudo labels of unlabeled data generated by abductive learning, and the background knowledge is refined via the label distribution predicted by semi-supervised learning. The above framework can be optimized iteratively and can be naturally interpretable. The effectiveness of our framework has been fully verified in the theft judicial sentencing of real legal documents. In the case of missing sentencing elements and mixed legal rules, our framework is apparently superior to many existing baseline practices, and provides explanatory assistance to judicial sentencing.