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An Overview Of Strategies For Neurosymbolic Integration
, 1995
"... This paper will give an overview of the various approaches to neurosymbolic integration. Roughly, these can be divided into two strategies: unified strategies aim at attaining neural and symbolic capabilities using neural networks alone, while hybrid strategies combine neural networks with symbolic ..."
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Cited by 33 (1 self)
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This paper will give an overview of the various approaches to neurosymbolic integration. Roughly, these can be divided into two strategies: unified strategies aim at attaining neural and symbolic capabilities using neural networks alone, while hybrid strategies combine neural networks with symbolic models such as expert systems, casebased reasoning systems, 2 Chapter 2 and decision trees. These two approaches form the main subtrees of the classification hierarchy depicted in Figure 1. Symbol Proc. Neuronal Unified approach Symbol Proc. hybrids Connectionist Localist Hybrid approach Combined L/D Neurosymbolic integration Functional Chainprocessing Translational Subprocessing hybrids Metaprocessing Distributed Coprocessing Figure 1 Classification of integrated neurosymbolic systems.
Towards a New Massively Parallel Computational Model for Logic Programming
 PROCEEDINGS OF THE ECAI94 WORKSHOP ON COMBINING SYMBOLIC AND CONNECTIONIST PROCESSING, ECCAI
, 1994
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Dimensions of Neuralsymbolic Integration  A Structured Survey
 We Will Show Them: Essays in Honour of Dov Gabbay
, 2005
"... Introduction Research on integrated neuralsymbolic 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 ..."
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Cited by 21 (6 self)
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Introduction Research on integrated neuralsymbolic 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. Already in the pioneering days of computational models of neural cognition, the question was raised how symbolic knowledge can be represented and dealt with within neural networks. The landmark paper [McCulloch and Pitts, 1943] provides fundamental insights how propositional logic can be processed using simple artificial neural networks. Within the following decades, however, the topic did not receive much attention as research in arti
Fibring Neural Networks
, 2004
"... Neuralsymbolic systems are hybrid systems that integrate symbolic logic and neural networks. The goal of neuralsymbolic integration is to benefit from the combination of features of the symbolic and connectionist paradigms of artificial intelligence. This paper introduces a new neural network ..."
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Cited by 18 (6 self)
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Neuralsymbolic systems are hybrid systems that integrate symbolic logic and neural networks. The goal of neuralsymbolic integration is to benefit from the combination of features of the symbolic and connectionist paradigms of artificial intelligence. This paper introduces a new neural network architecture based on the idea of fibring logical systems. Fibring allows one to combine di#erent logical systems in a principled way. Fibred neural networks may be composed not only of interconnected neurons but also of other networks, forming a recursive architecture. A fibring function then defines how this recursive architecture must behave by defining how the networks in the ensemble relate to each other, typically by allowing the activation of neurons in one network (A) to influence the change of weights in another network (B). Intuitively, this can be seen as training network B at the same time that one runs network A. We show that, in addition to being universal approximators like standard feedforward networks, fibred neural networks can approximate any polynomial function to any desired degree of accuracy, thus being more expressive than standard feedforward networks.
Logic Programs, Iterated Function Systems, and Recurrent Radial Basis Function Networks
 Journal of Applied Logic
, 2004
"... Graphs of the singlestep operator for firstorder logic programs  displayed in the real plane  exhibit selfsimilar structures known from topological dynamics, i.e. they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be ..."
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Cited by 15 (11 self)
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Graphs of the singlestep operator for firstorder logic programs  displayed in the real plane  exhibit selfsimilar structures known from topological dynamics, i.e. they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which approximate logic programs in the presence of function symbols.
The integration of connectionism and firstorder knowledge representation and reasoning as a challenge for artificial intelligence
 In Proceedings of the Third International Conference on Information
, 2006
"... Intelligent systems based on firstorder 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 ..."
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Cited by 11 (7 self)
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Intelligent systems based on firstorder 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 stateoftheart 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 neuralsymbolic systems. 1
On the Adequateness of the Connection Method
 In Proceedings of the AAAI National Conference on Artificial Intelligence
, 1993
"... Roughly speaking, adequatness is the property of a theorem proving method to solve simpler problems faster than more difficult ones. Automated inferencing methods are often not adequate as they require thousands of steps to solve problems which humans solve effortlessly, spontaneously, and with rema ..."
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Cited by 10 (6 self)
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Roughly speaking, adequatness is the property of a theorem proving method to solve simpler problems faster than more difficult ones. Automated inferencing methods are often not adequate as they require thousands of steps to solve problems which humans solve effortlessly, spontaneously, and with remarkable efficiency. L. Shastri and V. Ajjanagadde  who call this gap the artificial intelligence paradox  suggest that their connectionist inference system is a first step toward bridging this gap. In this paper we show that their inference method is equivalent to reasoning by reductions in the wellknown connection method. In particular, we extend a reduction technique called evaluation of isolated connections such that this technique  together with other reduction techniques  solves all problems which can be solved by Shastri and Ajjanagadde's system under the same parallel time and space requirements. Consequently, we obtain a semantics for Shastri and Ajjanagadde's logic. But,...
Connectionist Model generation: A FirstOrder Approach
, 2007
"... Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes as expressed e.g., by means of firstorder predicate log ..."
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Cited by 8 (2 self)
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Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes as expressed e.g., by means of firstorder predicate logic, it is not obvious at all what neural symbolic systems would look like such that they are truly connectionist, are able to learn, and allow for a declarative reading and logical reasoning at the same time. The core method aims at such an integration. It is a method for connectionist model generation using recurrent networks with feedforward core. We show in this paper how the core method can be used to learn firstorder logic programs in a connectionist fashion, such that the trained network is able to do reasoning over the acquired knowledge. We also report on experimental evaluations which show the feasibility of our approach.
An Extension of the Temporal Synchrony Approach To Dynamic Variable Binding in a Connectionist Inference System
, 1995
"... The relationship between symbolism 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. A major open question in this field is the extent to which ..."
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Cited by 7 (0 self)
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The relationship between symbolism 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. A major open question in this field is the extent to which a connectionist architecture can accommodate basic concepts of symbolic inference, such as a dynamic variable binding mechanism and a rule and fact encoding mechanism involving nary predicates. One of the current leaders in this area is the connectionist rulebased system proposed by Shastri and Ajjanagadde. We demonstrate that the mechanism for variable binding which they advocate is fundamentally limited and show how a reinterpretation of the primitive components and corresponding modifications of their system can extend the range of inference which can be supported. Our extension hinges on the basic structural modification of the network components and further modifications of the rule a...
Challenge problems for the integration of logic and connectionist systems (Extended Abstract)
, 1999
"... ) Steen Holldobler Articial Intelligence Institute Department of Computer Science Dresden University of Technology D{01062 Dresden Phone: +493514638340 Fax: +493514638342 sh@inf.tudresden.de Keywords: Logic Programming, Recurrent Connectionist Networks 1 1 Motivation Connectionis ..."
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Cited by 7 (0 self)
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) Steen Holldobler Articial Intelligence Institute Department of Computer Science Dresden University of Technology D{01062 Dresden Phone: +493514638340 Fax: +493514638342 sh@inf.tudresden.de Keywords: Logic Programming, Recurrent Connectionist Networks 1 1 Motivation Connectionist systems exhibit many desirable properties of intelligent systems like, for example, being massively parallel, context{sensitive, adaptable and robust (see eg. [7]). It is strongly believed that intelligent systems must also be able to represent and reason about structured objects and structure{sensitive processes (see eg. [8, 23]). Unfortunately, we are unaware of any connectionist system which can handle structured objects and structure{sensitive processes in a satisfying way. Logic systems were designed to cope with such objects and processes and, consequently, it is a long{standing research goal to combine the advantages of connectionist and logic systems in a single system. There ha...