Rules and precedentes in legal reasoning

• Autore: Jürgen Hollatz
• Carica: Siemens AG, ZFE ST SN 41, Corporate Research and Development
• Pagine: 75-83

Page 75

@1. Introduction

If we learn a new skill such as driving a car or riding a bicycle, it would be disastrous to start without prior knowledge about the problem. Typically, we are told some basic rules, which we try to follow in the beginning, but which are then refined and altered through experience. The better our initial knowledge about a problem, the faster we can achieve good performance and the less training is required. It is highly desirable to exploit similar ideas when training a neural network. If prior knowledge can be used to pre-structure a neural network, 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 are available, especially in networks with a high-dimensional input space, prior knowledge can be used to constrain the degrees of freedom. This technique could be used in the area of legal reasoning by analogy. A couple of prototypical court decisions are available as well as a few rules defined by an expert. For judging a new case, a jurist would compare the new facts with precedents or decide how far a new case fits under a rule. In addition, the algorithm provides a tool to extract the structure of the precedent decisions. If the network learns only the behavior of prototypical decisions, the extracted rules provide a symbolic formulation of the reasoning process.

In this paper we consider prior knowledge which can be formulated in terms of uncertain domain-specific rules, The parameter values of the premises of these rules are weighted by membership functions. As inference mechanism, we use the normalized weighted sum of the outputs of all rales. The output of the network minimizes the expected error and can bePage 76 shown to be the optimal response In the framework of Bayes decision theory [HT].

The rule-based Inference system can be Implemented In form of a neural network of normalized basis functions, and training data can be employed to Improve and refine network performance. After training the altered rules can be extracted and interpreted. Introducing new basis functions (growing network architecture) corresponds to the generation of new rules, and merging of basis functions corresponds to joining local rules to form more global rules (generalization).

Neural networks have sometimes been criticized because features which are typically available in rule-based expert systems such as programmability, conceptual capabilities and structured schemes of knowledge are missing. To get insight Into working of Intelligent processes Is in general an important task of cognitive science. It is a fundamental contribution of neural networks that it explains how the knowledge may be distributed across the system in the connection weights, but this fact means that it is hard to cget the knowledge out' in order specify what has been learned. It is of little use to say that the system has learned something, if the only possible specification of this knowledge is a huge table of numbers. Thus, what is required is some way of 'decompiling' the distributed knowledge. Our approach demonstrates how symbolic and subsymbolic knowledge can be combined. It allows rule-based integrated learning, rule insertion, theory refinement and rule extraction.

In this contribution, a technique of including rule-based prior knowledge to structure the network is described as well as a technique to extract symbolic information. The organization of the paper Is as follows. The neural network Is Introduced in section 2. In the same section, the similarities to a rule-based system are discussed. In the third part of the paper, the practicability is demonstrated using an application in legal reasoning.

@2. Neural Network and Rules

In the following the neural network and its mathematical description is given. For a more detailed description of neural networks see [HKP], for example. We consider networks that describe a mapping from an input space x (euros) Rn (the facts of the case in legal reasoning) to an output space y (euros) R (the final decision). In the widest sense, we consider a rule...