Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neu-ral networks) has reached a critical mass which enables the community to

Bridging the gap between symbolic and subsymbolic representations is a – perhaps the – key obstacle along the path from the present state of AI achievement to human-level artificial general intelligence. One approach to bridging this gap is hybridization – for instance, incorporation of a subsymbolic system and a symbolic system into a integrative cognitive architecture. Here we present a detailed design for an implementation of this approach, via integrating a version of the DeSTIN deep learning system into OpenCog, an integrative cognitive architecture including rich symbolic capabilities. This is a ”tight” integration, in which the symbolic and subsymbolic aspects exert detailed real-time influence on each others ’ operations. Part I of this paper has described in detail the revisions to DeSTIN needed to support this integration, which are mainly along the lines of making it more ”representationally transparent, ” so that its internal states are easier for OpenCog to understand. We describe an extension of the approach beyond vision to include multi-sensory integration, and perception-action integration. We discuss the potential use of this integrated system to control mobile robots, as exemplified via a thought-experiment involving eye-hand coordination. 1

Abstract—Artificial Neural Networks have previously been applied in neuro-symbolic learning to learn ground logic pro-gram 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. I.

In real-world applications, the effective integration of learning and reasoning in a cognitive agent model is a difficult task. However, such integration may lead to a better understanding, use and construction of more realistic models. Unfortunately, existing models are either oversimplified or require much processing time, which is unsuitable for online learning and reasoning. Currently, controlled environments like training simulators do not effectively integrate learning and reasoning. In particular, higher-order concepts and cognitive abilities have many unknown temporal relations with the data, making it impossible to represent such relationships by hand. We introduce a novel cognitive agent model and architecture for online learning and reasoning that seeks to effectively represent, learn and reason in complex training environments. The agent architecture of the model combines neural learning with symbolic knowledge representation. It is capable of learning new hypotheses from observed data, and infer new beliefs based on these hypotheses. Furthermore, it deals with uncertainty and errors in the data using a Bayesian inference model. The validation of the model on real-time simulations and the results presented here indicate the promise of the approach when performing online learning and reasoning in real-world scenarios, with possible applications in a range of areas.

Methods that use latent representations of data, such as matrix and tensor factorization or deep neural methods, are becoming increasingly popular for applications such as knowledge base population and recommendation systems. These approaches have been shown to be very robust and scalable but, in con-trast to more symbolic approaches, lack interpretability. This makes debugging such models difficult, and might result in users not trusting the predictions of such systems. To over-come this issue we propose to extract an interpretable proxy model from a predictive latent variable model. We use a so-called pedagogical method, where we query our predictive model to obtain observations needed for learning a descrip-tive model. We describe two families of (presumably more) descriptive models, simple logic rules and Bayesian networks, and show how members of these families provide descriptive representations of matrix factorization models. Preliminary experiments on knowledge extraction from text indicate that even though Bayesian networks may be more faithful to a matrix factorization model than the logic rules, the latter are possibly more useful for interpretation and debugging. 1

The goal of neural-symbolic computation is to integrate ro-bust connectionist learning and sound symbolic reasoning. With the recent advances in connectionist learning, in par-ticular deep neural networks, forms of representation learn-ing 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. 1.

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