Giovanni Sartor

Argument-based extended logic programming with defeasible priorities

ABSTRACT Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logic-programming language with both weak and strong negation, conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled. The semantics of the system is given with a fixpoint definition, while its proof theory is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument: an argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks.

A dialectical model of assessing conflicting arguments in legal reasoning

Inspired by legal reasoning, this paper presents a formal framework for assessing conflicting arguments. Its use is illustrated with applications to realistic legal examples, and the potential for implementation is discussed. The framework has the form of a logical system for defeasible argumentation. Its language, which is of a logic-programming-like nature, has both weak and explicit negation, and conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled.The proof theory of the system is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument. An argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. Despite this dialectical form, the system reflects a ‘declarative’, or ‘relational’ approach to modelling legal argument. A basic assumption of this paper is that this approach complements two other lines of research in AI and Law, investigations of precedent-based reasoning and the development of ‘procedural’, or ‘dialectical’ models of legal argument.

Modelling Reasoning with Precedents in a Formal Dialogue Game

This paper analyses legal reasoning with precedents in the setting of a formally defined dialogue game. After giving a legal-theoretical account of judicial reasoning with precedents, a formal method is proposed for representing precedents and it is discussed how such representations can be used in a formally defined dialectical protocol for dispute. The basic ideas are to represent cases as argument structures (including pro and con arguments, and the arguments for adjudicating their conflicts) and to define certain case-based reasoning moves as strategies for introducing information into a dispute. In particular, analogizing and distinguishing are conceived as elementary theory construction moves, which produce new information on the basis of an existing stock of cases. The approach also offers the possibility of using portions of precedents and of expressing criteria for determining the outcome of precedent-based disputes.

A model of legal reasoning with cases incorporating theories and values

Reasoning with cases has been a primary focus of those working in AI and law who have attempted to model legal reasoning. In this paper we put forward a formal model of reasoning with cases which captures many of the insights from that previous work. We begin by stating our view of reasoning with cases as a process of constructing, evaluating and applying a theory. Central to our model is a view of the relationship between cases, rules based on cases, and the social values which justify those rules. Having given our view of these relationships, we present our formal model of them, and explain how theories can be constructed, compared and evaluated. We then show how previous work can be described in terms of our model, and discuss extensions to the basic model to accommodate particular features of previous work. We conclude by identifying some directions for future work.

Temporalised normative positions in defeasible logic

We propose a computationally oriented non-monotonic multi-modal logic arising from the combination of temporalised agency and temporalised normative positions. We argue about the defeasible nature of these notions and then we show how to represent and reason with them in the setting of Defeasible Logic.

The Role of Logic in Computational Models of Legal Argument: A Critical Survey

This article surveys the use of logic in computational models of legal reasoning, against the background of a four-layered view on legal argument. This view comprises a logical layer (constructing an argument); a dialectical layer (comparing and assessing conflicting arguments); a procedural layer (regulating the process of argumentation); and a strategic, or heuristic layer (arguing persuasively). Each further layer presupposes, and is built around the previous layers. At the first two layers the information base is fixed, while at the third and fourth layer it is constructed dynamically, during a dialogue or dispute.

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.

Heuristics in Argumentation: A Game-Theoretical Investigation

This paper provides a game-theoretical investigation on how to determine optimal strategies in dialogue games for argumentation. To make our ideas as widely applicable as possible, we adopt an abstract dialectical setting and model dialogues as extensive games with perfect information where optimal strategies are determined by preferences over outcomes of the disputes. In turn, preferences are specified in terms of expected utility combining the probability of success of arguments with the costs and benefits associated to arguments.

Normative autonomy and normative co-ordination: Declarative power, representation, and mandate

AbstractIn this paper we provide a formal analysis of the idea of normative co-ordination. We argue that this idea is based on the assumption that agents can achieve flexible co-ordination by conferring normative positions to other agents. These positions include duties, permissions, and powers. In particular, we explain the idea of declarative power, which consists in the capacity of the power-holder of creating normative positions, involving other agents, simply by „proclaiming“ such positions. In addition, we account also for the concepts of representation, namely the representative’s capacity of acting in the name of his principal, and of mandate, which is the mandatee’s duty to act as the mandator has requested. Finally, we show how the framework can be applied to represent the contract-net protocol. Some brief remarks on future research and applications conclude this contribution.

Theory based explanation of case law domains: 38

In this paper we put forward a formal description of theories which can be used to record understanding of, and explain decisions in, case law domains. We believe that reasoning with cases involves all of theory construction, use and evaluation, and that awareness of the theory which provides a context for case based arguments is essential to understanding such arguments. Moreover, our account of these theories includes a systematic link between factors and values, which we believe is necessary to explain why some arguments prove to be more persuasive than others. We begin by formalising the various elements that the theories contain, and then provide a set of theory constructors which allow theories to built up from the background of decided cases. We show how such theories can be used to explain decisions on particular cases. We discuss how theories can be compared and evaluated. We then show how the argument moves of HYPO and CATO can be understood in terms of our framework. We conclude with a brief discussion of an implementation of the framework, and a summary of the major features of our approach.