Jürgen Hollatz

Analogy making in legal reasoning with neural networks and fuzzy logic

Analogy making from examples is a central task in intelligent system behavior. A lot of real world problems involve analogy making and generalization. Research investigates these questions by building computer models of human thinking concepts. These concepts can be divided into high level approaches as used in cognitive science and low level models as used in neural networks. Applications range over the spectrum of recognition, categorization and analogy reasoning. A major part of legal reasoning could be formally interpreted as an analogy making process. Because it is not the same as reasoning in mathematics or the physical sciences, it is necessary to use a method, which incorporates first the ability to specify likelihood and second the opportunity of including known court decisions. We use for modelling the analogy making process in legal reasoning neural networks and fuzzy systems. In the first part of the paper a neural network is described to identify precedents of immaterial damages. The second application presents a fuzzy system for determining the required waiting period after traffic accidents. Both examples demonstrate how to model reasoning in legal applications analogous to recent decisions: first, by learning a system with court decisions, and second, by analyzing, modelling and testing the decision making with a fuzzy system.

Representing Probabilistic Rules with Networks of GaussianBasis Functions

There is great interest in understanding the intrinsic knowledge neural networks have acquired during training. Most work in this direction is focussed on the multi-layer perceptron architecture. The topic of this paper is networks of Gaussian basis functions which are used extensively as learning systems in neural computation. We show that networks of Gaussian basis functions can be generated from simple probabilistic rules. Also, if appropriate learning rules are used, probabilistic rules can be extracted from trained networks. We present methods for the reduction of network complexity with the goal of obtaining concise and meaningful rules. We show how prior knowledge can be refined or supplemented using data by employing either a Bayesian approach, by a weighted combination of knowledge bases, or by generating artificial training data representing the prior knowledge. We validate our approach using a standard statistical data set.

Modelling and optimisation of a refining process for fibre board production

Abstract For many processes in the pulp and paper industry there exist no reliable analytical models, but qualitative linguistic expert knowledge and data from on-line and laboratory measurements. Knowledge about the wood chip refiner in fibre board production is used to formulate the if-parts of Takagi–Sugeno fuzzy rules. Laboratory and on-line data are then used to fit the then-parts of these rules. The rule-based model serves as a soft sensor that enables the operators to manually control and optimise this process. An optimisation module based on sequential quadratic programming and/or simulated annealing automates this process. All modules are integrated in the commercial Siemens tool WinCC.

The `detailed balance' net: a stable asymmetric artificial neural system for unsupervised learning

A dynamically stable artificial neural network with graded-response neurons employing an unsupervised learning rule for connection weights of restricted asymmetry is investigated. In particular, the quality of performance of the network after fixing the constants entering the model (passive decay constants, forgetting constants, asymmetry factors, and the steepness of the signal function) is discussed. Subsequent to an estimation of the passive decay and forgetting constants, based on the stationary solutions of the differential equations describing the dynamics of the net, and of the asymmetry factors, the constants are quantified further by optimizing the recognition rate in a computer simulation for a specific model problem in the highly nonlinear (high-gain) limit. Working in the high-gain limit is justified from the behavior of the storage capacity of the net as a function of the steepness of the signal function. First results for applications to a real-world problem (work-piece recognition) indicate that the numerical values obtained for the constants are independent of net size

Integrating Rule-Based Knowledge into Neural Computing

We demonstrate how certain forms of rule-based knowledge can be used to prestructure a network prior to training. Through prestructuring, the initial performance of the network is improved and reaching satisfactory performance requires less training time and fewer training exemplars. Also, in cases where not enough data is available, especially in networks with a high-dimensional input space, prior knowledge can be used to constrain the degrees of freedom. After training the network, the altered rules can be extracted and interpreted. We demonstrate the viability of this approach on two examples: training a network to control a bicycle and a legal application.