A theory of legal reasoning and a logic to match

This paper describes a model of legal reasoning and a logic for reasoning with rules, principles and goals that is especially suited to this model of legal reasoning. The paper consists of three parts. The first part describes a model of legal reasoning based on a two-layered view of the law. The first layer consists of principles and goals that express fundamental ideas of a legal system. The second layer contains legal rules which in a sense summarise the outcome of the interaction of the principles and goals for a number of case types. Both principles, goals and rules can be used in legal arguments, but their logical roles are different. One characteristic of the model of legal reasoning described in the first part of the paper is that it takes these logical differences into account. Another characteristic is that it pays serious attention to the phenomena of reasoning about the validity and acceptance of rules, respectively principles and goals, and about the application of legal rules, and the implications of these arguments for the use of rules, principles and goals in deriving legal conclusions for concrete cases.The second part of the paper first describes a logic (Reason-Based Logic) that is especially suited to deal with legal arguments as described in terms of the previously discussed model. The facilities of the logic are illustrated by means of examples that correspond to the several aspects of the model.The third part of the paper deals with a number of logico-philosophical reflections on Reason-Based Logic. The occasion is also used to compare these presuppositions with theories of defeasible reasoning based on the comparison of arguments.The ideas developed in this paper are based on the draft of my book Reasoning with rules which will be published by Kluwer Academic Publishers in the Law and Philosophy Series. The book offers not only more elaborate and sometimes different treatments of the topics of this paper, but also pays more attention to the philosophical background of this work.     

Argument in Artificial Intelligence and Law

In this paper I shall discuss the notion of argument, and the importanceof argument in AI and Law. I shall distinguish four areas where argument hasbeen applied: in modelling legal reasoning based on cases; in thepresentation and explanation of results from a rule based legal informationsystem; in the resolution of normative conflict and problems ofnon-monotonicity; and as a basis for dialogue games to support the modellingof the process of argument. The study of argument is held to offer prospectsof real progress in the field of AI and law, and the purpose of this paperis to provide an overview of work, and the connection between the various strands.     

The IKBALS project: Multi-modal reasoning in legal knowledge based systems

In attempting to build intelligent litigation support tools, we have moved beyond first generation, production rule legal expert systems. Our work integrates rule based and case based reasoning with intelligent information retrieval.When using the case based reasoning methodology, or in our case the specialisation of case based retrieval, we need to be aware of how to retrieve relevant experience. Our research, in the legal domain, specifies an approach to the retrieval problem which relies heavily on an extended object oriented/rule based system architecture that is supplemented with causal background information. We use a distributed agent architecture to help support the reasoning process of lawyers.Our approach to integrating rule based reasoning, case based reasoning and case based retrieval is contrasted to the CABARET and PROLEXS architectures which rely on a centralised blackboard architecture. We discuss in detail how our various cooperating agents interact, and provide examples of the system at work. The IKBALS system uses a specialised induction algorithm to induce rules from cases. These rules are then used as indices during the case based retrieval process.Because we aim to build legal support tools which can be modified to suit various domains rather than single purpose legal expert systems, we focus on principles behind developing legal knowledge based systems. The original domain chosen was theAccident Compensation Act 1989 (Victoria, Australia), which relates to the provision of benefits for employees injured at work. For various reasons, which are indicated in the paper, we changed our domain to that ofCredit Act 1984 (Victoria, Australia). This Act regulates the provision of loans by financial institutions.The rule based part of our system which provides advice on the Credit Act has been commercially developed in conjunction with a legal firm. We indicate how this work has lead to the development of a methodology for constructing rule based legal knowledge based systems. We explain the process of integrating this existing commercial rule based system with the case base reasoning and retrieval architecture.     

基于冲突强度和非正则化的证据合成方法研究

证据推理广泛应用于不确定推理和数据融合等许多方面,但D-S合成规则对于高冲突证据的处理不是十分合理的。论文在分析D-S合成规则以及一些改进方法的基础上,提出了一种基于冲突强度和非正则化的冲突证据合成规则,并引入确定度的概念来衡量合成的效果。仿真实验结果表明,该规则比D-S合成规则有了明显的改进。     

An Integrated View on Rules and Principles

In the law, it is generally acknowledged that there are intuitive differences between reasoning with rules and reasoning with principles. For instance, a rule seems to lead directly to its conclusion if its condition is satisfied, while a principle seems to lead merely to a reason for its conclusion. However, the implications of these intuitive differences for the logical status of rules and principles remain controversial.A radical opinion has been put forward by Dworkin (1978). The intuitive differences led him to argue for a strict logical distinction between rules and principles. Ever since, there has been a controversy whether the intuitive differences between rules and principles require a strict logical distinction between the two. For instance, Soeteman (1991) disagrees with Dworkin's opinion, and argues that rules and principles cannot be strictly distinguished, and do not have a different logical structure.In this paper, we claim that the differences between rules and principles are merely a matter of degree. We give an integrated view on rules and principles in which rules and principles have the same logical structure, but different behavior in reasoning. In this view, both rules and principles are considered to consist of a condition and a conclusion. The observed differences between rules and principles are, in our view, the result of different types of relations that they have with other rules and principles. In the integrated view, typical rules and typical principles are the extremes of a spectrum.We support our claim by giving an explicit formalization of our integrated view using the recently developed formal tools provided by Reason-Based Logic. As an application of our view on rules and principles, we give three ways of reconstructing reasoning by analogy.     

New method for measuring the degree of conflict among general basic probability assignments

There is doubt about Dempster’s rule of combination because of counter-intuitive results when dealing with conflict information in intelligent reasoning.Therefore,many modified combination rules have been presented in the literature on multi-source information fusion and reasoning with uncertainty.However,the issue of identifying conflict among evidence has been ignored.A new parameter measuring conflict evidence called the conflict distance parameter is defined to determine whether there are conflicts in evidence based on the analysis of existing conflict parameters.At the same time,a decisive rule,which a reasonable conflict measure function should satisfy,is put forward.Finally,an analysis of two typical counter-intuitive situations is given,showing that the new parameter can not only satisfy the decisive rule,but can also attain the same effect as a two-dimensional measure when deciding whether to use the Dempster’s rule of combination,and can exceed its effect when deciding whether to use Dezert-Smarandache theory.     

一种度量广义基本概率赋值冲突的方法

Dempster-Shafer(D-S)证据理论在组合冲突信息时,会得出与直觉相反的结论,为此研究人员提出很多改进方法,但是如何度量证据之间的冲突程度却常常被人们忽视.在分析现有冲突系数的基础上,在推广幂集空间框架下提出了一个冲突距离系数,用来刻画证据之间的冲突程度.进一步提出了合理的冲突度量参数应满足的判定准则,通过两种典型的悖论情况,分析了经典冲突系数和二元组冲突表示方法的不足,说明所提出的冲突系数不但满足判定准则,而且在判断冲突使用Dempster组合规则方面可以达到二元组表示方法的同等效果,甚至在判断冲突使用Dezert-Smarandache theory(DSmT)方面可以超过二元组表示方法的效果.     

粒及粒计算在逻辑推理中的应用

讨论了信息粒的结构及其实例。基于Rough集方法定义了决策规则粒,构造了决策规则粒库,它被用作逻辑推理。定义了粒语言,描述了这种语言的语法、语义、粒语句的运算法则和粒之相关的几个性质。定义了粒之间的相互包含(inclusion)和相似(closeness)。基于这些概念,构造了一种逻辑推理的新模型。这种推理模式的特点在于它既是逻辑的又是集合论的。所谓逻辑的就是说推理是遵循一种逻辑运算;所谓集合论的是指这种推理可利用对应于这种逻辑公式的意义集的运算进行推理,还用实例说明了这种推理模式是可行和有效的。     

On formalisation of the goal concept in law

The paper raises a problem of formalising several key concepts in legal theory, namely, goal, function and value. The law is viewed from a perspective of computer science in law. I intend to apply requirements engineering methods in law. The Berman and Hafner's [1993. Representing teleological structure in case based legal reasoning: the missing link. In: Proceedings of the Fourth International Conference on AI and Law. ACM Press, New York, pp. 50–59] challenge to model case-based reasoning in legal domain and the more systematic research, which is collected in Artificial Intelligence and Law journal in 2002, are considered as possible approaches to solutions. The term “goal” covers purposes, policies, interests, values, etc. I find a formalisation to have different levels depending on a distinct meaning of the term “law”. E.g., legal drafting is closer to engineering than to legal reasoning. European Union law and implementation of EU directives provide us with court decisions based on the teleological method. National implementation measures could employ goal-driven systems engineering techniques. Conclusions: (1) the formalisation is a challenging problem, (2) experts from other domains will gain from explicit representation of aims behind the law, (3) analysis of the structure of law is not enough; the studies of the content of law are required, too.     

Fuzzy concepts in an object oriented expert system shell

Fuzzy logic is one of the methods to model the vagueness and imprecision of human knowledge. Some rule-based expert system shells have been successfully developed and have demonstrated the power of fuzzy logic in dealing with inexact reasoning and rule inferences. However, using rules for knowledge representation is not structured enough. In addition, knowledge cannot be easily represented in an abstracted (hierarchical) from. In this article the introduction of fuzzy concepts into object oriented knowledge representation (OOKR), which is a structured knowledge representation scheme, is presented. A framework for handling all the possible fuzzy concepts in OOKR at both the dynamic and static levels is proposed. In order to handle the inheritance mechanism and to model the relations among classes, instances, and attributes, some new fuzzy concepts and operations are introduced. These concepts and operations are developed from the semantic meaning rather than by an ad hoc approach. A prototype of the expert system shell. System FX-I, has been successfully developed based on the above framework, showing the feasibility of handling inexact knowledge in a structural way.     

Belief rule-base inference methodology using the evidential reasoning Approach-RIMER

In this paper, a generic rule-base inference methodology using the evidential reasoning (RIMER) approach is proposed. Existing knowledge-base structures are first examined, and knowledge representation schemes under uncertainty are then briefly analyzed. Based on this analysis, a new knowledge representation scheme in a rule base is proposed using a belief structure. In this scheme, a rule base is designed with belief degrees embedded in all possible consequents of a rule. Such a rule base is capable of capturing vagueness, incompleteness, and nonlinear causal relationships, while traditional if-then rules can be represented as a special case. Other knowledge representation parameters such as the weights of both attributes and rules are also investigated in the scheme. In an established rule base, an input to an antecedent attribute is transformed into a belief distribution. Subsequently, inference in such a rule base is implemented using the evidential reasoning (ER) approach. The scheme is further extended to inference in hierarchical rule bases. A numerical study is provided to illustrate the potential applications of the proposed methodology.     

Designing intelligent litigation support tools: The IKBALS perspective

In the legal domain, it is rare to find solutions to problems by simply applying algorithms or invoking deductive rules in some knowledge‐based program. Instead, expert practitioners often supplement domain‐specific knowledge with field experience. This type of expertise is often applied in the form of an analogy. This research proposes to combine both reasoning with precedents and reasoning with statutes and regulations in a way that will enhance the statutory interpretation task. This is being attempted through the integration of database and expert system technologies. Case‐based reasoning is being used to model legal precedents while rule‐based reasoning modules are being used to model the legislation and other types of causal knowledge. It is hoped to generalise these findings and to develop a formal methodology for integrating case‐based databases with rule‐based expert systems in the legal domain.     

A fuzzy theoretical approach to case-based representation and inference in CISG

In a legal expert system based on CBR (Case-Based Reasoning), legal statute rules are interpreted on the basis of precedents. This interpretation, because of its vagueness and uncertainty of the interpretation cannot be handled with the means used for crisp cases. In our legal expert system, on the basis of the facts of precedents, the statute rule is interpreted as a form of case rule, the application of which involves the concepts of membership and vagueness. The case rule is stored in a data base by means of fuzzy frames. The inference based on a case rule is made by fuzzy YES and fuzzy NO, and the degree of similarity of cases. The system proposed here will be used for legal education; its main area of application is contract, especially in relation to the United Nations Convention on Contracts for the International Sale of Goods (CISG).     

On Resolving Conflicts Between Arguments

Argument systems are based on the idea that one can construct arguments for propositions—structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of which (sub‐) arguments can be subject to defeat. In legal argumentation, metarules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, can a conflict be resolved by considering only the last defeasible rules of the arguments involved? We propose a new argument system where, instead of deriving a defeat relation between arguments, arguments for the defeat of defeasible rules are constructed. This system allows us to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, allows conflicts to be resolved using only the last rules of the arguments, allows us to establish a relation with Default Logic, and allows closure properties such as cumulativity to be proved. We propose an extension of the argument system based on a proposal for reasoning by cases in default logic.     

基于可拓规则的故障诊断专家系统推理机的研究

针对传统产生式规则在知识表示、匹配冲突等方面存在的局限,提出了一种将可拓规则用于故障诊断专家系统推理机的方法;该方法重点研究了可拓规则的匹配原理和可拓推理机算法思想,提出了匹配度计算方法并用来计算故障条件与规则前件的匹配度;根据研究表明,利用可拓规则进行推理,不仅在知识表示上比传统产生式规则推理有所提高,而且还解决了传统专家系统容易出现匹配冲突等问题;最后以AMU故障推理为例,说明可拓推理机具有推理速度快、效率高等优点,取得了较好的推理效果.     

云推理方法及其在预测中的应用

不确定性推理是当前人工智能研究领域中的一项重要研究内容。云模型实现了定性概念与其定量表示之间的不确定转换,在云模型基础上构建的规则发生器能有效描述用自然语言表示的定性规则,实现不确定性推理。将基于云模型的不确定性推理方法用于预测实际工作环境中电子产品的使用寿命,说明了云推理方法的有效性和实用性。     

Handling interaction in fuzzy production rule reasoning

When fuzzy production rules are used to approximate reasoning, interaction exists among rules that have the same consequent. Due to this interaction, the weighted average model frequently used in approximate reasoning does not work well in many real-world problems. In order to model and handle this interaction, this paper proposes to use a nonadditive nonnegative set function to replace the weights assigned to rules having the same consequent, and to draw the reasoning conclusion based on an integral with respect to the nonadditive nonnegative set function, rather than on the weighted average model. Handling interaction in fuzzy production rule reasoning in this way can lead to a good understanding of the rules base and an improvement of reasoning accuracy. This paper also investigates how to determine from data the nonadditive set function that cannot be specified by a domain expert.     

粗糙集理论在故障诊断规则获取中的应用

本文的目的是给出一种利用粗糙集理论解决故障诊断的规则获取问题的方法 ,该方法的特点是可以处理由于类重叠引起的样本信息不精确、不一致情况下的规则获取 .以规则形式表示的知识接近于人脑推理过程 ,因此基于规则的诊断方法在故障诊断中得到广泛使用 ,但规则获取是其瓶颈之一 .粗糙集 (RS)理论是为开发自动规则生成系统而提出的 ,其主要思想是在保持分类能力不变的前提下 ,通过知识约简 ,导出概念的分类规则 .因此 ,可以把 RS理论用于规则的故障诊断中 .本文给出了基于决策矩阵和决策函数的获取规则方法的流程图 ,以故障诊断实例说明其使用方法 ,并验证了其有效性     

证据推理的鲁棒性研究

在处理不确定信息的方法中,证据推理性能突出、应用广泛,它的鲁棒性分析十分必 要.首先基于证据推理的目的和要求,给出证据推理鲁棒性的定义,并提出冲突率的新概念,以 此为尺度对Dempster规则、加权分配冲突法和吸收法的鲁棒性进行了深入分析,证明了各方法 鲁棒性结果.仿真结果表明改进的组合规则鲁棒性能得到了明显增强.最后给出证据推理的一 般情形的鲁棒性分析.