This chapter provides an introduction to the field of hybrid neural systems. Hybrid neural systems are computational systems which are based mainly on artificial neural networks but also allow a symbolic interpretation, or interaction with symbolic components. In this overview, we will describe recent results of hybrid neural systems. We will give a brief overview of the main methods used, outline the work that is presented here, and provide additional references. We will also highlight some important general issues and trends.

This paper describes techniques for integrating neural networks and symbolic components into powerful hybrid systems. Neural networks have unique processing characteristics that enable tasks to be performed that would be di cult or intractable for a symbolic rule-based system. However, a stand-alone neural network requires an interpretation either by ahuman or a rulebased system. This motivates the integration of neural/symbolic techniques within a hybrid system. Anumber of integration possibilities exist: some systems consist of neural network components performing symbolic tasks while other systems are composed of several neural networks and symbolic components, each component acting as a self-contained module communicating with the others. Other hybrid systems are able to transform subsymbolic representations into symbolic ones and vice-versa. This paper providesanoverview and evaluation of the state of the artofseveral hybrid neural systems for rule-based processing. 1

This paper describes preference classes and preference Moore machines as a basis for integrating different hybrid neural representations. Preference classes are shown to pro- vide a basic link between neural preferences and fuzzy representations at the preference class level. Preference Moore machines provide a link between recurrent neural networks and symbolic transducers at the preference Moore machine level. We demonstrate how the concepts of preference classes and preference Moore machines can be used to interpret neural network representations and to integrate knowledge from hybrid neural represen- tations. One main contribution of this paper is the introduction and analysis of neural preference Moore machines and their link to a fuzzy interpretation. Furthermore, we il- lustrate the interpretation and combination of various neural preference Moore machines with additional real world examples.

Introduction In practice, a doctor-diagnostician applies the diagnostic rules that consist of subjective and objective features (called as symptoms) to accurately distinguish one disease ore state of the patient from others. Subjective features that reflect the complaints, the anamnesis, and the inquiry results of the patient have fuzzy, unquantitable evaluations. In contrast, objective features are the results of laboratory and tool researches that can be represented in quantitative, interval or nominal forms. A doctor interested in that confidence of diagnostic rules would be maximal. Diagnostic rules should be not only accurate but also understandable for a doctor, which wish to know how these rules work and why their usage brings the best decisions [1, 11]. For extraction and validation of diagnostic rules, a doctor must beforehand collect a representative data set involving the observations of the symptoms that occur in similar clinical cases. In practice, the data set is usuall

Neural network based agents were trained on incomplete sets of classified instances that experienced doctors could suggest. Trained neural networks correctly classified the presented examples. A user does not give additional instructions to train the neural network based agents. The algorithm of selforganization is capable for define minimal number of features, as well as the number of neurons and layers in the trained neural networks. Trained neural networks were adequately represented in symbolic form that is easy to understanding. One simple form is similar to a syndrome-complex that the doctors use typically. Other is the set of logical formulas that can be easily tabulated and interpreted to be useful for diagnostic goals. The decision rules provide the evaluations of their confidence in which interested a doctor. The conducted clinical verification has shown that most decisions that symbolic rules that were discovered in databases have coincided with the doctor's conclusions.

d would be able first to extract the relevant regularities from web documents used to train a simple recurrent network and second to interpret these regularities in an easy-to-understand form. Extracted models of regularities have to be accuracy and involve the most significant features used to describe text documents. Highest accuracy would be achieved when, first, neural network complexity evaluated by number its units and their synaptic links has been optimal, and second, a user has not configured the neural network (i.e., neither connection interconnection, nor the number of units and layers, nor memory order). To be represented in the human-understand form, the extracted models have to be interpreted as a concise set of the symbolic rules. Such the rules can be generated in case if the different levels of abstractions would be used to represent the knowledge extracted from documents. The goal of project is achieved by applying the self-organizing neural networks to extract the

high accuracy of neural network, a subjective user's knowledge that a priori is used has not been used to configure the neural network. A user can not define on intuitive base the number of units and layers of neural network, as well as configuration of its synaptic links. For representing knowledge in human-understand form, the extracted models have to be interpreted as a concise set of the symbolic rules, for example, in syndrome form. To represent the rules in simple form, the set of logical formulas from two arguments would be used. The goal of project is achieved by using the self-organizing neural networks to extract knowledge from classified data and represent the trained network as set of symbolic rules. Self-organizing neural networks are able to select most significant features and learn most plausible regularities. Algorithms of self-organization first generate all the possible combinations of links in candidate-network, and second test their fidelity on the data set. Fide

to extract the relevant regularities from web documents used to train a simple recurrent network and second to interpret these regularities in an easy-tounderstand form. Extracted models of regularities have to be accuracy and involve the most significant features used to describe text documents. Highest accuracy would be achieved when, first, neural network complexity evaluated by number its units and their synaptic links has been optimal, and second, a user has not configured the neural network (i.e., neither connection interconnection, nor the number of units and layers, nor memory order). To be represented in the human-understand form, the extracted models have to be interpreted as a concise set of the symbolic rules. Such the rules can be generated in case if the different levels of abstractions would be used to represent the knowledge extracted from documents. The goal of project is achieved by applying the self-organizing neural networks to extract the knowledge from web docu

Introduction In practice, a doctor-diagnostician applies the diagnostic rules that consist of subjective and objective features (called as symptoms) to accurately distinguish one disease ore state of the patient from others. Subjective features that reflect the complaints, the anamnesis, and the inquiry results of the patient have fuzzy, unquantitable evaluations. In contrast, objective features are the results of laboratory and tool researches that can be represented in quantitative, interval or nominal forms. A doctor interested in that confidence of diagnostic rules would be maximal. Diagnostic rules should be not only accurate but also understandable for a doctor, which wish to know how these rules work and why their usage brings the best decisions [1, 11]. For extraction and validation of diagnostic rules, a doctor must beforehand collect a representative data set involving the observations of the symptoms that occur in similar clinical cases. In practice, the data set is usuall

The background image shown on the cover is a 43-neighbor dihedral tiling discovered by Berend Jan van der Zwaag; this is a tiling of the plane using two different tiles, where each tile has exactly 43 neighboring tiles [E. Friedman and B.J. van der Zwaag (2002), “Constant neighbor dihedral tilings with 15, 32, and 43 neighbors,” Geombinatorics, vol. XI, no. 3 (Jan.), pp. 74-77]. The illustration on the front cover was drawn by Irene van der Zwaag-Tong, who also made the drawing of a biological neuron shown on page 8. Zwaag, Berend Jan van der Using domain-specific basic functions for the analysis of supervised artificial neural networks (Nederlandse titel: Domeinafhankelijke basisfuncties voor de analyse van gesuperviseerde kunstmatige neurale netwerken)