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The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.

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Fractures of the wrist are common in Emergency Departments, where some patients are treated with a procedure called Manipulation under Anaesthesia. In some cases this procedure is unsuccessful and patients need to visit the hospital again where they undergo surgery to treat the fracture. This work describes a geometric semi-automatic image analysis algorithm to analyse and compare the x-rays of healthy controls and patients with dorsally displaced wrist fractures (Colles' fractures) who were treated with Manipulation under Anaesthesia. A series of 161 posterior-anterior radiographs from healthy controls and patients with Colles' fractures were acquired and analysed. The patients' group was further subdivided according to the outcome of the procedure (successful/unsuccessful) and pre- or post-intervention creating five groups in total (healthy, pre-successful, pre-unsuccessful, post-successful, post-unsuccessful). The semi-automatic analysis consisted of manual location of three landmarks (finger, lunate and radial styloid) and automatic processing to generate 32 geometric and texture measurements, which may be related to conditions such as osteoporosis and swelling of the wrist. Statistical differences were found between patients and controls and pre- and post-intervention, but not between the procedures. The most distinct measurements were those of texture. Although the study includes a relatively low number of cases and measurements, the statistical differences are encouraging.

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Abstract-Artificial Neural Networks have previously been applied in neuro-symbolic learning to learn ground logic program rules. However, there are few results of learning relations using neuro-symbolic learning. This paper presents the system PAN, which can learn relations. The inputs to PAN are one or more atoms, representing the conditions of a logic rule, and the output is the conclusion of the rule. The symbolic inputs may include functional terms of arbitrary depth and arity, and the output may include terms constructed from the input functors. Symbolic inputs are encoded as an integer using an invertible encoding function, which is used in reverse to extract the output terms. The main advance of this system is a convention to allow construction of Artificial Neural Networks able to learn rules with the same power of expression as first order definite clauses. The system is tested on three examples and the results are discussed.