Burden of Proof in Legal Argumentation Arthur M. Farley (art@ s.uoregon.edu) Kathleen Freeman (kfreeman@s.uoregon.edu) Computer and Information Siene University of Oregon Eugene, OR 97403 USA ABSTRACT We present a omputational model of dialetial argumentation that ould serve as a basis for studying elements of legal reasoning. Argumentation is well-suited to deisionmaking in the legal domain, where knowledge is inomplete, unertain, and inonsistent, We model an argument both as information struture, i.e., argument units onneting laims with supporting data, and as dialetial proess, i.e., an alternating series of moves made by opposing sides. Inspired by the legal domain, our model inludes burden of proof as a key element, indiating the level of support that must be ahieved by a partiular side to an argument. Burden of proof ats as a move filter and termination riterion during argumentation and determines the eventual winner. We demonstrate our model by onsidering two examples that have been disussed previously in the artifiial intelligene and legal reasoning literature. INTRODUCTION As the artifiial intelligene (AI) and legal reasoning ommunities are well aware, most deisions are reahed against a bakground of inomplete, unertain, and inonsistent knowledge (i.e., weak theory domains; Porter, et. al., 1990). The most widely used AI methods for reasoning under unertainty either rely on an absene of outright ontraditions (e. g., probabilisti reasoning; Pearl, 1987) or are unable to support motivated deision-making in the fae of inonsistent information (e.g., default reasoning; Ginsberg, 1987). Both solutions put the problem of deiding what to believe outside their respetive domains of disourse. Choosing the proposition with highest Permission to opywithoutfee all or part of this material is granted provided that the opies are not made or distributed for diret ommerial advantage, the ACM opyright notie and the title of the publiation and its date appea, and notie is given that opying is by permission of the Assoiation for Computing Mahinery. To opy otherwise, or to republisb, requires a fee andlor speifi permission. 0 1995 ACM 0-89791-758-8/95/0005/0156 $1.50 probability or rando~y hoosing one of a set of onsistent extensions are most often proposed as simplisti deision proedures. The orret propagation of probabilities and expansion of onsistent extensions onstitute the primary onerns of these theoretial approahes. The legal domain, however, is onerned primarily with deisionmaking under diffiult irumstanes. Thus, an adequate theory of legal reasoning must provide a sound basis for hoosing what to believe, e.g., guilt or liability, The pratie of legal reasoning suggests a method for reasoning in weak theory domains that permits onlusions to be drawn relative to available evidene and pereived risks. Argumentation, with its emphasis on both supporting and refuting laims under situations of unertainty and inonsisteny, is well suited to serve as a framework for a pratial definition of proof and proof proedure (Pollok 1992, 1994). Burden of proof introdues a mehanism for determining the outome of an argument, alloating osts and risks in the fae of inevitable unertainty. 156
We present a omputational model of dialetial argument. Ourmodel omprises both argument as supporting explanation and argument as dialetial proess. As an explanation struture, argument onsists of argument units onneting laims with supporting data. As dialetial proess, an argument onsists of an alternating series of moves made by opposing sides, Inspired by legal reasoning, our model of argument inorporates the notion of burden of proof, roughly defined as what level of support must be ahieved by whih side of an argument. Burden of proof ats as a move filter and termination riterion during argumentation. We will provide operational definitions for several burden of proof levels that are derived from those used in legal settings. Argumentation moves, oupled with burden of proof requirements, will provide us with means to make deisions that are skeptial, redulous, or loated appropriately between these two extremes. In the following, we desribe our model of argumentation and operational definition of burden of proof. We then demonstrate the model by onsidering two examples previously disussed in the AI and legal reasoning literature, illustrating the effets that different burdens of proof an have on argument proess and outome. We onlude with a disussion of related researh and diretions for future work. MODELING ARGUMENT STRUCTURE The representation of an argument as a strutured entity and as a dialetial proess are ruial elements of our theory. For argument as supporting explanations, we reate argument strutures that serve to organize relevant, available, and plausible support for a laim and its negation. We represent these argument strutures in a form derived from that desribed in The Uses of Amument (Toulmin, 1958). An argument omprises data (i.e., input evidene, grounds) supporting or refuting a laim. The onnetion between data and laim or the authorization for moving from data to laim is alled a warrant. Data and warrant may not be enough to establish a laim onlusively; a laim has a qualifiation. Furthermore, any laim is subjet to rebuttals, i.e., arguments supporting its negation, All laims, inluding input data, must be supported, i.e., have baking. We define two types of baking: atomi, for information from outside the immediate realm of the argument (Homer, 1988) and tau ( zoulmin ~rgument Lmit ), where the laim is supported by data through appliation of a warrant. Most input laims have atomi baking while most onlusions of an argument have tau baking. A single laim may have multiple bakings. A warrant is a rule-like piee of knowledge, having anteedent and onsequent aspets. The anteedent and onsequent fields onsist of one or more propositional lauses. Multiple lauses in either the anteedent or onsequent are taken to represent onjuntive elements. In addition, a warrant has two type fields. The wtypel field lassifies the relationship between the anteedent and onsequent as explanatory (ex) or sign (si), as in (Freeley, 1990). An example of an explanatory relationship is a ausal link, where knowledge of the anteedent explains knowledge of the onsequent, e.g., where there s smoke (as the onsequent), there s fire. A sign relationship represents a orrelational link between anteedent and onsequent, e.g., Summer weekends are generally rainy. The wtype2 field of a warrant represents the strength with whih its onsequent an be drawn from its anteedent. The values we use are suffiient (s), default (df), and evidential (ev). A suffiient warrant is meant to represent onlusive relationships, suh as definitions. Default and evidential warrants are meant to represent levels of unertain knowledge, with default indiating relationships that are usually (almost always) the ase (e.g., birds fly ) and evidential referring to less ertain, but still likely, links (e.g., persons who live in Bermuda are more often British subjets ). TABLE 1. Reasoning Stem Given a warrant with anteedent p and onsequent q, we define allowable reasoning steps in Table 1. The latter two reasoning steps are fallaies in the ontext of dedutive reasoning (asserting the onsequent and denying the anteedent, respetively). However, they an be appropriate and are are often applied in reasoning ontexts where knowledge is inomplete or unertain, as in the legal domain. Polya (1968) and Resher (1976) disuss suh reasoning as patterns of plausible inferene. When dedutive and plausible reasoning types are present in the same system, are must be taken 157
to avoid inappropriate reasoning ombinations (Pearl, 1987). For example, if the reasoner knows that rain auses wet-grass and sprinkleron auses wet-grass, an unrestrited ombination of modus ponens and diret abdutive reasoning would allow the reasoner to derive support for the laim sprinkler-on from the input data rain, To blok the generation of suh unaeptable arguments, MP/ABD ombinations are not permitted aross two explanatory warrants. Qualifiations are used to apture the level of support for laims, reahed as a result of arguments based upon unertain knowledge and plausible reasoning steps. Presently, we use the following qualifiations: valid(!), strong (!-), redible (+), weak(-), and unknown (?). The first four are ranked in order of dereasing level of support, while the last indiates no support in the urrent argument. The qualifiation on a laim is that assoiated with its strongest supporting argument. The qualifiation afforded a laim from a tau baking is the least of the qualifiations assoiated with the warrant appliation, being qualifiations on the data support, on the warrant itself, and from the link. The link qualifiation is derived from the warrant type and reasoning step applied, as presented in Table 2. We apture the plausible nature of most modus tollens reasoning by propagating only a weak qualifiation when not involving a suffiient warrant. The weakest link approah to propagating support aross warrants and its appropriateness for plausible reasoning has been disussed (Pollok, 1992; Resher, 1976). We represent all laims in an argument struture only in their positive (i.e., unnegated) forms. Thus, eah laim in the struture has two assoiated qualifiations, summarizing the strength of support for the laim and for its negation. TABLE 2. Link Qualifiations warrant tvue reasoning steu link qualifiation ->s MP, MT valid ->s ABD, ABC weak ->&- MP strong ->& MT, ABD, ABC weak ->ev MP re&ble ->t=v MT, ABD. ABC weak MODELING ARGUMENT PROCESS A strutural model does not apture the proedural, sequential harater of dialetal argumentation. Dialetial argumentation results in the intertwining, over time, of argument strutures generated by Side-1 in support of a laim and by Side-2 in support of its negation. An argument begins with Side-1 attempting to find support for the input laim. Given a laim, searh for support proeeds from the input laim toward input data, using warrants as intermediate steps. The proess has been ompleted when all (sub)laims are supported by propositions in the input. A new tau struture is generated for eah warrant applied; the qualifiation and baking fields of the laims are updated to reflet the new support. If no initial support an be found, the argument ends with a loss for Side-1; all burdens of proof require that at least one supportive argument for an input laim be found. If Side-1 is able to find support for the laim, ontrol passes to Side-2, whih tries to refute the argument for laim(s) established by Side-1. We distinguish two types of refutation ations: (a) rebutting and (b) underutting, as derived from Pollok (1987). Rebutting finds new arguments diretly supporting the negation of a laim. Underutting is aomplished by finding weaknesses in purported support for a laim, questioning the suffiieny of the input support or tau fields, i.e., by rebutting sublaims. Argument moves implementing the various tasks of dialetial argumentation are desribed in Table 3. If an underutting move is suessful, it may result in a hange to the qualifiation of a laim or the withdrawal of a supporting argument. In the latter ase, suh moves are said to be defeating arguments and are indiated by the * entries in Table 3. These moves are in response to an argument for whih an exeption is found (i.e., a more speifi ounterargument is found) or to a weak amument made bv-the other side. i.e.. those based & plausible, ~ot dedutive, reasoning steps. Note that arguments defeat steps in other arguments, not the laim supported by that argument. Rebutting arguments that merely find alternative, unrelated arguments for the negation of a laim only serve to make the original onlusion ontroversial, hanging its qualifiation. Whether this is a suffiient outome for a given side of an argument will depend on the burden of proof. For example, suppose we make the default argument that a penguin flies beause it is a bird. An argument based on an evidential warrant stating that most things whose names start with the letter p don t fly would only serve to make the laim ontroversial. In fat, the orginal laim would still have stronger support. However, our 158
...... rable 3. lhletial Argument Moves ARG TASKS MOVES GIVEN SHOW support (a) support X-> C->x --C->x A -x x ->- A -x refute C underut C (b) invalid X-> -x anteedent () exeption X-> xay_> - x J- Y (d) inappliable x->- Y->- evidene A -x Y (e) unneeded C->x Y->x explanation AY rebut C (f) redutio ad C-->z absurdum A-z (g) rival x->- support (h) missing X-> support A-x (i) rival -C->x impliation 159
initial argument ould be defeated by the argument that penguins are an exeptional sort of bird that does not fly. This would leave our laim that penguins fly with no positive support and a strong argument against. When a side is in ontrol of the argument proess, it must selet whih argument move to apply next from a set of possible moves. Heuristis that serve to order argument moves for seletion are meant to reflet two goals: generate the strongest arguments possible for the ative side and generate oherent arguments that are responsive to those put forward by the other side. As suh, agument moves are ordered, as follows: (a) valid reasoning steps are preferred over plausible steps; (b) moves that are defeating are preferred over moves that only make a laim ontroversial; () moves that attak a supporting argument loser to the overall laim are preferred; and (d) underutting moves are preferred over rebutting moves. Warrants are also ordered aording to the following riteria: (a) speifi warrants (i.e., those with more anteedents) are preferred over more general warrants; (b) stronger warrant types are preferred; and () warrants for whih the anteedent urrently has no known ontraditory support are preferred. These ordering heuristis antiipate moves that the other side may use in trying to refute a laim. Strong reasoning steps are more diffiult to defeat; those loser to the root laim leave fewer opportunities for alternative support; defeating arguments eliminate ontroversial elements; weaker reasoning types allow more opportunities for defeating refutations. Controversial or negated data an be used to support a laim weakly at best. This ompletes an overview of the basi elements of our model of dialetial argumentation. Given a set of warrants, some input data, a laim, and a burden of proof, our system proeeds to generate a dialetial argument, both struture and proess. Control swithes from side to side as hek onditions, i.e., suffiient refutations for a given burden of proof, are realized. Deiding whih moves are suffiient to generate a hek ondition for a partiular side, when an argument proess is omplete, and who wins, all depend upon a given burden of proof. BURDEN OF PROOF Now we turn our attention to the definition of burden of proof and disuss its impat on argument generation and outome deision. There are two elements to the notion of burden of proof as we will define it: (1) whih side of the argument bears the burden; (2) what level of support is required of that side. As we onsider only two sides to an argument (for and against the input laim), we assume that Side-1 always bears the burden of proof for the input laim, whih might be stated as the negation of a proposition. One ontext in whih the notion of burden of proof has been defined historially and applied formally is the legal domain, Different burden of proofs are mandated at different stages of the legal proess and for different types of legal ation. For example, the arguments required to indit someone need not be as onvining as those needed to onvit; the arguments needed to onvit in one type of trial need not be as strong as those needed to onvit in another type of trial. The higher the ost of being wrong, the more strit are the requirements that should be imposed. A defendable argument is one that annot be defeated with the given warrants and input data. This has been alled a plausible argument (Sartor, 1993). We define the following levels of support: sintilla of evidene (se) at least one weak, defendable argument 8preponderane of the evidene (pe) at least one weak, defendable argument outweigh the other side s arguments dialetial validity (dv) at least one redible, defendable argument defeat all of the other side s arguments beyond a reasonable doubt (brd) at least one strong, defendable argument defeat all of the other side s arguments beyond a doubt (bd) at le~t one valid, defendable argument defeat all of the other side s arguments Burden of proof plays several roles in the proess of argumentation: (i) as basis for deiding relevane of partiular argument moves; (ii) as basis for deiding suffiieny of a side s move (i.e., whether a hek ondition has been realized); (iii) as a basis for delaring an argument over; and (iv) as a basis for determining the outome (i.e., deision or winner) of an argument. For example, if we have imposed a burden of proof of dialetial validity and Side-2 has presented an argument refuting Side- 1 s laim, Side- 1 annot merely find another argument supporting the input laim; Side- 1 must defeat the refutation or onede the argument. However, if the burden of proof were only preponderane of the evidene, then another argument in favor of the 160
laim by Side-1 ould be suffiient to outweigh Side-2 s rebuttal. For a burden of proof of beyond a reasonable doubt, Side-1 must find an initial argument based upon valid appliation of a suffiient or default warrants; otherwise, it must onede defeat without Side-2 even needing to make a move, as strong support must be found for the input laim under this burden of proof. LEGAL REASONING EXAMPLES The soure of inspiration for inluding burden of proof in our model of argumentation omes from the legal domain. Western legal proess has long relied on this notion as a means for making deisions in unertain, onfusing, or ontraditory ontexts. We demonstrate our model of argument and burden of proof by onsidering two examples that have previously appeared in the AI and legal reasoning literature. The first problem, whih has been used to demonstrate appliation of default and rule-based reasoning in a legal ontext, is from (Prakken, 199 1). The knowledge from the problem is represented by the following warrants and data: (w1 ((loose briks)) --> ex df ((maintenane defiieny)) (!? GIVEN)) (w2 ((maintenane defiieny)) --> ex df ((landlord responsible)) (!? GIVEN)) (w3 ((landlord responsible))--> exs ((not (tenant responsible))) (!? GIVEN)) (w4 ((loose briks)(near road)) --> ex df ((danger)) (!? GIVEN)) (w5 ((danger)) --> ex df ((tenant responsible)) (!? GIVEN)) (w6 ((loose briks)(near road)(seldom used)) --> ex df ((not (danger))) (!? GIVEN)) (dl (loose briks) (!? GIVEN)) (d2 (near road) (!? GIVEN)) (d3 (seldom used) (!? GIVEN)) (laim (landlord responsible) (?? NIL)) That is, loose briks in a rental unit are usually a maintenane defiieny, and taking are of maintenane defiienies is usually the responsibility of the landlord, not the tenant. However, if the loose briks are near a road, they onstitute a danger; the tenant, not the landlord, is usually responsible for any danger. However, loose briks near a road that is seldom used is usually onsidered not be onsidered a danger, In this ase, there were loose briks near a road, and the road was seldom used. Who s responsible? Side- 1 is able to find strong support for the input laim (landlord responsible) through MP appliation of warrants w 1 and W2 based on input data dl, However, Side-2 an refute this argument by finding an argument for the negation of the input laim, showing that loose briks near a road onstitute a danger, for whih the landlord is not responsible (i.e., using warrants W4 and W5 and an MT appliation of the suffiient warrant W3). But this argument an be underut and defeated by Side-1, whih an show that the data d3 in the urrent situation mathes the onditions of warrant w6, a more speifi exeption to the W2 default rule as to danger, Warrant W6 an be used to show that loose briks near a road that is seldom used do not onstitute a danger after all. Side-2 s argument for there being danger is thereby defeated, reinstating the original argument that the landlord is responsible as the dominant argument. At this point, Side-2 an generate no more ounterarguments; Side-1, having defended a strong argument for the landlord responsibility, will win this argument for any proof level up to and inluding beyond a reasonable doubt. Note that if the burden of proof on Side-1 had been sintilla of evidene, Side-2 would not have attempted its one refutation; even if suessful, it would not have been strong enough to defeat Side- 1 s argument outright, as would have been needed for Side-2 to win the argument at this proof level. On the other hand, if the burden of proof on Side- 1 had been beyond a doubt, Side-1 would have oneded the argument immediately, as there are no suffiient warrants available to support the input laim with valid qualifiation. If we onsider the ounterlaim, i.e., (not (landlord responsible)), as the input laim, Side-1 ould generate a supporting argument based on warrants w4, w5, and W3 as above, with input data dl and d2. But, as we have seen, W4 an be defeated by w6. Side-1 would have no other argument for (not (landlord responsible)) and would have to onede. We see that the laim (not (landlord responsible)) annot be established with even a sintilla of evidene. Suppose we onsider that the input evidene about the road being seldom used is only hearsay and at best an be given a qualifiation of redible, This would hange the input now to inlude (dl (seldom used) (+? GIVEN)). In this ase, the underutting argument by Side-1 using warrant W6 would not be onsidered a defeating argument; it is of lower qualifiation than the argument it is attaking. However, it still serves to make the laim (danger) ontroversial by providing support 161
for its negation; this would weaken Side-2 s ounterargument, leaving the input laim with the qualifiation (!- +). Side- 1 has no way of outright defeating Side-2 s ounterargument. Thus, in this ase, Side- 1 an only win arguments up through preponderane of the evidene. With this input, the ounterlaim (not (landlord responsible)) now ould win with a burden of proof of sintilla of evidene, as well; Side-1 an only make its initial argument at most ontroversial. In the our seond example, adapted from (Marshall, 1989), we show how the argument model deals straightforwardly with inonsistent information and no defeating exeption. We onsider the following, initial knowledge regarding the ase: (w1 ((burglar)) --> exs ((felon)) (!? GIVEN)) (w2 ((fleeing suspet) (felon)) --> ex df ((deadly fore reasonable)) (!? GIVEN)) (w3 ((not (apprehension possible))) --> ex df ((deadly fore reasonable)) (!? GIVEN)) (w4 ((two offiers present)) --> ex df ((apprehension possible)) (!? GIVEN)) (dl (burglar) (!? GIVEN)) (d2 (fleeing suspet) (!? GIVEN)) (d3 (not (armed suspet)) (!? GIVEN)) (d4 (private residene) (!? GIVEN)) (d5 (unoupied residene) (!? GIVEN)) (d6 (C ten dollars taken) (!? GIVEN)) (d7 (two offiers present) (!? GIVEN)) (laim (deadly fore is reasonable) (?? NIL)) Aording to the warrants given, a burglar is, by definition, a felon. When pursuing a fleeing felon or when apprehension is not possible, the use of deadly fore is reasonable. When two offiers are present, non-violent apprehension is usually possible. In the given situation, an unarmed burglar is fleeing from an unoupied, private residene, from whih less than ten dollars has been stolen. There are at least two offiers available to stop the burglar, Is deadly fore reasonable in this ase? Side-1 is able to make a strong argument for the input laim (deadly fore is reasonable) based on MP appliations of warrants w 1 and W2 with input data d 1 and d2. Side-2 an respond only with an argument based on MP appliation of W4 followed by plausible, ABC appliation of warrant w3, leading only to weak support for the ounterlaim. Under all burdens of proof, Side-2 would onede the argument prior to generating the above argument, as the burden of proof would filter the moves leading to its generation. Warrant W2 is meant to reflet the import of a Tenessee law intending to disourage felons from fleeing the sene of a rime. The law gives polie free reign to use deadly weapons as means to stop them. The U.S. Supreme Court felt the rule was open to abuse and ontrary to the intent of federal statutes requiring some indiation of threat of danger to property, the publi, or the polie prior to allowing the use of deadly fore. Suppose we now hange W2 to w2 to reflet this perspetive and add W5 as one of several, possible supporting warrants, as follows: (w2 ((dangerous suspet) (fleeing suspet) (felon)) --> ex df ((deadly fore reasonable)) (!? GIVEN)) (w5 ((armed suspet)) --> ex ev ((dangerous suspet)) (!? GIVEN)) In this ase, Side-1 an not even generate an argument in favor of the input laim and thus an win no argument at any proof level. If the laim is hanged to the ounterlaim, Side-1 then has two weak arguments. One is based on ABC appliation of warrant W3 as disussed above, and the other is based on ABC appliations of both W5 and then w2, i.e., (not (armed)) leads to (not (dangerous)), whih supports (not (deadly fore reasonable)). Note that support for the negation of only one proposition of a onjuntive ondition allows ABC appliation of the warrant. Thus, the ounterlaim of deadly fore not being reasonable an win sintilla of evidene arguments. This argument setting is obviously highly ontroversial; neither side an generate strong arguments in its favor. This leaves suggests the opportunity for introdution of new warrants providing arguments in support of either side. The use of dynami sets of warrants, where new warrants an be introdued (as is often done during legal arguments), is an element of argumentation yet to be addressed by our model. RELATED RESEARCH There has been inreasing interest in formal models of argumentation in both the artifiial intelligene and legal reasoning ommunities. We have referred to some of that work above. The notion of interargument defeat has been addressed by several reent efforts. The idea of more speifi arguments viewed as exeptions, and thus defeaters, has been pursued by Poole 162
(Poole, 1985) and adopted by others (Prakken, 1991, Loui, et.al., 1993). We ontinue that notion, inheriting this general approah to defeating arguments. Sine we allow unsound, weak reasoning steps to be applied, we have other opportunities for defeating arguments. Any ounterargument based solely on MP reasoning steps, regardless of qualifiation on the links, is seen as suffiient to defeat an unsound, weak argument. As suh, a weak arguments is fragile, but may prove to be ruial if left unanswered. In other related researh, the work of Sartor (Sartor, 1993) omes losest to apturing our various notions of proof level. He defines a plausible argument to be one with no defeating ounerargument. This would be an argument suffiient to win a sintilla of evidene argument for a partiular laim. He then desribes a justifying argument as a plausible argument for a laim and no plausible argument for its ounterlaim or negation, This is what we require of a dialetially valid argument. Prakken introdues related onepts as well (Prakken, 199 1). Neither explore the appliation of burdsen of proof an different proof levels as an element of ontrol for generating oherent, dialetial argument proesses. They assume all arguments are generated and then uses these relationships to prune these sets or ontrast ompeting arguments. CONCLUSION We see that burden of proof is a partiularly useful aspet of a omputation model of argumentation as a basis for pratial reasoning in the legal domain. Our model omprises both argument as supporting explanation and argument as dialetial proess. It inorporates other features appropriate for reasoning in weak theory domains, inluding plausible inferene and unertainty representation. We demonstrate the appliation and impats of different burden of proof levels in two simple, legal argument ontexts. Our model of dialetial argumentation has been implemented and evaluated on a signifiant number of lassi reasoning problems in weak theory domains, inluding those disussed here. The model as implemented exhibits reasonable behavior when applied to these benhmark examples taken from formal argumentation and artifiial intelligene researh (Freeman, 1993). We hope our model an serve as a framework for further exploration of argumentation as a means for pratial and legal reasoning. We are investigating several extensions to the model, inluding addition of a new warrant type ase that will inorporate elements of ase-based reasoning. Suh warrants would have fats of prior ases as anteedents, with onlusions representing ase outomes. A partiular ase may give rise to multiple warrants, representing various, differing interpretations of the reasoning or outome of a ase (Ashley, 1989). To reflet adequately the way ases are used in arguments, partial mathing and mathing by analogy on the struture of fat sets involved would have to be allowed (Branting, 1989). How this would interat with warrant qualifiations and burden of proof to generate typial argument strategies involving ases (Rissland, 1985; Skalak and Rissland, 1993) poses further, interesting researh questions, As in the seond example disussed above, where the federal law takes preedene over state statute, giving differing weights or preferenes to warrants (beyond that of qualifiation) is another diretion for exploration. This fator has been used by a number of reent researhers, who put expliit, hierarhial preferenes on warrants (Loui et. al, 1993; Prakken, 1993; Sartor, 1993). Combining these new modelling apabilities with a generalized definition of burden of proof in a dialetial, proess model of argumentation would signifiantly advane efforts toward an adequate model of legal argumentation and deisionmaking. REFERENCES Ashley, K. (1989) Toward a omputational theory of arguing with preedents: Aommodating multiple interpretations of ases. Proeedimzs of ICAIL-89, 93-102. Branting, K.L. (1989) Representing and reusing explanations of legal preedents, P~, 103-110. Freeley, A. (1990). Armmentation and debate: Critial thinkinz for reasoned deision making (7th d.). Belmont, CA: Wadsworth Publishing Company. Freeman, K. (1993). Toward Formalizing Dialetial Am umentation. PhD Dissertation, Department of Computer and Information Siene, University of Oregon. 163
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