Why do lawyers pay so little attention to logic? The main problem is that logic in its classical appearances (such as propositional or predicate logic) is not sufficiently satisfying as a model of legal argument: it is too far from the argument forms that lawyers use in practice. In recent years, there has been a large amount of research on the development of logical tools for legal argument (see, e.g., the work of Gordon [1993, 1995], Hage , Lodder , Prakken [1993, 1997] and Verheij ). Argument forms that have been studied include arguments concerning exceptions to rules, conflicts of reasons and rule applicability.
The logical tools that have recently been developed can be categorized under three headings: defeasibility, integration of logical levels, and the process character of argument [Verheij et al., 1997].
Defeasibility is a characteristic of arguments and, in a derived sense, of conclusions. A conclusion is defeasible if it is the conclusion of a defeasible argument. Defeat occurs if a conclusion is no longer justified by an argument because of new information. For instance, the conclusion that a thief should be punished is no longer justified if it turns out that there was a legal justification for the theft, such as an authorized command.
The integration of logical levels is for instance required if reasons are weighed. If arguments lead to incompatible conclusions, weighing of reasons is necessary to determine which conclusion follows. Additional information is necessary to determine the outcome of the weighing process. In some views, this information is on a higher logical level than the facts of cases, and the rules of law. However, since there can also be arguments about the weighing of reasons, the integration of levels is required.
The process character of argument also led to the development of new logical tools. For instance, the defeasibility of arguments cannot be separated from the process of taking new information into account. During the process of argumentation conclusions are drawn, reasons are adduced, counterarguments are raised, and new premises are introduced. In traditional models, only the end products of the process are modeled.
The focus has been primarily on the technical development of the logical tools, and only in the second place on their practical adequacy for modeling legal argument. Presently a convergence of opinions on the necessary logical tools takes shape, and a systematic practical assessment of the logical tools becomes essential.
In the research reported on in this paper, a step towards the practical assessment is made by the development of two experimental computer systems for argument mediation for lawyers. In computer-supported argument mediation, one or more users of the system engage in an argument that is mediated by the system: the system administers the argument moves and safeguards that the rules of argument are observed. It can, if appropriate, give advice to the user.
A new problem for argument researchers, as posed by the development of systems for argument mediation is how arguments should be presented to the users of the system. In this paper, we describe two experimental computer systems, the Argue!-system and the Argumentation Mediator, each using a different way of argument presentation. The two systems are based on a simplified version of Verheij's  CumulA-model, which is a procedural model of argumentation with arguments and counterarguments.
Section 2 briefly discusses argument mediation and the two experimental systems of the present paper. In section 3, an example case of Dutch tort law is summarized, that will be used to illustrate the two systems of argument mediation. Section 4 contains an introduction of CumulA, the procedural model of argumentation with arguments and counterarguments, that underlies the two experimental systems. Section 5 and 6 contain sample sessions of the two systems. In section 7, the two systems are compared with each other and selected related systems, especially with regards to their underlying argumentation theories and user interfaces. Section 8 suggests a shift from argument mediation systems as theoretical to practical tools.
Verheij, Bart (1998). Argument mediation for lawyers: the presentation of arguments. Proceedings of the Fourth International Conference of the International Society for the Study of Argumentation (eds. Frans H. van Eemeren, Rob Grootendorst, J. Anthony Blair, Charles A. Willard), pp. 820-828. SIC SAT, Amsterdam.