prakken - sartor_the three faces of defeasibility in the law

8/12/2019 Prakken - Sartor_The Three Faces of Defeasibility in the Law

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The Three Faces of Defeasibilityin the Law

HENRY PRAKKEN AND GIOVANNI SARTOR

Abstract. In this paper we will analyse the issue of defeasibility in the law, takinginto account research carried out in philosophy, artificial intelligence and legaltheory. We will adopt a very general idea of legal defeasibility, in which we willinclude all different ways in which certain legal conclusions may need to be aban-doned, though no mistake was made in deriving them. We will argue that defeasi-bility in the law involves three different aspects, which we will call inference-baseddefeasibility, process-based defeasibility, and theory-based defeasibility. Only the

integration of these three perspectives allows us to provide a satisfactory account ofthe role of defeasibility in legal reasoning.

1. Inference-Based Defeasibility

The first aspect of defeasibility which has attracted the attention of legalthinkers has been what we may call inference-based defeasibility.

Inference-based defeasibility covers the fact that legal conclusions, thoughcorrectly supported by certain pieces of information, cannot be inferredwhen the theory including this information is expanded with further piecesof information (we use the term theory to mean in general any set ofpremises intended to provide an account of a legal domain). This idea isalso frequently expressed by saying that common sense reasoning (asopposed to logical deduction) is nonmonotonic: The conclusions of thereasoning process do not grow inevitably as further input information isprovided.

This is a feature of human reasoning which has been studied by scholars

working in different areas.In epistemology the idea of defeasible inference has been developed byauthors such as Chisholm (1977) and Pollock and Cruz (1999). Pollock, inparticular, relates defeasible reasoning to a general feature of human cogni-tion. He argues that a reasoning agent starts with perceptual inputs, andgoes on inferring beliefs from the reasons which are available to him (his

Ratio Juris. Vol. 17 No. 1 March 2004 (11839)

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Defeasibility in the Law 119

Blackwell Publishing Ltd 2004.

percepts plus the beliefs which he has previously inferred). Such a belief-formation process must satisfy two apparently incompatible desiderata.Firstly, the agent must be able to form beliefs on the basis of a partial per-

ceptual input (the agent cannot wait until he has a complete representationof his environment). Secondly, the agent must be able to take into accountan unlimited set of perceptual inputs.

The only obvious way to achieve these desiderata simultaneously is to enable theagent to adopt beliefs on the basis of small sets of perceptual inputs but then retractthem in the face of additional perceptual inputs if those additional inputs conflict invarious ways with the original basis for the beliefs. This is a description of defeasiblereasoning. Beliefs are adopted on the basis of arguments that appeal to small sets ofpreviously held information, but the beliefs can later be retracted in the face of newinformation. (Pollock 1995a, 40)

One usual example for epistemological defeasibility concerns an agenthaving an image of a red object (see ibid.). This percept is usually a goodenough reason for that agent to conclude that the object is indeed red.However, if the agent sees that the object is under a red light, then the agentshould retract the conclusion that the object is red, since when an objectis under a red light, its looking red does not support the conclusion that

it is red (also objects having different colours look red under a red light).Similarly, Pollock argues, in statistical reasoning the fact that most Fs areGs (e.g., most pieces of information in a newspaper are true), combinedwith the fact that x is an F (x is a statement in a newspaper) provides adefeasible reason for concluding that x is a G (the statement is true).However, if one has (better) reasons for believing that the x statement isfalse, one should retract this belief.

In moral reasoning, a similar idea of defeasibility is at the centre of D.Rosss theory of prima facie moral obligations (Ross 1930, 1939). In Rosss

account, moral intuition plays the same role that perception plays inPollocks account: Both provide starting points for defeasible inferences. AsPollocks account of empirical reasoning is grounded upon the recognitionthat our reasonings cannot directly take into account all possibly relevantcircumstances, so Rosss account of moral reasoning starts with the idea thatany single moral principle cannot take into account all morally relevantaspects of our actions:

Any possible act has many sides to it which are relevant to its rightness or wrong-ness; it will be pleasure to some people, pain to others; it will be the keeping of apromise to one person, at the cost of being a breach of confidence to another, and soon. We are quite incapable of pronouncing straight off on its rightness or wrongnesson the totality of these aspects; it is only by recognising these different features oneby one that we can approach the forming of a judgement on the totality of its nature.(Ross 1939, 84)


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This view implies that our moral principles can lead us to conflicting con-clusions. For example, D. Ross considers that sometimes we cannot obeyone without disobeying another; that often we cannot obey the principle

of telling the truth without disobeying the principle of not causing need-less pain, or the principle of keeping promises without disobeying the prin-ciple of producing the maximum good (Ross 1939, 83). Correspondingly,Ross argues that the conclusions which are licensed by our moral intuitionsmay be overridden by other moral intuitions in concrete cases. To establishour real obligations we need to balance our conflicting prima facieconclusions.

Moral intuitions are not principles by the immediate application of which our duty

in particular circumstances can be deduced. They state [ . . . ] prima facie obligations.[ . . . ] We are not obliged to do that which is only prima facie obligatory. We are onlybound to do that act whose prima facie obligatoriness in those respects in which it isprima facie obligatory most outweighs its prima facie disobligatoriness in those aspectsin which it is prima facie disobligatory. (Ross 1939, 845)

In artificial intelligence (AI) defeasible reasoning has also been the focus ofa considerable amount of research (for a review, see Prakken and Vreeswijk2002; for some major contributions, see Ginsberg 1987). In fact, in the attemptto build intelligent systems which could act in a complex and partially

unknown environment, the need emerged to provide such systems with thecapacity to jump to conclusions which are supported only by a subsetof the potentially relevant information (McCarthy 1987a). One of the mostcelebrated examples is Tweetys case, originally put forward by MarvinMinsky. Given the information that Tweety is a bird, and the common sensegeneralisation that birds can fly, the reasoner should jump to the conclusionthat Tweety can fly. However, this conclusion (which is derived only fromthe fact that Tweety is a bird) should be abandoned if it comes out thatTweety is a penguin, that he has a broken wing, that he is sick, etc. Thisexample well exemplifies the so called qualification problem: An agentcannot be expected to make an action or form a belief only after havingchecked all possible conditions required for ensuring the successful per-formance of the action or the truth of the belief (McCarthy 1987b, 1). Usuallyit would be impossible to verify that all such conditions obtain (to verifythat Tweety does not belong to any species of non flying bird, that he hasno kind of impairment that impedes flying, etc.), or even to spell out all ofthem in advance. An agent should therefore derive defeasible conclusions

from circumstances normally sufficient to support them, that is, accordingto principles which apply under normal circumstances.Many theories of defeasible reasoning in artificial intelligence have been

produced, such as default logic (Reiter 1987), circumscription (McCarthy1987b), autoepistemic logic (Moore 1987a, 1987b), negation by failure (Clark1987; Kowalski 1979), and various argumentation systems (Simari and Loui

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1992). Our preference goes to those models that explicitly ground thejump to a certain conclusion upon the articulation of the reasons for andagainst drawing such a conclusion, making the jump dependent upon the

interaction of reasons and counter-reasons.In this regard, possibly, the most attractive logical account of defeasible

inference is that provided by John Pollock (Pollock 1995a, 1995b; Pollockand Cruz 1999). Pollock provides us with a distinction in two ways in whichone inference may defeat another one. The first is by rebutting. The rebut-ter of an inference concluding for p is an inference concluding for the nega-tion of p, that is for p. For example, the inference that leads me to concludethat Ann is Johns killer on the basis of Sylvias testimony can be rebutted

by Marys testimony that Adrian is (and therefore Ann is not) Johns killer.

The second is by undercutting. The undercutter of an inference concludingfor p on the basis of a certain ground q is an inference that, under the exist-ing circumstances, q is not a proper ground for p. For example, the inferencethat leads me to conclude that Adrian is Johns killer on the basis of Sylviastestimony can be undercut by the information that Sylvia was paid forgiving such a testimony. This fact is not a reason for concluding that Adriandid not kill John (it does not say anything about it), but it casts doubts onthe probational force of Sylvias testimony.

Besides the idea of defeat, Pollocks account of the process of defeasible

justification (for a concise account, cf. Pollock and Cruz 1999, 197ff.) includesan analysis of the connections between multiple arguments. This is requiredsince a defeated argument may be reinstated when a broader picture is con-sidered: this happens when the defeater is in turn defeated. So, for example,the conclusion that Ann is Johns killer, though attacked by the argumentthat Adrian is Johns killer since Sylvia testifies so, is reinstated whenSylvias testimony is shown to be unreliable (since Sylvia was paid for givingit). We cannot provide here a formal discussion of Pollocks method, but wewill discuss a fairly similar approach by Prakken and Sartor (1996).

After considering defeasible inference in epistemology, moral philosophyand epistemology, let us go back to legal thinking. The notion of defeasibil-ity, quite usual in legal practice and in doctrinal work, was brought to theattention of legal theorists by Hart:

When the student has learned that in English law there are positive conditionsrequired for the existence of a valid contract, he has still to learn what can defeat aclaim that there is a valid contract, even though all these conditions are satisfied. The

student has still to learn what can follow on the words unless, which shouldaccompany the statement of these conditions. This characteristic of legal concepts isone for which no word exists in ordinary English. The law has a word which withsome hesitation I borrow and extend: this is the word defeasible, used of a legalinterest in property which is subject to termination or defeat in a number of dif-ferent contingencies but remains intact if no such contingencies mature. (Hart 1951,152)


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More recently, various ideas related to defeasible inference have been dis-cussed in legal reasoning. Let us first mention the idea of legal reasoning asincluding non-deductive jumps, discussed by Peczenik (1983). Secondly,

we recall the opposition of prima facie legal obligation and all-consideredlegal obligations, as proposed by Peczenik (1989). This opposition providesa model of legal reasoning similar to the account of morality provided byD. Ross. Legal norms and principles, when applied to the facts of a case,only provide prima facie legal conclusions. All things considered legal con-clusions can only be obtained by considering all relevant rules and princi-ples, as applied to all relevant facts. This opposition implies a notion ofdefeasibility, when one considers the limitations of human knowledge. Onemust be able to form legal beliefs (or derive legal conclusions) though one

only has a limited legal knowledge (one may not be aware of all legally rel-evant factors, rules, principles, concepts) and a limited factual knowledge(one may not be aware of all circumstances of the case). In fact, as Peczenikobserves, [n]o human being has the resources sufficient to formulate all-things-considered statement sensu stricto (Peczenik 1989, 77). The situationof a legal reasoner, therefore, parallels the situation of Pollocks agent. Thelegal reasoner, though endowed with limited knowledge, energy, time andresources, must be able to make reasonable decisions. However, he must also

be able to take into account a potentially unlimited amount of further rele-

vant information, as soon as he is aware of it. This is exactly what a methodfor defeasible legal reasoning should do: It should enable a legal agent toform judgements on the basis of the knowledge he has, and the thinking heis presently able to do, and correct (and possibly withdraw) such conclu-sions as soon as he is able to take into account further legally relevantinformation.

A further idea which points to a defeasible model of legal inference is thatof weighing and balancing conflicting considerations as the appropriate wayof reaching considered legal conclusions. This method of reasoning is notexclusively appropriate to the law. As Mill said, on any subject on whichdifference of opinion is possible, the truth depends on a balance to be struck

between two sets of conflicting reasons (Mill 1974, 98). However, in prac-tical reasoning, and in particular in legal reasoning, the need to take intoaccount conflicting considerations is particularly important. As A. Peczenicksays, in order to justify an all-things-considered practical statement, onemust weigh and balance prima facie practical statements which support itagainst such statements supporting the contrary conclusion (Peczenik 1989,

77). The weighing and balancing metaphor, that is, the idea that legal con-clusions are based upon the comparison of the weight of sets of reasonsfavouring opposed outcomes, naturally leads to defeasibility. Let us assumethat the reasoner believes that outcome p is supported by the set A ofreasons, while outcome not p is supported by set B, and that he also believesthat setA is heavier than set B. When considering only reasons inA and B,




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the reasoner should conclude for p. However, let us assume that the reasonerdiscovers that there is an additional reason r promoting outcome not p, andsuch that B + r is heavier then A. When taking into account also r, the

reasoner should retract conclusion p, and accept not p. Further reasonsweighing for p may still change the result of the weighing.

Though the idea of defeasibility in legal inference has been discussed inlegal theory, as we saw above, it is only within research on AI & Law thatthis idea has been thoroughly analysed.

This research has pointed to various structures of legal knowledge whichsupport defeasible reasoning. One is the combination of rules and excep-tions. Consider, for example, the Italian rule that if one causes an unjustdamage then one is liable, and the exception saying that if one causes an

unjust damage in a situation of necessity, one is not liable. Such combina-tions prompt for defeasible reasoning: One should derive the conclusion ofthe rule when one knows that its antecedent is satisfied, but one shouldabandon this conclusion if it appears that an exception was also satisfied.Another structure which prompts for defeasibility is the use of unlessclauses. For example, Italian law says that a person is not liable for an actionif he is incapable at the moment of that action, unless he put himself in sucha state. This is clearly a case of undercutting: Having made oneself incapableis not a reason for being liable (one is liable for causing an unjust damage,

and not because one is drunk), but rather a reason for incapability not toexclude liability.

Moreover, researchers in AI have been investigating defeasibility result-ing from clashes of rules and principles. As we have remarked, legal infer-ences can be defeated when competing inferences can be developed. To givemore concreteness to the metaphor of weighing and balancing, AI & Lawresearchers have used various legal criteria for dealing with such conflicts,establishing what inference is defeated. Both wellknown general priorityrules such as the principles of specificity (Lex Specialis), temporality (LexPosterior) and hierarchy (Lex Superior) and domaindependent priorityrules have been considered.

A deeper question is whether those specific criteria are to be seen as spe-cific applications of the idea of weighing and balancing reasons (a viewtaken by Hage 1997), or whether, on the contrary, the idea of combining theweight of reasons is only a possible criterion for solving conflicts, alongsideother criteria (this is the view taken by Prakken and Sartor 1996). We cannothere examine all approaches to non-monotonic reasoning in the law. We will

focus on an argument-based approach, which has the indisputable merit ofhaving been advanced by the authors of this paper. However, it is veryclose in spirit (though not in the technical solution) to other argument-

based models of defeasible legal reasoning (Gordon 1995; Hage 1997), andtherefore it may be considered representative of the broader researchcommunity. Let us briefly present this model of legal inference.


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The basic idea (as for other argument-based approaches to legal defeasi-bility) is that legal rules and principles are to be viewed as reasoning war-rants that, when certain antecedent reasons are available (being provided as

part of the input, or as the result of previous inference steps), supportthe derivation of legal conclusions. In this way basic legal inferences areobtained, which consist of chains of warrants leading to legal conclusions.

Such inferences, however, may lead to conflicts, by providing incompati-ble conclusions. To adjudicate a conflict between two inferences, we need toestablish what inference is stronger, and this in general may be done throughfurther inferences (preference inferences), which use further (meta)warrants. By merging these inferences we obtain a complex inference, whichcan include a basic inference, the comparison inference supporting the first

one, and so on.According to the result of such judgements, we can, as a first approxima-

tion, say that any inference which is not stronger than one of its competi-tors is defeated, and its conclusions need to be retracted, while theconclusions of the stronger inference can be safely asserted. However, thepicture is complicated by the idea of reinstatement: Defeated inferences can

be recovered if their defeaters are, in their turn, defeated by stronger infer-ences. So we obtain a model of legal reasoning as the dialectical interactionof competing inferences: The outcome of this competition determines what

conclusions will be legally justified in the framework of the available legalknowledge.

This account can be precisely stated in a very intuitive way, viz. in thedialectical form of a dispute. The idea is that a statement is warranted(relative to a certain body of information) if its proponent can successfullydefend it in a dispute, or argument game with an opponent (obviously,the reasoner who checks on his own whether a statement is warrantedshould take both positions). One form that such a game can take is the oneof Prakken and Sartor (1996).1 The proponent starts with an argument forthe statement he wants to prove, after which the players take turns, movingone argument at a time. The opponents task is to attack the proponentslast-moved argument with a conflicting argument. The proponents taskthen is to prove that this attack is unsuccessful. The proponent can do thisin two ways. The first is to move a priority argument which neutralisesthe opponents attack, i.e., which says that the opponents argument is infact refuted by its target. For instance, consider the following dispute:

Proponent: The newspapers may publish this piece of information about

politician B since it is relevant for assessing his political functioning.Opponent: The newspapers may not publish this piece of informationsince it is about Bs income, information about income is, according to

1 Several games are possible, reflecting different notions of defeasible consequence; cf., e.g.,Prakken and Vreeswijk 2002. For present purposes their differences do not matter.




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Section x of statute S, private information, so publishing it would violate Bsprivacy.

Then proponent might reply:

Proponent: For politicians the value of openness about functioning over-rides the value of privacy, so my argument is stronger then the opponentsargument.

(Note that the above rules of the game now allow opponent to attack pro-ponents priority argument. For instance, opponent could argue that open-ness about functioning of politicians is not more important than protectionof privacy.)

A second option for proponent is to attack some intermediate step inopponents argument, combined with the reasons why proponents attack

succeeds. For instance, proponent might argue:Proponent: Information about the income of politicians is not private

information, as stated by sectiony of statute S, andy is a Lex Specialis of x.(Again, opponent may try to attack proponents argument, for instance,

by arguing thaty is not a Lex Specialis of x.)Note that these rules build a form of dialectical asymmetry into the game,

capturing the idea that the initial statement must be provably warranted,while objections just need to interfere with the proof for impeding it fromsucceeding: This is captured by the fact that proponents counterarguments

must refute their target, while opponents counterarguments are allowed tomerely cast sufficient doubt on their target.

In Prakken (2001a) the game above is refined to cope with shifts of theburden of proof. Suppose, for instance, in a civil case that the plaintiff claimsa contract was created while defendant argues for an exception becauseof insanity. Then the plaintiff will receive the burden of proving offer andacceptance, so the plaintiff will be proponent with respect to these state-ments. However, the defendant will be assigned the burden of proving herinsanity, so she will be the proponent with respect to that statement. Thisextension takes us into the second type of defeasibility, process-based defea-sibility, which will be examined in the following section.

2. Process-Based Defeasibility

Theories of inference-based defeasibility (i.e., nonmonotonic logics) essen-tially take a static view of reasoning, since they just look at a given body ofinformation, and say which beliefs are warranted on the basis of that infor-

mation. Even the definition of nonmonotonicity is stated in essentially staticterms: It just says that the beliefs warranted on the basis of an informationset S need not be included in the beliefs warranted on the basis of a largerinformation set S. This definition abstracts from whether S precedes S inthe reasoning process or not; and if S did precede S, it is silent on how thereasoning progressed from S to S. Most importantly, standard non-


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monotonic logics say nothing about in which circumstances S can be takenas a basis for decision, and in which circumstances it is better to search formore information.

Process-based defeasibility addresses such dynamic aspects ofdefeasible reasoning. As for legal reasoning, a crucial observation hereis that it often proceeds according to the rules of legal procedures. In par-ticular, the following features of legal procedures are relevant.

Firstly, the outcome of a legal dispute often depends not only on the state-ments and arguments exchanged, but also on the propositional attitudesexpressed by the parties involved (such as when a claim was disputed, con-ceded, or not responded to) and on how the burden of proof is allocated.To illustrate this, let us again look at our example, first purely in terms of

inference-based defeat. Then we see that the arguments exchanged makeproponents initial statement provable (since opponent did not find a coun-terargument against his last argument). However, suppose that the oppo-nent has disputed that the piece of information is about Bs income (e.g.,since the information was not clearly about B), and that the judge has allo-cated the burden of proof to proponent, after which the proponent failed toprovide any evidence. Procedural laws then often say that proponent hasfailed to prove his initial statement, since he failed to provide evidence fora premise for which he had the burden of proof; therefore, his final argu-

ment should be ignored. In sum, it is not only important which argumentswere exchanged, but also which premises of these arguments were disputed,conceded (or withdrawn), and how the burden of proof was allocated.

Even if we only look at arguments and the statements from which theyconsist of, procedural law has a lot to say that is left out by a purely infer-ence-based notion of defeasibility. A central question here is what it meansto have the burden of proof for a certain statement.2 This involves twoaspects, viz. the task to provide an (evidential) argument for a claim and thetask to defend this argument in dispute. As for the first task, legal proce-dures regulate that kinds of evidence are admissible (e.g., illegally obtainedevidence and hearsay evidence is often ruled inadmissible). The second taskin turn has three aspects: whether the argument is internally acceptable,whether counterarguments are admissible, and whether the argument isdialectically acceptable, i.e., whether it survives the competition with theadmissible counterarguments.

Whether an argument is internally acceptable means whether in itself itsufficiently supports its conclusion, apart from possible counterarguments.

Sometimes a judge is free to assess the strength of arguments (as is thegeneral rule in Dutch civil law). Of course, this legal-procedural freedom is(at least ideally) bound by rational theories of what counts as a good argu-

2 The role of the burden of proof in legal defeasibility has been stressed before by, e.g,MacCormick 1995; Sartor 1995.




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ment (see, e.g., Walton 1996). But some types of evidence are declared con-clusive, i.e., if no counterevidence is provided, the judge must accept it. Forinstance, in Dutch law an affidavit is conclusive evidence that its content is

true. As for the second aspect, whether counterarguments are admissible,this is purely a matter of procedural law. Some kinds of evidence aredeclared incontrovertible, which means that no counterevidence is allowed.An example in Dutch civil law is an oath by one of the parties. The finalaspect of the burden of proof is that ones admissible evidence shouldsurvive the competition with all (admissible) counterevidence. Above all,this is, of course, a matter of evaluation by the judge. However, the judgesevaluations are in fact arguments on the strength of other arguments, i.e.,undercutting or priority arguments. So, once the evidence has been evalu-

ated, (defeasible) logic comes into play: We end up with a collection of argu-ments, counterarguments, and priority arguments, and if we add to that theallocation of the burden of proof, we can compute with a logical argumentgame whether the initial claim is proven.

So far we have only discussed the static aspects of the burden of proof,viz. how it determines the provability of the initial claim at a certain stageof a dispute. However, the burden of proof also has a dynamic role: As soonas one party has fulfilled his burden of proof, the dispute is not over but theother party must be given a fair opportunity to provide counterevidence.

That is, once a proof burden is met, the burden should shift to the otherparty. For instance, (recall Hart) once the plaintiff has proven offer andacceptance, the defendant must be given the opportunity to prove an excep-tion, such as insanity or a hidden defect. Of course, this must once come toan end, and this highlights an important dynamic feature of defeasibility,viz. the question of when a dispute must be terminated. This relates to theabove question under which conditions a certain body of information is suf-ficient to decide the dispute, and under which conditions it is better to searchfor more information. In law this is, of course, partly regulated by the rele-vant procedure; however, such procedures usually leave some freedom tothe judge, at which point rational criteria for termination are called for; andsuch criteria are another process-based aspect of defeasibility.

Consider, for instance, a criminal case where one witness says that thesuspect shot the victim to death and another witness says that the suspectstabbed the victim to death. This is a case with two conflicting arguments,

but whichever argument is preferred, one always ends up with the conclu-sion that the suspect killed the victim. In the literature on inference-based

defeasible reasoning, there is a discussion about whether such floating con-clusions should be accepted if this is all the information one has. For instance,Horty (2002) argues that it is rational not to accept the conclusion that thesuspect killed the victim, since the conflicting witness statements undermineeach others credibility: It may well be that neither speaks the truth.However, whatever the merits are of this analysis, any good lawyer would


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in such a situation defer judgement and instead ask further questions to thewitnesses to investigate their credibility (e.g., did you hear any sound?).Again we see that a narrow, inference-based view of the defeasibility of legal

reasoning is too limited: It does not take the dynamic aspects of reasoninginto account (see Hintikka 1999 for a similar view on standard logic).

Summarising, when one wants to rationally reconstruct a certain piece oflegal reasoning, it often does not suffice to apply only the rules of logic, evenif the logic is nonmonotonic. One must also take into account how the rele-vant legal procedure regulates such things as the burden of proof, the effectof disputing, conceding or ignoring a claim, the admissibility of evidenceand counterevidence, and the conclusive force of certain kinds of evidence.Only if these issues have been accounted for, i.e., only if the arguments

exchanged in a dispute have gone through a procedural filter, can theremaining arguments be used as the input of a nonmonotonic logic. More-over, this process evolves in time: The arguments that pass the filter at acertain stage in a dispute may favour the plaintiff, but the dispute mayproceed (e.g., the burden of proof may switch to the defendant) and a newset of arguments passing the procedural filter at a later stage may favourinstead the defendant. A final issue that evades a purely inference-basedaccount is at what stage a dispute should come to an end. This issue is gov-erned by issues of fairness, rationality (asking the right question) and

resource limitations, especially time and money. All these issues can be mod-elled, but clearly not in a purely logical way.

While, as noted in section 1, formal models of inference-based aspects ofdefeasibility abound (in the form of nonmonotonic logics), the formal studyof its process-based aspects is less developed. Yet a promising research lineis evolving, sometimes called computational dialectics. It originated in theseventies, when such logicians as Hamblin, MacKenzie, Woods and Waltonembedded standard propositional logic in dialogue game models for argu-mentation, with speech for such things as claiming, disputing, conceding orretracting a proposition, and providing grounds for a proposition (seeWalton and Krabbe 1995 for an overview). In such games, proponent winsif he succeeds in opponent accepting his initial claim, while opponent winsif she succeeds in making proponent withdraw his claim. In the nineties, AI& Law researchers such as Gordon (1995), Hage et al. (1994), Lodder (1999),Loui (1998), Bench-Capon et al. (2000), Prakken (2001b) applied suchdialogue games to legal disputes, meanwhile adding the very importantpossibility of counterarguments, thus effectively shifting from deductive to

defeasible reasoning. These models regulate when certain speech acts mayor must be made, what effect they have on the (current) outcome of adispute, and (sometimes) that a dispute terminates. Their aim is to provideidealised models of legal dispute, i.e., rules for how a dispute can be con-ducted and resolved in a fair, rational and effective way. Thus these modelsare inspired by a procedural view on rationality and justice as expressed by,




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e.g., Rescher (1977) and Alexy (1978). Another important feature of thesemodels is that they in fact formalise unless shown otherwise phrases inthe law not naively as unless logically proven otherwise from the available

premises but as unless shown otherwise by a process of argumentationand the presenting of evidence to an authorised decision-maker (cf. Allenand Saxon 1989).

Space limitations prevent us from discussing these models in detail(for two recent overviews see Hage 2000 and Prakken and Sartor 2002).Rather, we will give an example of the kinds of dialogues regulated by suchmodels. Our main point here is to highlight that such dialogues can now beformalised in ways that capture not only inference-based but also process-

based aspects of defeasibility. The example dispute is about contract forma-

tion. It contains a claim, concessions and disputations, decisions about theburden of proof, an argument and a counterargument, and a decision thata piece of evidence was illegal.

Plaintiff: I claim that defendant owes me 500 euros. Defendant: I dispute plaintiffs claim. Judge: Plaintiff, prove your claim. Plaintiff: Defendant owes me 500 euros since we concluded a valid sales

contract, I delivered but defendant did not pay.

Defendant: I concede that plaintiff delivered and I did not pay, but Idispute that we have a valid contract.

Judge: Plaintiff, prove your claim that you have a valid contract. Plaintiff: This document is an avidavit, signed by us. Defendant: I dispute that this document is an avidavit. Judge: Defendant, since the document looks like an avidavit, prove that

it is not. Defendant: This lab report shows that the notarys signature was forged. Plaintiff: That evidence is inadmissible, since I received it too late. Judge: I agree: The evidence is inadmissible.

At this point, both plaintiff and defendant have constructed one argu-ment, displayed in Figures 1 and 2 (the warrants connecting premisesand conclusion are left implicit, as is so often the case in legal reasoning).Plaintiffs argument passes the procedural filter, since its premise (8) wasnot replied to by defendant, its premises (3) and (5) were conceded by defen-dant, while with respect to the remaining premise (7), the burden of proving

the opposite was assigned to defendant. Defendants argument, on the otherhand, does not pass the procedural filter, since one of its premises (11) isdeclared inadmissible evidence. Observe, finally, that the judge has notattacked plaintiffs argument with an undercutter, so that the judge hasimplicitly ruled this argument internally acceptable. The argument gamethen computes that plaintiff wins (at least at this stage of the dispute!).


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Of course, current process-based models of legal reasoning are far fromcomplete or perfect. To start with, they should be complemented with the-ories on what counts as a good legal argument, and on what are good waysto question or attack such arguments. Some important investigations of thiskind already exist, such as Alexy 1978; Hage 1997; Walton 2002, to name but

a few. However, more work remains to be done, especially on formalisingthese accounts. Other important research issues are what are good strategiesfor playing a dialogue game, e.g., what are the right questions to ask, andwhat are good criteria for the termination of disputes? Finally, it should bestudied how process-based models of legal reasoning can be combined withan important kind of legal reasoning, viz. coherence-based theory construc-tion. Let us now turn to this kind of reasoning.

3. Theory-Based Defeasibility

The third form of defeasibility we will consider is theory-based defeasibil-ity. This results from the evaluation and the choice of theories which explainand systematise the available input information: When a better theory

becomes available, inferior theories are to be abandoned.The basic inspiration is given by theories of the development of science

centered upon the idea of competition between alternative theories. As iswell known, in the first half of the last century the idea of an incremental

growth of knowledge was countered by the Popperian idea of theories asrefutable conjectures (Popper 1959), to be abandoned when contradicted byobservations. However, this idea also appears inadequate in relation to thefact that humans need theories to interpret, systematise, and anticipate theirexperience. We only abandon a theory when a better theory is available tous (Lakatos 1978). Substituting a better theory for the old one can be viewed



Figure 2: Defendants argument

Figure 1: Plaintiffs argument

(7) affidavit (8) signed

(6) offer & acceptance

(3) I delivered (4) valid contract (5) you didnt pay

(2) breach of contract

(1) you owe me 500

(11) lab report

(10) notarys signature forged

(9) no affidavit


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as a move that is appropriate when a scientific revolution (Thagard 1992) istaking place, i.e., in those crucial moments in the development of sciencewhen a new paradigm is emerging and displacing the once dominant view,

now irremediably degenerating for its incapacity to address new issues(cf. Kuhn 1962, and on paradigm change in the law, cf. Aarnio 1984).

However, the idea of theory change has a broader significance: It alsocovers cases where only a portion of a theory is substituted with a newtheory, that is, where from theory A1 a new theory A2 is produced, by can-celling fromA1 subtheory S1 and substituting S1 with the new subtheory S2.As is well known, the issue of theory change has been considered to a largeextent in philosophy, law and computing. However, the focus in mostapproaches (such as Alchourron et al. 1985; Gardenfors 1987) has been on

how to update a consistent theory into a new consistent theory whichcontains some new information.

In the study of change in legal theories one has to adopt a different focus,since legal theories are defeasible theories, as we said in section 1, so thatthey can accommodate new knowledge without the need for retracting pre-vious information, even when there is a contradiction. Moreover, if oneagrees that defeasible inference and in particular weighing and balancing ofconflicting rules and principles is the appropriate way of approaching legalissues, then one should reject all attempts to provide a consistent represen-

tation of the law. Such a representation would indeed not respect the intu-itive understanding of legal knowledge, and would not support its normalutilisation. A set of decisional criteria, each one supported by its rationale,susceptible of being compromised through defeasible inferences accordingto further criteria and rationales, would be translated into a set of muchmore complex rules, having no recognisable grounding. Such a representa-tion would not be able to support the dynamic adjustment which takes placewhenever new information concerning the conflicting principles and the cri-teria for adjudicating their contest is taken into consideration.

The rejection of consistency does not imply that legal knowledge shouldbe a chaotic bag that anything can be thrown into. We should build our rep-resentations of the law (our legal theories) by using (only) the materials thatwe believe to be useful (or needed) in such a construction. Each one of thoserepresentations may (and indeed should) include conflicting (and thereforelogically inconsistent) knowledge, when this is appropriate, but it shouldnevertheless provide an adequate framework for legal thinking andproblem-solving.

Since different theories of the same legal domain are possible, we needways of comparing those theories and of selecting the most appropriate one.Note that the need of a choice is not excluded by the fact that the largestpart of such theories may overlap. What matters is that we have to comparethe competing theories as wholes: If we have to decide whether to substitute,within theoryA1, subtheory S1 with the new subtheory S2, we do not have


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to compare S1 against S2, but rather we need compare the whole theory A2with the whole theory A2 that would be obtained by subtracting S1 fromAand adding S2. The most general way of synthesising the idea of the ade-

quacy of a body of knowledge is by appealing to the idea of coherence. Wecannot get into a discussion of the general notion of coherence (cf., forexample, Lehrer 1990; Thagard 2001). This would also require discussing theconnections between this idea and other notions such as the notions of con-silience (Wilson 1999) and integrity (Dworkin 1986). As an example of ananalysis of this notion in legal theory, we could mention the contribution ofAlexy and Peczenik (1990) who have focused their attention on the fre-quency and the intensity of connections between statements in a theory. Ina recent work, Peczenik defines coherence as follows:

The more the statements belonging to a given theory approximate a perfect sup-portive structure, the more coherent the theory is.

Ceteris paribus, the degree of coherence of a theory depends on such circumstancesas how great a number of supported statements belong to it, how long chains ofreasons support one and the same conclusion, how great number of general conceptsbelong to it, how high the degree of generality of these concepts, how great numberof cases it covers, and how great number of fields it covers. The degree of coherenceis determined by weighing and balancing of the criteria. (Peczenik 1997, 196)

In legal theory, coherence has usually been approached as an ideal whichshould inspire legal theory and legal decision-making, rather than as a cri-terion for choosing between alternative theories. The latter idea has beenespecially discussed in research on artificial intelligence and law. So,McCarty observes that:

A judge rendering a decision in a case is constructing a theory of that case. It follows,then, that a lawyers job (in an appellate argument) is to construct a theory of thecase, too, and one that just happens to coincide with his clients interest. Since the

opposing lawyer is also constructing a theory of the case, which coincides with herclients interest, the argument boils down to this: Which theory should the judgeaccept? There are several constraints here, but they are weak ones. Legal theoriesshould be consistent with past cases, and they should give acceptable results onfuture cases. They should not be too hard to understand, or too hard to administer,which means that they should be free of major anomalies. One term that is some-times used to describe these requirements is coherence. Although difficult tospecify precisely, the link between coherent legal theories and persuasive legalarguments seems to be quite strong. (McCarty 1997, 221)

The notion of coherence so sketched by McCarty has a pragmatic flavour. Itpoints to the features of a legal theory that make it useful or appropriate asan instrument for legal thinking and problem solving. A similar notion ofcoherence has been used as a criterion for theory choice in some recent con-tributions by Bench-Capon and Sartor (Sartor 2002; Bench-Capon and Sartor2001a, 2001b, 2003).




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These papers provide a model of legal reasoning which is centered upontheory construction and theory comparison. The parties in a case, given ashared legal background, develop alternative legal theories, and victory

goes to the party who develops the better theory. This leads to the idea oftheory-based argumentation, i.e., the idea that legal debates consist of thedialectical exchange of competing theories, supporting opposing legal con-clusions in the issue at stake. A central aspect of theory-based argumenta-tion is, as we shall see, theory-based defeasibility, in the sense that theweaker (less coherent) theory is defeated by the stronger one.

Before introducing this model, let us briefly present the original exampleof Berman and Hafner (1993) which is used as a test example in all thosecontributions. The example consists of three American cases, where the

plaintiff (p) was chasing wild animals, and the defendant (d) interrupted thechase, preventing p from capturing those animals. The issue to be decidedis whether p has a legal remedy (a right to be compensated for the loss ofthe game) against d or not. In the first case, Pierson v Post, p was hunting afox on open land in the traditional manner using horse and hound, and hadnot yet gained possession of the fox, when d killed and carried off the fox.In this case p was held to have no right to the fox. In the second case, Keeblev Hickeringill, p owned a pond and made his living by luring wild ducksthere with decoys and shooting them. Out of malice d used guns to scare

the ducks away from the pond. Here p won. In the third case, Young vHitchens, both parties were commercial fisherman. While p was closing hisnets, d sped into the gap, spread his own net and caught the fish. Theissue at stake is how this third case should be decided, that is, whether dshould compensate p for the loss of the game, or whether no such liabilityexists.

The shared legal background of the parties includes the recognition thatcertain possible features of cases in this domain are factors pointing tocertain conclusions. For example, ps owning the land where he is huntingfavours the conclusion that he ought to be compensated. On the other hand,ps not having yet gained possession of the game favours the conclusion thathe should not be compensated. Those (defeasible) connections betweenfactors and conclusions are called factor-links. The shared background alsocontains an understanding of why factor-links should be adopted: This is

because the adoption of a certain factor-link (its being used by legal agentsas a standard for their reasoning and practice) advances the achievement ofcertain values. This connection between a factor-link and a value is called a

teleological link. Here is an example of a possible teleological link: Com-pensating hunters who were disturbed while hunting on their grounds is away of promoting the value of security (in enjoying ones own possessions).The assumption that factors, values, and their connections are shared notonly is a simplifying assumption in this model, but it also corresponds tothe idea that usually, within a certain culture, people tend to agree both on




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the evaluative recognition of certain values, and in the factual recognitionthat these values are going to be promoted by adopting certain decisionalpatterns (factor-links), while they are more likely to disagree on the relative

importance of the values (Peczenik 1989, 58ff.).Given this background, the parties try to build theories. We will not con-

sider the mechanism for building theories, which consists, according to theelementary model of Sartor 2002; Bench-Capon and Sartor 2001b, of com-

bining factors into rules and establishing priorities between such rules. Letus just remark that in Sartor (2002) each theory is viewed as an explanatoryhypothesis, i.e., as an explanans, in the terminology of Hempel (1966, 51).The theory aims both at accounting for the precedents, which are itsexplanandum, and to suggest an outcome for the new case. This suggestion

may be interpreted either as a normative justification or as a forecast, accord-ing to the objective of the construction, and corresponds to the anticipationof future experimental data in scientific theories.

For example, let us consider a pro-d theory according to which a disap-pointed hunter is to be compensated whenever he owns the land where heis hunting, in order to promote the value of security of possession. Thistheory allows the defendant to explain why in Pearson p lost (he washunting on open ground), why in Keeble he won (he was hunting in hisproperty), and why in Young p should lose (he was fishing at sea).

However, this is not the only possible theory. Another possible theory,which also explains all precedents, but gives a different result in the newcase (Young), is the theory that the disappointed hunter p should be com-pensated whenever he is pursuing his livelihood, in order to promote thevalues of work and productivity. This would still explain why p lost inPearson (where he was hunting for his pleasure), and why p won in Keeble(where he was a professional hunter), but would imply that p should winalso in Young (where he was a professional fisherman).

The possibility that different theories can be developed on the basis of thesame legal background leads to the issue of what theory is to be preferred.As a standard for comparing theories, Sartor 2002, Bench-Capon and Sartor2001b, and Bench-Capon and Sartor 2001a propose the idea of coherence,though intended in the broad (and pragmatic) sense indicated above, thatis, as the set of the requirements that make a legal theory a good (and useful)one. This idea is more specifically articulated, in a precedent-domain, intothe following requirement: case-coverage (a better theory explains moreprecedents), factor-coverage (a better theory takes into account more

features of those precedents), value-coverage (a better theory takes intoaccount a larger set of values), analogical connectivity (a better theoryincludes more analogical connections between its components), non-arbitrariness (a better theory contains fewer ad-hoc statements, requiredneither for explaining the past evidence nor for implementing the sharedassessment of value-priorities).




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For example, this would be a good theory (among those generated withelementary theory constructors) according to the account of Sartor 2002;Bench-Capon and Sartor 2001b.

When p is hunting in his grounds he should be compensated (in order topromote the value of security of possession). This rule prevails over therule that if p has not got hold of the game he should not be compensated(in order to limit litigation). When d is pursuing his livelihood, in the openground, and p has not yet caught the game, then p should not be compen-sated (to promote competition and prevent litigation). The latter rule pre-vails over the rule that when p is a professional hunter he should becompensated (since under those circumstances the need to prevent litiga-tion favours d who also is a professional hunter).

The implications of theories such as the one above are to be evaluatedaccording to the defeasible logic of Prakken and Sartor (1996)though otherdefeasible logics could equally be used. In particular, a theory explains acase when the decision of that case is a justified conclusion derivable fromthe theory plus the facts of the case.

To assess the goodness of a theory we need to combine all coherencerequirements into a comprehensive evaluation of the theory. This issue isdiscussed in Bench-Capon and Sartor (2001a) where a connectionistapproach is proposed, following the model of Thagard (1992). Thagards

essential idea is to represent the evidence to be accounted for by a theoryand the tenets of a theory as nodes connected by links representing supportand conflict. A set of initial scores (between 1 and -1) is assigned to thesenodes (this captures the idea that coherence in science concerns the abilityof accounting for external inputs). Then these scores are propagated, withsupport links increasing the scores of nodes, and conflict links decreasingthem. Moreover, links are subject to a rate of decay so that the score of iso-lated nodes decreases. This propagation is continued through a number ofcycles, until the values of the nodes stabilise. In Thagards interpretation ofthis process, nodes which end with a high activation can be considered partof a coherent, and hence acceptable theory, while those with a low activa-tion should be rejected. Thagards theory is attractive for two main reasons:first of all it provides an effective way of computing coherence, and sec-ondly it offers a reconciliation between foundationalism (at least of thedefeasible type; see Pollock and Cruz 1999) and coherentism.

In the latter regard, we must observe that Thagards approach assumesthat the input nodes (the experimental evidence, in scientific theories) have

an initial positive value which is independent of their role in the theory. Itis up to the input nodes to provide value to the theory, though the theory,once it has received value from the input nodes, can impact negatively onsome of them, possibly conducing to their rejection. In Bench-Capon andSartor (2001b) Thagards method is adapted as follows to the legal domain.First, more in line with an adversarial view of legal argument, the purpose




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is not to extract the best theory out of the body of existing evidence andhypotheses, but to measure the comparative coherence of competing theo-ries. Therefore, nodes having a low activation are not rejected, but they

lower the overall coherence of the theory containing them. Secondly, twotypes of inputs are given a positive initial score: on the one hand precedents(which play the role of empirical data), on the other hand values. Therefore,cases and values are viewed as the sources from which a legal theory drawsits merit. This corresponds to the idea that a coherent legal theory should

be more than an internally connected web of concepts. It should account forcertain experiences, i.e., in this model, the decisions of past cases and theappreciation of values. Values and cases have a prima-facie positive signif-icance in their own (independently of their connection to the theory), which

is reverberated on the theory (starting from the statements explaining casesor promoting values), though the theory may then retroact on cases andvalues, diminishing or increasing their individual score. Thirdly, in (Bench-Capon and Sartors (2001b) approach, theories are assumed to be defeasi-

ble: Therefore the fact that a theory includes conflicting information detractsvery little from its merit, when those conflicts are solved by further infor-mation in the theory (according to which one of the conflicting rules is over-ruled). On the contrary, unsolved conflicts are very damaging for a theory,

because they compromise its ability to explain the cases.

4. An Overall Framework for Legal Defeasibility

We believe that all three forms of defeasibility need to be integrated into acomprehensive account of legal reasoning. Inference-based defeasibility isan essential feature of rational reasoning within a legal theory, that is,reasoning that takes place when one is applying just one legal theory to aspecific issue. Theory-based defeasibility is not reducible to inference-basedor process-based defeasibility, since it concerns the holistic choice betweentheories, rather than the use of a theory. One may argue that such a reduc-tion is possible, since the moves through which we add information to atheory are defeasible inferences, and the moves through which one deletesinformation from a theory are the defeat of this information. However, thisdoes not seem to be the way in which human reasoners proceed. We rathertend to distinguish the construction and modification of our theories (thepremises of our reasoning) from the use of such theories in making infer-

ences. And we distinguish occasional conclusions we may derive from ourpremises from premises constituting knowledge. The first only possess thestrength they inherit, via inferences, from other premises. The latter derivetheir value from the function they play in the knowledge base in which theytake part, and from the global performance of that knowledge base, as com-pared to alternative ones.




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Finally, process-based defeasibility, when aimed at rational decision-making must make use of both other types of defeasibility. That is, it pro-vides the dynamic context in which inference-based and theory-based

defeasible reasoning take place, through the interaction of multiple agents.

(for H. Prakken)Institute of Information and Computing Sciences,

Utrecht UniversityThe Netherlands

E-mail: [email protected]

(for G. Sartor)

CirsfidUniversity of Bologna

Via Galliera 3, BolognaItaly

E-mail: [email protected]

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