First-order logic learning in artificial neural networks

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

Learning to Act with RVRL Agents

The use of reinforcement learning to guide action selection of cognitive agents has been shown to be a powerful technique for stochastic environments. Standard Reinforcement learning techniques used to provide decision theoretic policies rely, however, on explicit state-based computations of value for each state-action pair. This requires the computation of a number of values exponential to the number of state variables and actions in the system. This research extends existing work with an acquired probabilistic rule representation of an agent environment by developing an algorithm to apply reinforcement learning to values attached to the rules themselves. Structure captured by the rules is then used to learn a policy directly. The resulting value attached to each rule represents the utility of taking an action if the conditions of the rule are present in the agent’s current set of percepts. This has several advantages for planning purposes: generalization over many states and over unseen states; effective decisions can therefore be made with less training data than state based modelling systems (e.g. Dyna Q-Learning); and the problem of computation in an exponential state-action space is alleviated. The results of application of this algorithm to rules in a specific environment are presented, with comparison to standard reinforcement learning policies developed from related work

Symbolic knowledge extraction from trained neural networks: A sound approach

Although neural networks have shown very good performance in many application domains, one of their main drawbacks lies in the incapacity to provide an explanation for the underlying reasoning mechanisms. The “explanation capability” of neural networks can be achieved by the extraction of symbolic knowledge. In this paper, we present a new method of extraction that captures nonmonotonic rules encoded in the network, and prove that such a method is sound. We start by discussing some of the main problems of knowledge extraction methods. We then discuss how these problems may be ameliorated. To this end, a partial ordering on the set of input vectors of a network is defined, as well as a number of pruning and simplification rules. The pruning rules are then used to reduce the search space of the extraction algorithm during a pedagogical extraction, whereas the simplification rules are used to reduce the size of the extracted set of rules. We show that, in the case of regular networks, the extraction algorithm is sound and complete. We proceed to extend the extraction algorithm to the class of non-regular networks, the general case. We show that non-regular networks always contain regularities in their subnetworks. As a result, the underlying extraction method for regular networks can be applied, but now in a decompositional fashion. In order to combine the sets of rules extracted from each subnetwork into the final set of rules, we use a method whereby we are able to keep the soundness of the extraction algorithm. Finally, we present the results of an empirical analysis of the extraction system, using traditional examples and real-world application problems. The results have shown that a very high fidelity between the extracted set of rules and the network can be achieved

Geometric semi-automatic analysis of radiographs of Colles’ fractures

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 revisit the hospital 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, as well as between 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

Reasoning in non-probabilistic uncertainty: logic programming and neural-symbolic computing as examples

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means); and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: Logic Programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of Input/Output logic for dealing with uncertainty in dynamic normative context

Zika virus impairs the development of blood vessels in a mouse model of congenital infection

Zika virus (ZIKV) is associated with brain development abnormalities such as primary microcephaly, a severe reduction in brain growth. Here we demonstrated in vivo the impact of congenital ZIKV infection in blood vessel development, a crucial step in organogenesis. ZIKV was injected intravenously in the pregnant type 2 interferon (IFN)-deficient mouse at embryonic day (E) 12.5. The embryos were collected at E15.5 and postnatal day (P)2. Immunohistochemistry for cortical progenitors and neuronal markers at E15.5 showed the reduction of both populations as a result of ZIKV infection. Using confocal 3D imaging, we found that ZIKV infected brain sections displayed a reduction in the vasculature density and vessel branching compared to mocks at E15.5; altogether, cortical vessels presented a comparatively immature pattern in the infected tissue. These impaired vascular patterns were also apparent in the placenta and retina. Moreover, proteomic analysis has shown that angiogenesis proteins are deregulated in the infected brains compared to controls. At P2, the cortical size and brain weight were reduced in comparison to mock-infected animals. In sum, our results indicate that ZIKV impairs angiogenesis in addition to neurogenesis during development. The vasculature defects represent a limitation for general brain growth but also could regulate neurogenesis directly

Neural-Symbolic Learning and Reasoning: Contributions and Challenges

The goal of neural-symbolic computation is to integrate robust connectionist learning and sound symbolic reasoning. With the recent advances in connectionist learning, in particular deep neural networks, forms of representation learning have emerged. However, such representations have not become useful for reasoning. Results from neural-symbolic computation have shown to offer powerful alternatives for knowledge representation, learning and reasoning in neural computation. This paper recalls the main contributions and discusses key challenges for neural-symbolic integration which have been identified at a recent Dagstuhl seminar