Henry Prakken

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.

An abstract framework for argumentation with structured arguments

An abstract framework for structured arguments is presented, which instantiates Dungs (‘On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n-Person Games’, Artificial Intelligence, 77, 321–357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it...

Logics for Defeasible Argumentation

Logic is the science that deals with the formal principles and criteria of validity of patterns of inference. This chapter surveys logics for a particular group of patterns of inference, namely those where arguments for and against a certain claim are produced and evaluated, to test the tenability of the claim. Such reasoning processes are usually analysed under the common term ‘defeasible argumentation’. We shall illustrate this form of reasoning with a dispute between two persons, A and B. They disagree on whether it is morally acceptable for a newspaper to publish a certain piece of information concerning a politician’s private life.1 Let us assume that the two parties have reached agreement on the following points.

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 general account of argumentation with preferences

This paper builds on the recent ASPIC^+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC^+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC^+@?s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung@?s framework and its extensions to accommodate preferences.

Credulous and Sceptical Argument Games for Preferred Semantics

This paper presents dialectical proof theories for Dungs preferred semantics of defeasible argumentation. The proof theories have the form of argument games for testing membership of some (credulous reasoning) or all preferred extensions (sceptical reasoning). The credulous proof theory is for the general case, while the sceptical version is for the case where preferred semantics coincides with stable semantics. The development of these argument games is especially motivated by applications of argumentation in automated negotiation, mediation of collective discussion and decision making, and intelligent tutoring.

Towards a formal account of reasoning about evidence: argumentation schemes and generalisations

This paper studies the modelling of legal reasoning about evidence within general theories of defeasible reasoning and argumentation. In particular, Wigmores method for charting evidence and its use by modern legal evidence scholars is studied in order to give a formal underpinning in terms of logics for defeasible argumentation. Two notions turn out to be crucial, viz. argumentation schemes and empirical generalisations.

Relating Protocols For Dynamic Dispute With Logics For Defeasible Argumentation

This article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols that are perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established.

A study of accrual of arguments, with applications to evidential reasoning

This paper presents a logical formalisation of accrual of arguments as a form of inference. The formalisation is given within the logical framework of Dung as instantiated by Pollock, and is shown to satisfy three principles that any treatment of accrual should satisfy. The formalisation of accrual as inference is contrasted to knowledge-representation treatments of accrual. Also, the formalisation is applied to some concepts from the theory of evidential legal reasoning.