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.     

Abductive logics in a belief revision framework

Abduction was first introduced in the epistemological context of scientific discovery. It was more recently analyzed in artificial intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from events E if H is a good explanation of E. The paper surveys four known schemes for abduction that can be used in both fields. Its first contribution is a taxonomy of these schemes according to a common semantic framework based on belief revision. Its second contribution is to produce, for each non-trivial scheme, a representation theorem linking its semantic framework to a set of postulates. Its third contribution is to present semantic and axiomatic arguments in favor of one of these schemes, ordered abduction, which has never been vindicated in the literature.     

SNePSwD: A newcomer to the SNePS family

Abstract

SNePS 2.1 is a knowledge representation and reasoning system that records the dependencies among propositions that are needed to perform a revision of beliefs when a contradiction is detected. The reasoning of SNePS 2.1 is based on a monotonic logic and the system has no provisos for performing an automatic revision of beliefs. In this paper we present SNePSwD that extends the capabilities of SNePS 2.1 along two dimensions: (1) it is able to represent default rules and to perform default reasoning, i.e. the logic underlying SNePSwD is non-monotonic; (2) it accepts the specification of preferences between hypotheses and uses them to decide which hypotheses to discard to resolve a contradiction. This latter possibility allows a semi-automatic contradiction resolution (in some cases, even completely automatic). We discuss the motivations for the creation of SNePSwD, present the form of default rules it uses, discuss the meaning of each of the three kinds of consequence, and describe how preferences can be specified among propositions and how these preferences are used in the process of belief revision. Finally we present examples that illustrate the aspects discussed in the paper.     

Normative conflict resolution in multi-agent systems

Norms (permissions, obligations and prohibitions) offer a useful and powerful abstraction with which to capture social constraints in multi-agent systems. Norms should exclude disruptive or antisocial behaviour without prescribing the design of individual agents or restricting their autonomy. An important challenge, however, in the design and management of systems governed by norms is that norms may, at times, conflict with one another; e.g, an action may be simultaneously prohibited and obliged for a particular agent. In such circumstances, agents no longer have the option of complying with these norms; whatever they do or refrain from doing will lead to a social constraint being broken. In this paper, we present mechanisms for the detection and resolution of normative conflicts. These mechanisms, based on first-order unification and constraint solving techniques, are the building blocks of more sophisticated algorithms we present for the management of normative positions, that is, the adoption and removal of permissions, obligations and prohibitions in societies of agents. We capture both direct and indirect conflicts between norms, formalise a practical concept of authority, and model conflicts that may arise as a result of delegation. We are able to formally define classic ways for resolving conflicts such as lex superior and lex posterior.     

Default reasoning and belief revision: A syntax-independent approach

As an important variant of Reiter‘s default logic.Poole(1988) developed a nonmonotonic reasoning framework in the classical first-order language,Brewka and Nebel extended Poole‘s approach in order to enable a representation of priorities between defaults.In this paper a general framework for default reasoning is presented,which can be viewed as a generalization of the three approaches above.It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al.(1997).This esult provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case .As a by-product,an answer to the the question,raised by Mankinson and Gaerdenfors(1991),is also given about whether there is a counterpart contraciton in nonmonotonic logic.     

Preorder-based triangle: a modified version of bilattice-based triangle for belief revision in nonmonotonic reasoning

Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle cannot handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover, the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.     

A logic programming system for nonmonotonic reasoning

The evolution of logic programming semantics has included the introduction of a new explicit form of negation, beside the older implicit (or default) negation typical of logic programming. The richer language has been shown adequate for a spate of knowledge representation and reasoning forms.The widespread use of such extended programs requires the definition of a correct top-down querying mechanism, much as for Prolog wrt. normal programs. One purpose of this paper is to present and exploit a SLDNF-like derivation procedure, SLX, for programs with explicit negation under well-founded semantics (WFSX) and prove its soundness and completeness. (Its soundness wrt. the answer-sets semantics is also shown.) Our choice ofWFSX as the base semantics is justi-fied by the structural properties it enjoys, which are paramount for top-down query evaluation.Of course, introducing explicit negation requires dealing with contradiction. Consequently, we allow for contradiction to appear, and show moreover how it can be removed by freely changing the truth-values of some subset of a set of predefined revisable literals. To achieve this, we introduce a paraconsistent version ofWFSX, WFSX _p , that allows contradictions and for which our SLX top-down procedure is proven correct as well.This procedure can be used to detect the existence of pairs of complementary literals inWESX _p simply by detecting the violation of integrity rulesf L, -L introduced for eachL in the language of the program. Furthermore, integrity constraints of a more general form are allowed, whose violation can likewise be detected by SLX.Removal of contradiction or integrity violation is accomplished by a variant of the SLX procedure that collects, in a formula, the alternative combinations of revisable literals' truth-values that ensure the said removal. The formulas, after simplification, can then be satisfied by a number of truth-values changes in the revisable, among true, false, and undefined. A notion of minimal change is defined as well that establishes a closeness relation between a program and its revisions. Forthwith, the changes can be enforced by introducing or deleting program rules for the revisable literals.To illustrate the usefulness and originality of our framework, we applied it to obtain a novel logic programming approach, and results, in declarative debugging and model-based diagnosis problems.     

New tractable classes for default reasoning from conditional knowledge bases

This paper refines the tractability/intractability frontier of default reasoning from conditional knowledge bases. It presents two new tractable cases with relation to lexicographic entailment. In particular, we have introduced nested conditional knowledge bases and co-nested conditional knowledge bases, which are meaningful conditional knowledge bases. Both tractable classes presented in this paper can be recognized in linear time.     

Fundamental legal concepts: A formal and teleological characterisation*

We shall introduce a set of fundamental legal concepts, providing a definition of each of them. This set will include, besides the usual deontic modalities (obligation, prohibition and permission), the following notions: obligative rights (rights related to other’s obligations), permissive rights, erga-omnes rights, normative conditionals, liability rights, different kinds of legal powers, potestative rights (rights to produce legal results), result-declarations (acts intended to produce legal determinations), and sources of the law. ^* Supported by the EU projects ONE-LEX (Marie Curie Chair) and ESTRELLA (6th Framework).     

An ontology in OWL for legal case-based reasoning

The paper gives ontologies in the Web Ontology Language (OWL) for Legal Case-based Reasoning (LCBR) systems, giving explicit, formal, and general specifications of a conceptualisation LCBR. Ontologies for different systems allows comparison and contrast between them. OWL ontologies are standardised, machine-readable formats that support automated processing with Semantic Web applications. Intermediate concepts, concepts between base-level concepts and higher level concepts, are central in LCBR. The main issues and their relevance to ontological reasoning and to LCBR are discussed. Two LCBR systems (AS-CATO, which is based on CATO, and IBP) are analysed in terms of basic and intermediate concepts. Central components of the OWL ontologies for these systems are presented, pointing out differences and similarities. The main novelty of the paper is the ontological analysis and representation in OWL of LCBR systems. The paper also emphasises the important issues concerning the representation and reasoning of intermediate concepts.

智能体行动推理中的信念修正

信念修正中的加强修正算法在保留低秩非矛盾信念时存在不足,流演算由于其表示公式的局限,无法较好的与信念修正结合来进行行动推理。针对以上不足,提出了依赖信念修正算法和Strategy-Axiom-Reasoning模型。该算法满足Ind假设并且较好的保留了条件信念和低秩非矛盾信念,SAR模型继承并改进了流演算的公理系统,用公式集表示信念集,较好的实现了与信念修正的结合。最后将依赖信念修正算法运用到SAR模型中,用实验证明了其可行性。     

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.     

弱化矛盾信息的一种修正方法

信念修正中一个关键的问题就是对不一致信息的处理。文中提出一种新的策略，在对不一致信息的处理过程中，通过弱化矛盾信息而不是完全丢弃来维护知识库的一致性。这种方法遵循了最小改变原则，使信息丢失尽可能小从而保留了更多的有用信息。并讨论了其性质及满足AGM公设的情况。