In recent years, the Neurosymbolic framework has attracted a lot of attention in various applications, from recommender systems and information retrieval to healthcare and finance. This success is due to its stellar performance combined with attractive properties, such as learning and reasoning. The new emerging Neurosymbolic field is currently experiencing a renaissance, as novel frameworks and algorithms motivated by various practical applications are being introduced, building on top of the classical neural and reasoning problem setting. This article aims to provide a comprehensive review of significant recent developments in real-world applications of Neurosymbolic Artificial Intelligence. Specifically, we introduce a taxonomy of common Neurosymbolic applications and summarize the state-of-the-art for each of those domains. Furthermore, we identify important current trends and provide new perspectives pertaining to the future of this burgeoning field.

Deep Reinforcement Learning uses a deep neural network to encode a policy, which achieves very good performance in a wide range of applications but is widely regarded as a black box model. A more interpretable alternative to deep networks is given by neuro-fuzzy controllers. Unfortunately, neuro-fuzzy controllers often need a large number of rules to solve relatively simple tasks, making them difficult to interpret. In this work, we present an algorithm to distill the policy from a deep Q-network into a compact neuro-fuzzy controller. This allows us to train compact neuro-fuzzy controllers through distillation to solve tasks that they are unable to solve directly, combining the flexibility of deep reinforcement learning and the interpretability of compact rule bases. We demonstrate the algorithm on three well-known environments from OpenAI Gym, where we nearly match the performance of a DQN agent using only 2 to 6 fuzzy rules.

Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to integrate NNs and DTs explicitly or implicitly. In this survey, these approaches are organized in a school which we term as neural trees (NTs). This survey aims to present a comprehensive review of NTs and attempts to identify how they enhance the model interpretability. We first propose a thorough taxonomy of NTs that expresses the gradual integration and co-evolution of NNs and DTs. Afterward, we analyze NTs in terms of their interpretability and performance, and suggest possible solutions to the remaining challenges. Finally, this survey concludes with a discussion about other considerations like conditional computation and promising directions towards this field. A list of papers reviewed in this survey, along with their corresponding codes, is available at: https://github.com/zju-vipa/awesome-neural-trees

Answering complex first-order logic (FOL) queries on knowledge graphs is a fundamental task for multi-hop reasoning. Traditional symbolic methods traverse a complete knowledge graph to extract the answers, which provides good interpretation for each step. Recent neural methods learn geometric embeddings for complex queries. These methods can generalize to incomplete knowledge graphs, but their reasoning process is hard to interpret. In this paper, we propose Graph Neural Network Query Executor (GNN-QE), a neural-symbolic model that enjoys the advantages of both worlds. GNN-QE decomposes a complex FOL query into relation projections and logical operations over fuzzy sets, which provides interpretability for intermediate variables. To reason about the missing links, GNN-QE adapts a graph neural network from knowledge graph completion to execute the relation projections, and models the logical operations with product fuzzy logic. Experiments on 3 datasets show that GNN-QE significantly improves over previous state-of-the-art models in answering FOL queries. Meanwhile, GNN-QE can predict the number of answers without explicit supervision, and provide visualizations for intermediate variables.

This paper questions the feasibility of a strong (general) data-centric artificial intelligence (AI). The disadvantages of this type of intelligence are discussed. As an alternative, the concept of co-evolutionary hybrid intelligence is proposed. It is based on the cognitive interoperability of man and machine. An analysis of existing approaches to the construction of cognitive architectures is given. An architecture seamlessly incorporates a human into the loop of intelligent problem solving is considered. The article is organized as follows. The first part contains a critique of data-centric intelligent systems. The reasons why it is impossible to create a strong artificial intelligence based on this type of intelligence are indicated. The second part briefly presents the concept of co-evolutionary hybrid intelligence and shows its advantages. The third part gives an overview and analysis of existing cognitive architectures. It is concluded that many do not consider humans part of the intelligent data processing process. The next part discusses the cognitive architecture for co-evolutionary hybrid intelligence, providing integration with humans. It finishes with general conclusions about the feasibility of developing intelligent systems with humans in the problem-solving loop.

Tracking control has been a vital research topic in robotics. This paper presents a novel hybrid control strategy for an unmanned underwater vehicle (UUV) based on a bioinspired neural dynamics model. An enhanced backstepping kinematic control strategy is first developed to avoid sharp velocity jumps and provides smooth velocity commands relative to conventional methods. Then, a novel sliding mode control is proposed, which is capable of providing smooth and continuous torque commands free from chattering. In comparative studies, the proposed combined hybrid control strategy has ensured control signals smoothness, which is critical in real world applications, especially for an unmanned underwater vehicle that needs to operate in complex underwater environments.

Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is discarded after training, even if it is still useful at test time. Instead, we ensure neural network predictions satisfy the knowledge by refining the predictions with an extra computation step. We introduce differentiable refinement functions that find a corrected prediction close to the original prediction. We study how to effectively and efficiently compute these refinement functions. Using a new algorithm called Iterative Local Refinement (ILR), we combine refinement functions to find refined predictions for logical formulas of any complexity. ILR finds refinements on complex SAT formulas in significantly fewer iterations and frequently finds solutions where gradient descent can not. Finally, ILR produces competitive results in the MNIST addition task.

Road accidents have become the eight leading cause of death all over the world. Lots of these accidents are due to a driver's inattention or lack of focus, due to fatigue. Various factors cause driver's fatigue. This paper considers all the measureable data that manifest driver's fatigue, namely those manifested in the vehicle measureable data while driving as well as the driver's physical and physiological data. Each of the three main factors are further subdivided into smaller details. For example, the vehicle's data is composed of the values obtained from the steering wheel's angle, yaw angle, the position on the lane, and the speed and acceleration of the vehicle while moving. Ontological knowledge and rules for driver fatigue detection are to be integrated into an intelligent system so that on the first sign of dangerous level of fatigue is detected, a warning notification is sent to the driver. This work is intended to contribute to safe road driving.

High utility itemset mining approaches discover hidden patterns from large amounts of temporal data. However, an inescapable problem of high utility itemset mining is that its discovered results hide the quantities of patterns, which causes poor interpretability. The results only reflect the shopping trends of customers, which cannot help decision makers quantify collected information. In linguistic terms, computers use mathematical or programming languages that are precisely formalized, but the language used by humans is always ambiguous. In this paper, we propose a novel one-phase temporal fuzzy utility itemset mining approach called TFUM. It revises temporal fuzzy-lists to maintain less but major information about potential high temporal fuzzy utility itemsets in memory, and then discovers a complete set of real interesting patterns in a short time. In particular, the remaining measure is the first adopted in the temporal fuzzy utility itemset mining domain in this paper. The remaining maximal temporal fuzzy utility is a tighter and stronger upper bound than that of previous studies adopted. Hence, it plays an important role in pruning the search space in TFUM. Finally, we also evaluate the efficiency and effectiveness of TFUM on various datasets. Extensive experimental results indicate that TFUM outperforms the state-of-the-art algorithms in terms of runtime cost, memory usage, and scalability. In addition, experiments prove that the remaining measure can significantly prune unnecessary candidates during mining.

Many ontologies, i.e., Description Logic (DL) knowledge bases, have been developed to provide rich knowledge about various domains. An ontology consists of an ABox, i.e., assertion axioms between two entities or between a concept and an entity, and a TBox, i.e., terminology axioms between two concepts. Neural logical reasoning (NLR) is a fundamental task to explore such knowledge bases, which aims at answering multi-hop queries with logical operations based on distributed representations of queries and answers. While previous NLR methods can give specific entity-level answers, i.e., ABox answers, they are not able to provide descriptive concept-level answers, i.e., TBox answers, where each concept is a description of a set of entities. In other words, previous NLR methods only reason over the ABox of an ontology while ignoring the TBox. In particular, providing TBox answers enables inferring the explanations of each query with descriptive concepts, which make answers comprehensible to users and are of great usefulness in the field of applied ontology. In this work, we formulate the problem of neural logical reasoning across TBox and ABox (TA-NLR), solving which needs to address challenges in incorporating, representing, and operating on concepts. We propose an original solution named TAR for TA-NLR. Firstly, we incorporate description logic based ontological axioms to provide the source of concepts. Then, we represent concepts and queries as fuzzy sets, i.e., sets whose elements have degrees of membership, to bridge concepts and queries with entities. Moreover, we design operators involving concepts on top of fuzzy set representation of concepts and queries for optimization and inference. Extensive experimental results on two real-world datasets demonstrate the effectiveness of TAR for TA-NLR.