A System for Defeasible Argumentation, with Defeasible Priorities Henry Prakken?1 and Giovanni Sartor2 1
Computer/Law Institute, Free University, De Boelelaan 1105 Amsterdam email:
[email protected] 2 CIRFID, University of Bologna, Via Galliera 3, 40121, Bologna IDG-CNR, Via Panchiatichi 56/16, Firenze email sartor@cir d.unibo.it
Abstract. Inspired by legal reasoning, this paper presents an argument{
based system for defeasible reasoning, with a logic{programming{like language, and based on Dung's argumentation{theoretic approach to the semantics of logic programming. The language of the system has both weak and explicit negation, and con icts between arguments are decided with the help of priorities on the rules. These priorities are not xed, but are themselves defeasibly derived as conclusions within the system.
1 Introduction This paper presents an argument{based system for defeasible reasoning, with a logic{programming{like language. Argument{based systems analyze defeasible reasoning in terms of the interactions between arguments for alternative conclusions. Defeasibility arises from the fact that arguments can be defeated by stronger counterarguments. Argumentation has proved to be a fruitful paradigm for formalising defeasible reasoning (cf. [13, 17, 18]). Not only does the notion of an argument naturally point at possible proof theories, but also do notions like argument, counterargument, attack and defeat have natural counterparts in the way people think, which makes argument{based systems transparent in applications. Especially in legal reasoning these notions are prevalent, which explains why several argument{ based systems have been applied to that domain ([14, 10, 8, 16]). Also the present system is inspired by the legal domain. In particular, we want to capture the following features of legal reasoning (but also of some other domains, such as bureaucracies). The rst is that in law the criteria for comparing arguments are themselves part of the domain theory. For instance, in Italy, in town planning regulations we can nd a priority rule stating that rules on the protection of artistic buildings prevail over rules concerning town planning. ? Henry Prakken was supported by a research fellowship of the Royal Netherlands
Academy of Arts and Sciences, and by Esprit WG 8319 `Modelage'. The authors wish to thank Mark Ryan for his comments on an earlier version of this paper.
Apart from varying from domain to domain, priority rules can also be debatable, in the same way as `ordinary' domain information can be. For instance, if an artistic{buildings rule is of an earlier date than a con icting town planning rule, the just{mentioned con ict rule is in con ict with the temporal principle that the later rule has priority over the earlier rule. Other con ict rules may apply to this con ict, and this makes that also reasoning about priorities is defeasible. The second feature is that in law speci city is not the overriding standard for comparing arguments. In most legal systems it is subordinate to the hierarchical criterion (e.g. `the constitution has priority over statutes') and to the temporal criterion. This means that systems like [7], making speci city the overriding standard for comparison, are for our purposes inadequate. Finally, we want to model the fact that legal reasoning combines the use of priorities to choose between con icting rules with the use of assumptions, or `weak' negation, within a rule to make it inapplicable in certain circumstances. An example of such a rule is section 3:32{(1) of the Dutch Civil Code, which declares every person to have the capacity to perform juridical acts, \unless the law provides otherwise". Accordingly, our language will have both explicit and weak negation, which yields two di erent ways of attacking an argument: by stating an argument with a contradictory conclusion, or by stating an argument with a conclusion providing an `unless' clause of the other argument. It is not our aim to present a general theory of defeasible argumentation. Rather, we will analyse these phenomena within a logic{programming{like setting, in particular Dung's [6] argument{based approach to the semantics of extended logic programming. With the choice for a logic{programming like language we hope to increase the prospects for implementation, while our choice for Dung's approach is motivated by his emphasis on argumentation. We will present our system in two phases. In the rst phase the priorities are still externally given and xed (section 2) and in the second phase they are derived within the system itself (section 3). After that, the system is compared with related research (section 4). This paper is a revised version of [16], with more emphasis on formal aspects and less attention to legal applications. For an extensive discussion of examples and applications the reader is referred to [16].
2 The Formal System I: Fixed Priorities As most systems of defeasible argumentation, our system contains the following elements. To start with, it has an underlying formal language and, based on the language, a notion of an argument. Then it has a de nition of when an argument is in con ict with, or attacked by other arguments, a way of comparing con icting arguments and, most importantly, a de nition of the ultimate status of an argument, in terms of three classes: arguments with which a dispute can be `won', respectively, `lost' and arguments which leave the dispute undecided.
2.1 The Language The object language of our system is of familiar logic{programming style: it contains a twoplace one{direction connective that forms rules out of literals. The language has two kinds of negation, weak and classical negation. An atomic rstorder formula is a positive literal; a positive literal preceded by : is a negative literal; a positive or negative literal is a weak literal if preceded by ; otherwise it is a strong literal. For any atom P (x) we say that P (x) and :P (x) are the complement of each other; in the metalanguage L denotes the complement of L. Now a rule is an expression of the form
r : L 0 ^ : : : ^ L j ^ L k ^ : : : ^ L m ) Ln where r is the name of the rule and each Li (0 i k) is a strong literal. The conjunction at the left of the arrow is the antecedent and the literal at the right of the arrow is the consequent of the rule. As usual, a rule with variables is a scheme standing for all its ground instances. The input information of our system does not only contain rules, but also priorities. We call the input an ordered theory, which is a pair (T;
