Journal of Logic, Language, and Information 9: 379–387, 2000.

379

Book Review

Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law, Henry Prakken, Law and Philosophy Library, Volume 32, Dordrecht: Kluwer Academic Publishers, 1997. Price: NLG 242.00/USD 147.00/GBP 96.95, xiv + 314 pages, ISBN: 0-7923-4776-5.

Introduction Research on Artificial Intelligence (AI) and Law began to flourish in the eighties. AI and Law is a hype, especially in The Netherlands. It started with the Ph.D. Thesis “Logical Tools for Modelling Legal Argument” of Henry Prakken (1993). For many researchers, this thesis seemed to be an inspiration for their own research and they often referred to this work. This is easily demonstrated by the large number of dissertations in the AI and Law field that were published after Prakken’s thesis: Smith (1994); Van Kralingen (1995); Visser (1995); Den Haan (1996); Royakkers (1996); Verheij (1996); Van der Torre (1997); De Vey Mestdagh (1997); Leenes (1998); and Lodder (1998). All these dissertations roughly deal with the theme of the possibilities of mechanising legal reasoning. Interest in the field of AI and Law is not surprising if we take into account the development of nonmonotonic logics, which really took off after the early eighties. The restriction of classical logic was felt in the AI field. An important objection was that knowledge representation is “commonsense reasoning,” which cannot directly be represented by classical logic due to its monotonic nature (i.e., if a conclusion follows from a set of premises, then that conclusion also follows when extra premises are added).? In daily life, people seldom express themselves in a truly formal way. Human reasoning often contains steps that have a certain degree of uncertainty, as the information available is not always complete, reliable or consistent. Evidently, these problems also occur in legal reasoning. The Argentinians Carlos E. Alchourrón and Eugenio Bulygin, who became famous with their fundamental work Normative Systems (1971), hit upon the fact that legal systems had severe drawbacks concerning accuracy which cannot be dealt with in classical logic. This opinion rings throughout their view regarding inconsistency (1981): It is interesting to observe that lawyers (not contaminated by philosophy) readily accept the possibility of contradictions in law. This is shown by the fact that there are old, traditional principles designed to solve such conflicts. The principles lex posterior, lex superior and lex specialis would have no application at all if there were no inconsistencies in legal dispositions. The very fact that lawyers often resort to such principles shows at least that they believe that normative contradictions are quite possible. (. . . ) But it would be a mistake to regard the rules of preference (traditional or not) as logical rules (p. 114) and by Bulygin regarding incompleteness (1976): Covering the gaps in the law (supplements to law) is an important problem in practice. Jurists make use of a whole battery of rules that function as argumentation rules: the argumentum a ? Cf. Meyer (1989).

380

BOOK REVIEW

fortiori, analogy reasoning, the a contrario argument, etc. It is important to realise that none of these rules is a valid conclusion rule. Valid conclusions can only be drawn if silently accepted premises are taken into account. With purely logical tools we cannot fill the gaps of an incomplete legal system (p. 621). Alchourrón and Bulygin are of the opinion that these problems can be solved “only with the help of modern logic.” Nonmonotonic reasoning methods can be valuable tools to fill the gaps of an incomplete or inconsistent legal system. The advantage of these methods is that they can infer tentative (and logically unsound) conclusions that have to be withdrawn when new facts contradict them. Furthermore, the methods can be used in reasoning by default: if there is no indication to the contrary, an assumption is made for the time being, since this holds “almost always” (common-sense reasoning). In the book Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law, Prakken shows how nonmonotonic reasoning methods have made it possible to give a logical analysis of two aspects of legal reasoning: defeasible reasoning and reasoning with inconsistent information, which cannot be dealt with in classical logic. In this book review, I shall discuss Prakken’s book, which is a revised and extended version of his Ph.D. Thesis. First, I will give a summary of the book, and then I shall add some critical notes.

The Content In Chapter 1, the aim of the research is explained and an outline is given of the points of departure for the research. One important point of departure is formulated during the discussion of what AI is. [T]here are, roughly, two kinds of AI research, distinguished by their aims: some researchers try to let computer systems perform like intelligent human beings, while others restrict themselves to more practical aims. (. . . ) this book chooses for aims which are close to the practical side of the scale; when it comes to AI, it is not about logical aspects of making really intelligent artificial judges or solicitors but about logical aspects of legal knowledge-based systems: of systems of which a main feature is the separation of knowledge and ways of using it (p. 5). The aim of the research is as follows: [T]he aim of the present investigations is to give a logical analysis of two aspects of legal reasoning which are sometimes held to escape such an analysis: reasoning with defeasible information and reasoning with inconsistent information. (. . . ) [T]he relevance of the present study may be expected to exceed the legal domain, since I shall focus on issues which have also appeared in the general debate on the role of logic in AI (p. 8). Furthermore, the author gives an overview of the discussion in the literature about the role of logic in AI research. This results in two conclusions, which are relevant for his book: [I]t is impossible to make a sharp distinction between procedural and declarative or even between logical and nonlogical knowledge representation language: knowledge representation formalisms have both procedural and declarative aspects, and the importance of logic lies in its ability to analyze the declarative aspects. and [B]oth in case of nondeductive types of reasoning and in case of inconsistent knowledge logic can be useful: what is essential is that logic should be regarded as a tool in a larger framework, which is called reasoning; using logic to represent domain knowledge does not commit at all to a particular way of modelling reasoning: in particular, it does not commit to regarding reasoning as no more than mechanically deriving consequences from a set of logical formulas (p. 12). In Chapter 2, the author starts by removing four misunderstandings about the nature of logic in reasoning in general. The most persistent misunderstanding concerns “the criticism that using logical methods would imply a commitment to some naive, simplistic view on how to do justice”

BOOK REVIEW

381

(pp. 18–19). Prakken refers to the naive view as the naive deductivist view on legal reasoning: “It is the old-fashioned view that the law is consistent and complete body of rules which can somehow be discovered. In this view, all there is to legal reasoning is finding the valid rules and applying them to the facts in a deductive manner” (p. 19).? Prakken clearly explains that using logic to formalise legal knowledge does not commit us to the naive deductive view on how to do justice, since this criticism completely ignores the fact that a valid piece of reasoning does no more than what the possible truth of premises passes on to the conclusion: if the conclusion is not liked for some reason or another, logic stops the judge (or anybody else) from choosing other premises. However, “the untenability of the naive deductivist view on legal reasoning limits the applicability of standard logical methods, for which reason new logical tools are needed” (p. 33) and “the incompleteness, uncertainty and inconsistency of much legal knowledge requires that logic is used in a different way than in this axiomatic view on reasoning: drawing logical inferences should not be seen as a model of, but as a tool in reasoning” (p. 31). This important latter remark serves as the background to the book. The subject of Chapter 3 is the need for new logical tools. Though it may be true that logic offers instruments for reasoning, it is also true that for a large part of this century, logicians have mainly developed instruments for mathematical reasoning. In many respects, mathematical reasoning is far removed from the everyday practice of reasoning. Two aspects of common sense reasoning that are absent in mathematics are distinguished by Prakken. As law must be applied to the open, unpredictable nature of the world and because legislators can never completely estimate which possible situations will make a rule applicable, legal rules are generally formulated rather vaguely. In addition, legal rules often represent a socio-political compromise and this even makes them inconsistent to some extent considering the room left open for disputes in the science of law. Thus legal reasoning often operates on defeasible and inconsistent information. Nevertheless, jurists draw conclusions. Are juridical conclusions justifiable on formal grounds though? Such an analysis is both possible and meaningful according to Prakken, but not with classical logic. The monotonic nature and the ex falso sequitur quodlibet principle of classical logic disallow this. Nonmonotonic reasoning methods therefore seem the obvious choice. In Chapter 4, the author gives an excellent overview of various existing systems of nonmonotonic reasoning, such as the nonmonotonic logic of McDermott and Doyle (1980), the default logic of Reiter (1980, 1987), the auto-epistemic logic of Moore (1985), McCarthy’s (1980) circumscription, Poole’s (1988) framework for default reasoning and Brewka’s (1989) preferred subtheories. Following this overview, some research themes of nonmonotonic reasoning are discussed, including some often cited objections to the development of nonmonotonic logics. One of the objections raised in AI research is that these logics cannot be efficiently implemented in computer programs. Prakken concludes “although in their general form nonmonotonic logics cannot be implemented, they can still serve as a metric for evaluating and criticizing the behaviour of implemented systems” (p. 100). In Chapters 5 and 6 it is verified to what extent the logics (discussed in Chapter 4) prove capable of formalising nonmonotonic reasoning in law. The investigations are based on a distinction between two conceptual methods of dealing with exceptions: the method of using explicit exception conditions – which are assumed false unless the contrary is shown – to obtain unique answers and the method of leaving exceptions implicit and preferring the most specific of two conflicting conclusions. The first method is discussed in Chapter 5. It appears that this can be formulated quite well in most nonmonotonic logics, while simultaneously a reasonably efficient implementation is possible with logic-programming techniques. The advantages of this method only hold if undecided conflicts in standards can be avoided. As soon as a standard cannot be defined as an exception to another in a conflict of standards, this method becomes less usable, for it must supply one answer in all cases without having to resort to a choice. “In particular, attempts to model the adversarial aspect of legal reasoning, need ways of dealing with undecided conflicts without resolving and blocking them. ? In the deductive logical method hypotheses are deduced from a limited number of axioms and/or

rules.

382

BOOK REVIEW

(. . . ) In conclusion, in some applications, ways of dealing with exceptions are needed which allow for undecided conflicts and also for other conflicts resolution principles” (pp. 138–139). Another approach is required for this, i.e., the second method (or choice method), which is the subject of Chapter 6. After a critical investigation of the way in which Poole uses his semantic specificity definition, the author presents his own system for constructing and comparing arguments. The system consists of five elements: 1. An underlying logical language. Prakken shows that in a system for comparing arguments defeasible statements need to be formalised with a non-standard, one-directional conditional operator “⇒.” Therefore, he uses the language of default logic. Defaults are inference rules of the following form: p ⇒ q, which is to be read as follows: if p, and q can consistently be assumed, then q. So defaults “can be used to extend a classical first-order theory containing what is known with formulas that are not classically entailed by the theory but which are nevertheless plausible enough to believe on the basis of what is known” (p. 69). 2. The notion of argument. This corresponds to a proof in the logic of the underlying language. 3. The notion of a conflict between arguments. Two arguments are conflicting if they have contradictory conclusions. 4. The notion of comparing conflicting arguments, to see which arguments defeat which other arguments. 5. The status of arguments. Arguments can be divided into three classes: justified arguments (arguments with which a dispute can be “won”), overruled arguments (with which a dispute can be “lost”) and defensible arguments (which leave the dispute undecided). The last three elements are what makes the system suitable for adversarial argumentation. Prakken first compares conflicting arguments on specificity to define when an argument defeats another argument. The preference of an argument over another is based on a syntactic specificity: the argument with more conditions for its conclusions is more specific and therefore excludes the less specific argument. In other words, if the premises of the one argument are a subset of the premises of the other argument, then the existence of the latter more specific argument excludes the more general one. This can be simply illustrated on the level of rules. For example, p ∧ q ⇒ r is more specific than p ⇒ ¬r, since p can be deduced from p∧q, and since p∧q cannot be deduced from p, p ⇒ ¬r is not more specific than p ∧ q ⇒ r. The consequence is that the more specific rule has priority when both rules can be applied in a certain situation. Prakken extended this idea to arguments. In Chapter 7, the author slightly adapts his system to reasoning with inconsistent but ordered information. Consequently, he introduces hierarchical defeat. Consider rule d1: p ⇒ q and rule d2 ⇒ ¬q with d1 < d2 (rule d1 is more exposed than d2), then d2 is preferred over d1. This is also extended on the level of arguments. In other prioritisation approaches (such as the approach of Alchourrón and Makinson (1981), and Brewka’s (1989) preferred subtheories approach) all the rules of two conflicting arguments are regarded as relevant, which does not always give acceptable results. This can be illustrated by the following example (p. 192): (9) (10) (11) (12)

x misbehaves ⇒ x may be removed x is a professor ⇒ ¬x may be removed x snores ⇒ x misbehaves Bob is a professor ∧ Bob snores (9, 10) < (12); (9) = (10), (11) < (9, 10).

To determine whether Bob may be removed or not, some approaches compare the four maximal consistent sets: E = {9, 10, 11}, F = {9, 10, 12}, G = {9, 11, 12} and H = {10, 11, 12}. For example, according to the approach of Sartor (unpublished paper) F is the best, since it does not

BOOK REVIEW

383

contain the lowest norm (11). In this approach the conclusion is that “Bob may not be removed.” (The same result follows from Brewka’s preferred subtheories approach.) In the system of Prakken only the rules with conflicting conclusions are relevant to the conflict. In his approach [12, 9, 11] is an argument for “Bob may be removed” and while [12, 10] is an argument for “Bob may not be removed.” Since the rules that are responsible for the conflict (i.e., (9) and (10)) are of equal level, no argument is better (defensible arguments). To determine whether an argument is justified, overruled or defensible (the fifth element of Prakken’s system) the author uses the dialectical style for a logical system. In Chapter 8, the author describes a general method for representing priority rules. This is necessary, since a brief look at the legal domain already suffices to see that the hope that we can find useful domain-independent sources of preferences is unrealistic. In law, but also in many other domains of common-sense reasoning, such as bureaucracies, collision rules are themselves part of the domain theory. (. . . ) In, other words, reasoning about priorities is nonmonotonic reasoning. These observations mean that in a logic that is meant to formalize this kind of reasoning, the consequences of a set of premises do not only depend on the priorities, they also determine the priorities. In most current nonmonotonic logics these observations are ignored (p. 203). In Chapter 9, the author compares his argumentation system with other approaches. He concludes that further research is necessary to combine the attractive aspects of all the theories. The strong points of his system seem to be the nonmonotonic nature of the underlying logic; the room there is between justified and overruled arguments for defensible arguments; the possibility for random comparison criteria and the ability to combine such criteria. In Chapter 10, the author discusses some very relevant aspects for the use of the argumentation system, such as the prospects for implementation in computer programs and the role of the system as a tool in modelling legal argument. Chapter 11 contains a summary, conclusions, and suggestions for further research.

Some Critical Notes I will start with a critical note originating from Hage (1997). He states that the argument-based logics “do not specify the nature of the arguments which are to be compared, nor the criteria by means of which they are to be compared” and that they “divide arguments which originally seemed to be one, into basic arguments and arguments about arguments. This seems not so intuitive to me” (p. 245). In his own system – Reason-based logic (a model of the nature of the rules and reasons, which are the basis of argumentation) – the notion of reason takes the central place, and there is a two-step procedure that consists of collecting and weighing reasons which takes place on one and the same level of argumentation. In turn, Prakken supplied some critical notes for this system (pp. 240–247). However, both authors agree about the usefulness of combining both systems. In the argumentation system of Prakken, arguments are not only compared with respect to specificity, but can be compared to any ordering, which is an improvement of other approaches. Moreover, the freedom in language and derivation makes it possible to model almost any comparison between arguments. Although this is certainly an advantage of the system, this is also a serious drawback, since the modeller of the argumentation is hardly guided in his modelling activity. Therefore this system is primarily suited for studying aspects of argumentation in law, and less so for modelling legal reasoning. Recent insights into philosophy, argumentation theory, and the theory of law give reason to centralise the dialectical context of the juridical dispute. Law in casu is often recorded by means of a dialogue. In such a dialogue, the method with which the parties attempt to convince each other by means of appropriate or inappropriate moves is central. In a dialogue, the objective of an argument is not to deduce consequences from certain premises, but to obtain or increase the support of an

384

BOOK REVIEW

audience for the statements put before them for assessment (cf. Perelman, 1963). An argument is convincing if it convinces the person at whom it is aimed. So, the relation between an argument and its conclusion does not need to be (default) deductively valid, as is required in the argumentation system of Prakken. The rhetorical nature of a juridical dispute is completely ignored in the argumentation system. To me it is not clear why Prakken omits to include deontic notions in his argumentation system. He simply could add his article “Two approaches to the formalisation of defeasible deontic reasoning” (1996) to the book for completeness. In that article, arguments with deontic notions are compared. In Chapter 11, he refers to the article with the following comments: “[I]t should be noted that, although in my system the underlying logical language is first-order predicate logic plus defaults, there is no reason why the first-order part cannot be extended to modal logics” (p. 283). This is a little naive. In an article by Royakkers and Dignum (1997), we show that deontic defeasibility should be seen as a different kind of defeasibility (distinct from the normal alethic defeasibility), since the comparison of arguments for non-deontic rules is different from the comparison of arguments for norms. In the definition of defeating, only the rules with conflicting conclusions are considered. This does not hold for norms. For example, suppose we have the following three rules: (1) p ⇒ r, (2) O¬r (it is obligated that not-r) and (3) Op (it is obligated that p). In this case, there are no explicit conflicting conclusions, but from the rules (1) and (3), we can derive (in a default deductive system) Or which conflicts with rule (2). So, in the comparison of arguments for norms, we cannot only look to the conflicting conclusions, but we also have to look at the group statements deriving the conflict. Prakken’s definition of defeating raises questions with regard to its application in law. (1) A necessary condition for defeating is attacking: “two arguments must be defined as attacking each other iff they have conclusions that together with the necessary facts are inconsistent” (p. 157).? In other words, the requirement of contradiction between conclusions. However, there are many nonconflicting arguments for which a priority relationship applies. Consider the following very simple example: An emergency service vehicle driver A approaches a junction, where car driver B approaches from the right. According to section 15 of the Dutch Traffic Regulations 1990, A has to give way to B, who is approaching the junction from the right. Also, according to section 50, B has to give way to A as well, since drivers have to give way of emergency service vehicles. In a juridical sense, there is a nonexplicit specialis between section 15 and section 50. However, in a logical sense, there is no contradiction between the conclusions of these two rules; there is a deadlock: both drivers have to yield right of way. Section 15: x and y approach a junction ∧x approaches from the right ⇒ y has to give way to x. Section 50: y is an emergency service vehicle ⇒ x has to give way to y. One may argue that there is a contradiction regarding the principle of trust:?? the duty (obligation) of one means the right of the other. On the grounds of the rule in section 15 and the principle of trust, A has right of way, and B does not; on the grounds of the rule of section 20 and the principle of trust, B has right of way, and A does not. In this formulation A both has right of way and has not, we can deduce a contradiction. However, not in the theory of Prakken, since the principle of trust is not a necessary fact. Another example is the nonexplicit specialis relationship between tort and an unlawful act. There are countless examples of this. The use of the definition of attacking demands the addition of a meta-rule (or rule of interpretation) – such as the principle of trust – in which the contradiction is made explicit. (2) Defeating with respect to specificity takes place on the grounds of a comparison of the elements and structure of conflicting arguments. The definition requires that in all cases in which an argument is more specific than another argument, the collection of premises of the arguments overlap ? Necessary facts are necessary truths, such as “a man is a person.” ?? “Trust” here means that a road user can, in princicple, expect the other road users to observe the

rules.

BOOK REVIEW

385

each other and their conclusions are contradictory. In nearly all cases the required overlap makes the choice necessary for a similar method of formalisation of conditions formulated in various ways in legislation or the explicitation of implicit conditions. Now the above example will be formalised as follows:? Section 15: x and y approach a junction ∧x approaches from the right ⇒ y has to give way to x. Section 50: x and y approach a junction ∧x approaches from the right ∧y is an emergency service vehicle ⇒ x has to give way to y. In this example, this means that the formalisation of section 50 is based on the prior determination of a possible conflict, which is not expressed in the original working of the rule. This kind of determination is nearly always based on a completed discussion about the specificity relationship between the rules in question in the argumentation system of Prakken. “In all these cases it is simpler to indicate this relationship explicitly by means of meta-rules than to first bring about a partial uniformity of the rules and then to again conclude a specificity relationship on the basis of this uniformity” (De Vey Mestdagh, 1997: 92). Fortunately, in Chapter 8, Prakken initiates the extension of his system with meta-rules for representing priority rules as Lex Superior, Lex Specialis and Lex Posterior, which can overcome the above problem. With the priority rules, lawyers can avoid inconsistencies. Besides these syntactic inconsistencies, we also have semantic inconsistencies. The latter are related to the interpretations of legal concepts, especially open texturedness. Judges and legal experts have developed all sorts of interpretative methods, including literal, historical, and teleological methods. Next to these there are numerous other methods. In this way, a judge can move beyond books of law or legislation and turn to society to make a decision that is most desirable socially (a sociological method). It is also possible that the judge opts for the most equitable solution (an ethical method). By using different interpretative methods, one can reach different conclusions. Consequently, we are left with the personal choice of the judge. This choice is determined by his own opinion of what is most acceptable to society. His opinion is frequently determined by his moral beliefs. Thus, justice becomes more like careful guessing than like (nonmonotonic) logic. However, Prakken states that interpretation debates can be formalised in his argumentation system (pp. 216–217). This statement is not very convincing, since Prakken has to add several very simplifying assumptions (which emphasises again that the modeller of the argumentation is hardly guided in his modelling activity) to come to a formalisation. An assumption is that there is a rule on the priority of alternative interpretation methods. Although Prakken is aware of the fact that this is a matter of dispute in practice, the central point of the formalisation of an interpretation debate is exactly this dispute. And this dispute —which cannot be formalised – is relevant for the outcome of the debate. By defining only an (at random) ordering on interpretation methods, one cannot state that an interpretation debate can be formalised. Take the example above and assume that driver A is on a major road. According to the right-of-way signs the emergency vehicle driver B has to give right of way: ?? Right-of-way sign: x and y approach a junction ∧x is on a major road ⇒ y has to give way to x. Section 50: y is an emergency service vehicle ⇒ x has to give way to y. Section 63 solves this conflict: traffic signs override traffic rules in as far as specific rules are incompatible with specific signs. This means that “section 50 < right-of-way sign.” So, on the basis of section 63, B has to yield to A: a systematic interpretation. However, one can also argue that the intention of section 50 is that emergency vehicles drivers should always have right of way: a teleological interpretation, which results in “right-of-way sign < section 50.” Which interpretation must be applied is a “matter of dispute” and the outcome of this dispute depends on a personal choice of the judge, which cannot be formalised by (nonmonotonic) logic. ? Assuming that the “deadlock” is considered as a contradiction. ?? Assuming again that the “deadlock” is considered as a contradiction.

386

BOOK REVIEW

Conclusion Playing rigid formal logic off against a free informal argumentation theory is the gratuitous provocation of a senseless battle of methods (cf. Grice, 1975). It is far more interesting to know how much logical validity can be reconstructed in legal reasoning and how this can be accomplished. Prakken has shown that new logical tools (such as nonmonotonic logic) can contribute to a logical analysis of reasoning with defeasible and inconsistent information. Jurists interested in their own reasoning will be surprised about the opportunities logic presents as a problem-solving tool and at the same time they will be aware of the obstinated misunderstandings about logic. For these reasons I propose that every lawyer has to take note of this book, especially the first three chapters. The technical density of the other chapters could stand in the way of the reading by lawyers. These chapters are very interesting for logicians and researchers in the field of AI with respect to modelling nonmonotonic reasoning. The contribution of Prakken is certainly a progress in providing formal foundations of AI research. In spite of the critical notes, I am in total agreement with Loui, who wrote the following about Prakken’s Ph.D. thesis (which certainly holds for this work): He has written the best, most technically detailed, and fairest survey of the formal work on argument and defeasible reasoning. Anyone hoping to do mathematical work in this area should take note (p. 148). However, I doubt the usefulness of Prakken’s argumentation system in legal practice. The interesting issues of a legal case cannot be described or formalised in his system, such as the qualification of the facts or the selection and/or interpretation of the rules (cf. Smith, 1994). Such issues mostly are the focus of legal cases that come before court. In the argumentation system of Prakken, these issues are considered as assumptions.

References Alchourrón, C. and Bulygin, E., 1971, Normative Systems, Vienna: Springer-Verlag. Alchourrón, C. and Bulygin, E., 1981, “The expressive conception of norms,” pp. 95–124 in New Studies in Deontic Logic, R. Hilpinen, ed., Dordrecht: Reidel. Alchourrón, C. and Makinson, D., 1981, “Hierarchies of regulations and their logic,” pp. 125–148 in New Studies in Deontic Logic, R. Hilpinen, ed., Dordrecht: Reidel. Brewka, G., 1989, “Preferred subtheories: an extended logical framework for default reasoning,” pp. 1043–1048 in Proceedings of the Eleventh IJCAI, N.S. Sridharan, ed., Detroit, Michigan. Bulygin, E., 1976, “Logische Fragen der Gesetzgebungstechnik,” pp. 612–627 in Studien zu einer Theorie der Gesetzgebung, J. Rödig, ed., Berlin: Springer-Verlag. den Haan, 1996, “Automated Legal Reasoning,” Ph.D. Thesis, University of Amsterdam. de Vey Mestdagh, C.N.J., 1997, Juridische Kennissystemen Rekentuig of Rekenmeester? Het Onderbrengen van Juridische Kennis in een Expertsystem voor het Milieuvergunningenrecht, Deventer: Kluwer Academic Publishers. Grice, H.P., 1975, “Logic and conversation,” pp. 41–82 in Syntax and Semantics, Vol. III, Speech Acts, P. Cole and J. Morgan, eds., New York: Academic Press. Hage, J.C., 1997, Reasoning with Rules. An Essay on Legal Reasoning and Its Underlying Logic, Dordrecht: Kluwer Academic Publishers. Leenes, R.E., 1998, “Hercules of Karneades,” Ph.D. Thesis, Twente. Lodder, A.R., 1998, “DiaLaw. On legal justification and dialog games,” Ph.D. Thesis, Maastricht. Loui, R.P., 1995, “Book review: Foucault, Derrida, women’s speaking justified, and modelling legal argument,” Artificial Intelligence and Law 3, 143–150. McCarthy, J., 1980, “Circumscription – A form of nonmonotonic reasoning,” Artificial Intelligence 13, 27–39. McDermott, D. and Doyle, J., 1980, “Non-monotonic logic I,” Artificial Intelligence 13, 41–72.

BOOK REVIEW

387

Meyer, J.-J.Ch., 1989, “Formal methods in knowledge representation,” Nieuw Archief voor Wiskunde Serie 4 7, 205–213. Moore, R.C., 1985, “Semantical considerations on nonmonotonic logic,” Artificial Intelligence 25, 75–94. Perelman, Ch., 1963, The Idea of Justice and the Problem of Argument, London: Routledge & Kegan Paul. Poole, D.L., 1988, “A logical framework for default reasoning,” Artificial Intelligence 36, 27–47. Prakken, H., 1993, “Logical tools for modelling legal argument,” Ph.D. Thesis, Vrije Universiteit Amsterdam. Prakken, H., 1996, “Two approaches to the formalisation of defeasible deontic reasoning,” Studia Logica 57, 773–790. Reiter, R., 1980, “A logic for default reasoning,” Artificial Intelligence 13, 81–132. Reiter, R., 1987, “Nonmonotonic reasoning,” Annual Reviews of Computer Science 2, 147–186. Royakkers, L.M.M., 1996, “Representing legal rules in deontic logic,” Ph.D. Thesis, Tilburg. Royakkers, L.M.M. and Dignum, F., 1997, “Defeasible reasoning with legal rules,” pp. 263–286 in Defeasible Deontic Logic, D. Nute, ed., Dordrecht: Kluwer Academic Publishers. Smith, M., 1994, “Legal expert systems: Discussion of theoretical assumption,” Ph.D. Thesis, Utrecht. van der Torre, L., 1997, “Reasoning about obligations. Defeasibility in preference-based deontic logic,” Ph.D. Thesis, Rotterdam. van Kralingen, R., 1995, Frame-Based Conceptual Models of Statute Law, The Hague: Kluwer Law International. Verheij, H.B., 1996, “Rules, reasons, arguments, formal studies of argumentation and defeat,” Ph.D. Thesis, Maastricht. Visser, P.R.S., 1995, Knowledge Specification for Multiple Legal Tasks: A Case Study of the Interaction Problem in the Legal Domain, The Hague: Kluwer Law International. L.M.M. Royakkers Department of Philosophy and Methodology Faculty of Technology Management Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands E-mail: [email protected]