The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way that the strengths of either paradigm will be retained. Current state-of-the-art research, however, fails by far to achieve this ultimate goal. As one of the main obstacles to be overcome we perceive the question how symbolic knowledge can be encoded by means of connectionist systems: Satisfactory answers to this will naturally lead the way to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page

Dimensions of Neural-symbolic Integration - A Structured Survey

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 neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. We present a comprehensive survey of the field of neural-symbolic integration, including a new classification of system according to their architectures and abilities.Comment: 28 page

A connectionist representation of first-order formulae with dynamic variable binding

The relationship between symbolicism and connectionism has been one of the major issues in recent Artificial Intelligence research. An increasing number of researchers from each side have tried to adopt desirable characteristics of the other. These efforts have produced a number of different strategies for interfacing connectionist and sym¬ bolic AI. One of them is connectionist symbol processing which attempts to replicate symbol processing functionalities using connectionist components.In this direction, this thesis develops a connectionist inference architecture which per¬ forms standard symbolic inference on a subclass of first-order predicate calculus. Our primary interest is in understanding how formulas which are described in a limited form of first-order predicate calculus may be implemented using a connectionist archi¬ tecture. Our chosen knowledge representation scheme is a subset of first-order Horn clause expressions which is a set of universally quantified expressions in first-order predicate calculus. As a focus of attention we are developing techniques for compiling first-order Horn clause expressions into a connectionist network. This offers practical benefits but also forces limitations on the scope of the compiled system, since we tire, in fact, merging an interpreter into the connectionist networks. The compilation process has to take into account not only first-order Horn clause expressions themselves but also the strategy which we intend to use for drawing inferences from them. Thus, this thesis explores the extent to which this type of a translation can build a connectionist inference model to accommodate desired symbolic inference.This work first involves constructing efficient connectionist mechanisms to represent basic symbol components, dynamic bindings, basic symbolic inference procedures, and devising a set of algorithms which automatically translates input descriptions to neural networks using the above connectionist mechanisms. These connectionist mechanisms are built by taking an existing temporal synchrony mechanism and extending it further to obtain desirable features to represent and manipulate basic symbol structures. The existing synchrony mechanism represents dynamic bindings very efficiently using tem¬ poral synchronous activity between neuron elements but it has fundamental limitations in supporting standard symbolic inference. The extension addresses these limitations.The ability of the connectionist inference model was tested using various types of first order Horn clause expressions. The results showed that the proposed connectionist in¬ ference model was able to encode significant sets of first order Horn clause expressions and replicated basic symbolic styles of inference in a connectionist manner. The system successfully demonstrated not only forward chaining but also backward chaining over the networks encoding the input expressions. The results, however, also showed that implementing a connectionist mechanism for full unification among groups of unifying arguments in rules, are encoding some types of rules, is difficult to achieve in a con¬ nectionist manner needs additional mechanisms. In addition, some difficult issues such as encoding rules having recursive definitions remained untouched

End-to-End Differentiable Proving

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.Comment: NIPS 2017 camera-ready, NIPS 201

Connectionist Inference Models

The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule-based reasoning, and whether they involve distributed or localist representations. The benefits and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used for cognitive modeling

Holistic processing of hierarchical structures in connectionist networks

Despite the success of connectionist systems to model some aspects of cognition, critics argue that the lack of symbol processing makes them inadequate for modelling high-level cognitive tasks which require the representation and processing of hierarchical structures. In this thesis we investigate four mechanisms for encoding hierarchical structures in distributed representations that are suitable for processing in connectionist systems: Tensor Product Representation, Recursive Auto-Associative Memory (RAAM), Holographic Reduced Representation (HRR), and Binary Spatter Code (BSC). In these four schemes representations of hierarchical structures are either learned in a connectionist network or constructed by means of various mathematical operations from binary or real-value vectors.It is argued that the resulting representations carry structural information without being themselves syntactically structured. The structural information about a represented object is encoded in the position of its representation in a high-dimensional representational space. We use Principal Component Analysis and constructivist networks to show that well-separated clusters consisting of representations for structurally similar hierarchical objects are formed in the representational spaces of RAAMs and HRRs. The spatial structure of HRRs and RAAM representations supports the holistic yet structure-sensitive processing of them. Holistic operations on RAAM representations can be learned by backpropagation networks. However, holistic operators over HRRs, Tensor Products, and BSCs have to be constructed by hand, which is not a desirable situation. We propose two new algorithms for learning holistic transformations of HRRs from examples. These algorithms are able to generalise the acquired knowledge to hierarchical objects of higher complexity than the training examples. Such generalisations exhibit systematicity of a degree which, to our best knowledge, has not yet been achieved by any other comparable learning method.Finally, we outline how a number of holistic transformations can be learned in parallel and applied to representations of structurally different objects. The ability to distinguish and perform a number of different structure-sensitive operations is one step towards a connectionist architecture that is capable of modelling complex high-level cognitive tasks such as natural language processing and logical inference

Faith in the Algorithm, Part 1: Beyond the Turing Test

Since the Turing test was first proposed by Alan Turing in 1950, the primary goal of artificial intelligence has been predicated on the ability for computers to imitate human behavior. However, the majority of uses for the computer can be said to fall outside the domain of human abilities and it is exactly outside of this domain where computers have demonstrated their greatest contribution to intelligence. Another goal for artificial intelligence is one that is not predicated on human mimicry, but instead, on human amplification. This article surveys various systems that contribute to the advancement of human and social intelligence