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25
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 19 (5 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.
A fully connectionist model generator for covered firstorder logic programs
 Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI07), Hyderabad, India, Menlo Park CA, AAAI Press (2007) 666–671
, 2007
"... We present a fully connectionist system for the learning of firstorder logic programs and the generation of corresponding models: Given a program and a set of training examples, we embed the associated semantic operator into a feedforward network and train the network using the examples. This resu ..."
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Cited by 12 (5 self)
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We present a fully connectionist system for the learning of firstorder logic programs and the generation of corresponding models: Given a program and a set of training examples, we embed the associated semantic operator into a feedforward network and train the network using the examples. This results in the learning of firstorder knowledge while damaged or noisy data is handled gracefully. 1
The core method: Connectionist model generation
 In Proceedings of the 16th International Conference on Artificial Neural Networks (ICANN
, 2006
"... Abstract. Knowledge based artificial networks 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 it is not obvious at all how neural symbol ..."
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Cited by 9 (4 self)
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Abstract. Knowledge based artificial networks 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 it is not obvious at all how neural symbolic systems should look like such that they are truly connectionist and allow for a declarative reading 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. After an introduction to the core method, this paper will focus on possible connectionist representations of structured objects and their use in structuresensitive reasoning tasks. 1
Extracting reduced logic programs from artificial neural networks
 Applied Intelligence
, 2010
"... Artificial neural networks can be trained to perform excellently in many application areas. Whilst they can learn from raw data to solve sophisticated recognition and analysis problems, the acquired knowledge remains hidden within the network architecture and is not readily accessible for analysis o ..."
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Cited by 7 (2 self)
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Artificial neural networks can be trained to perform excellently in many application areas. Whilst they can learn from raw data to solve sophisticated recognition and analysis problems, the acquired knowledge remains hidden within the network architecture and is not readily accessible for analysis or further use: Trained networks are black boxes. Recent research efforts therefore investigate the possibility to extract symbolic knowledge from trained networks, in order to analyze, validate, and reuse the structural insights gained implicitly during the training process. In this paper, we will study how knowledge in form of propositional logic programs can be obtained in such a way that the programs are as simple as possible — where simple is being understood in some clearly defined and meaningful way. 1 1
Unification Neural Networks: Unification by ErrorCorrection Learning
"... We show that the conventional firstorder algorithm of unification can be simulated by finite artificial neural networks with one layer of neurons. In these unification neural networks, the unification algorithm is performed by errorcorrection learning. Each timestep of adaptation of the network c ..."
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Cited by 4 (4 self)
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We show that the conventional firstorder algorithm of unification can be simulated by finite artificial neural networks with one layer of neurons. In these unification neural networks, the unification algorithm is performed by errorcorrection learning. Each timestep of adaptation of the network corresponds to a single iteration of the unification algorithm. We present this result together with the library of learning functions and examples fully formalised in MATLAB Neural Network Toolbox.
Applying category theory to improve the performance of a neural architecture
 Neurocomputing, (Article in
, 2009
"... NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been m ..."
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Cited by 3 (0 self)
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NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. The article is now in press. A recentlydeveloped mathematical semantic theory explains the relationship between knowledge and its representation in connectionist systems. The semantic theory is based upon category theory, the mathematical theory of structure. A product of its explanatory capability is a set of principles to guide the design of future neural architectures and enhancements to existing designs. We claim that this mathematical semantic approach to network design is an effective basis for advancing the state of the art. We offer two experiments to support this claim. One of these involves multispectral imaging using data from a satellite camera.
Neurons or symbols: why does or remain exclusive
 in: Proceedings of ICNC’09
, 2009
"... NeuroSymbolic Integration is an interdisciplinary area that endeavours to unify neural networks and symbolic logic. The goal is to create a system that combines the advantages of neural networks (adaptive behaviour, robustness, tolerance of noise and probability) and symbolic logic (validity of com ..."
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Cited by 3 (3 self)
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NeuroSymbolic Integration is an interdisciplinary area that endeavours to unify neural networks and symbolic logic. The goal is to create a system that combines the advantages of neural networks (adaptive behaviour, robustness, tolerance of noise and probability) and symbolic logic (validity of computations, generality, higherorder reasoning). Several different approaches have been proposed in the past. However, the existing neurosymbolic networks provide only a limited coverage of the techniques used in computational logic. In this paper, we outline the areas of neurosymbolism where computational logic has been implemented so far, and analyse the problematic areas. We show why certain concepts cannot be implemented using the existing neurosymbolic networks, and propose four main improvements needed to build neurosymbolic networks of the future. 1
Neural Networks for State Evaluation in General Game Playing
"... Abstract. Unlike traditional game playing, General Game Playing is concerned with agents capable of playing classes of games. Given the rules of an unknown game, the agent is supposed to play well without human intervention. For this purpose, agent systems that use deterministic game tree search nee ..."
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Abstract. Unlike traditional game playing, General Game Playing is concerned with agents capable of playing classes of games. Given the rules of an unknown game, the agent is supposed to play well without human intervention. For this purpose, agent systems that use deterministic game tree search need to automatically construct a state value function to guide search. Successful systems of this type use evaluation functions derived solely from the game rules, thus neglecting further improvements by experience. In addition, these functions are fixed in their form and do not necessarily capture the game’s real state value function. In this work we present an approach for obtaining evaluation functions on the basis of neural networks that overcomes the aforementioned problems. A network initialization extracted from the game rules ensures reasonable behavior without the need for prior training. Later training, however, can lead to significant improvements in evaluation quality, as our results indicate. 1
Unification by ErrorCorrection
"... The paper formalises the famous algorithm of firstorder unification by Robinson by means of the errorcorrection learning in neural networks. The significant achievement of this formalisation is that, for the first time, the firstorder unification of two arbitrary firstorder atoms is performed b ..."
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Cited by 2 (2 self)
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The paper formalises the famous algorithm of firstorder unification by Robinson by means of the errorcorrection learning in neural networks. The significant achievement of this formalisation is that, for the first time, the firstorder unification of two arbitrary firstorder atoms is performed by finite (twoneuron) network.
Neural Networks for HighResolution State Evaluation in General Game Playing
"... C−IL2P is an algorithm that transforms a propositional domain theory to a neural network that correctly represents the domain theory and is readytouse without prior training. Its original intention was to transform explicit symbolic knowledge into a neural network to allow for learning. The game ..."
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C−IL2P is an algorithm that transforms a propositional domain theory to a neural network that correctly represents the domain theory and is readytouse without prior training. Its original intention was to transform explicit symbolic knowledge into a neural network to allow for learning. The game playing agent system presented in (Michulke and Thielscher 2009) uses the algorithm differently: By transforming the symbolic description of the goal of a game to a neural network it obtains an evaluation function for states of that game. Much like fuzzy logic, the network can be used for graded inference while retaining correctness. But in contrast to fuzzy logic, the network is able to learn and may consequently improve with experience, which is unique among competing agents and arguably an important advantage in a game playing setting. However, since not intended for this use, the transformation algorithm produces networks that cannot correctly represent complex domain theories without losing their ability to distinguish some input vectors that ought to have a different evaluation. In this paper we introduce a generalization of C − IL2P that addresses the above issue. It structures the formerly monolithic approach of logictonetwork transformation to allow for lower weights in the network. This increases the output resolution by several orders of magnitude, as experiments demonstrate, while maintaining correctness. 1