Donald Nute (ed.), Defeasible Deontic Logic

Artificial Intelligence and Law 8: 75–91, 2000. 75 Book Review Donald Nute (ed.), Defeasible Deontic Logic. Synthese Library, Vol. 263, Kluwer Academic Publishers: Dordrecht, 1997. ix + 354 pages. ISBN 0-7923-4630-0. Deontic Logic and Legal Ontology The book under review here, Defeasible Deontic Logic, consists of thirteen papers and an introduction, dealing with the combination of the two themes deontic reasoning and defeasible reasoning. Many of the papers are quite technical and although some of the authors are familiar in the AI & Law community, the question why workers in this field should pay attention to the book deserves an explicit answer. The very first issue of the Artificial Intelligence and Law journal contains a paper by Andrew Jones and Marek Sergot (1992). In this paper, the authors argue that deontic logic ‘needs to be taken seriously whenever it is necessary to make explicit, and then reason about, the distinction between what ought to be the case and what is the case . . . ’. I readily agree that in the law it is often necessary to reason about what ought to be the case, and about what ought to be done if what is actually the case is not as it ought to be. Nevertheless, I fail to see why we need deontic logic to deal with this kind of issue. The distinction between what is the case and what ought to be the case can very well be made and reasoned about without recourse to deontic logic. In the same paper the authors also address another topic, namely the topic of normative positions. Such normative positions include being under an obligation, having a right, being entitled, etc. (see e.g., Hohfeld, 1913; Lindahl, 1977; Allen and Saxon, 1993). The study of these positions and their mutual relations is a study of basic (legal) ontology, and includes the study of the relations between what ought to be done, what is permitted, and what is obligated. In short, the central topics of deontic logic are part of the study of normative positions, which is in turn part of legal ontology. In my opinion, deontic logic is important for the field of AI & Law, because it provides a crucial part of legal ontology. The study of the logical relations between deontic sentences requires the development of a conceptual ap- 76 BOOK REVIEW paratus that is an important contribution to legal ontology. The papers in Defeasible Deontic Logic aptly illustrate this point. Prima Facie Obligations It is sometimes felt that deontic reasoning is somehow more defeasible than ‘normal’ reasoning, whatever normal reasoning may be. Two phenomena explain this feeling, namely the occurrence of so-called prima facie obligations, and the occurrence of contrary to duty (CTD) obligations. The name ‘prima facie obligations’ derives, to my knowledge, from Ross (1930, p. 19). Ross suggests to use the expression ‘prima facie duty’ to refer ‘to the characteristic (quite distinct from that of being a duty proper) which an act has, in virtue of being of a certain kind (e.g., the keeping of a promise), of being an act which would be a duty proper if it were not at the same time of another kind which is morally significant. Whether an act is a proper or actual duty depends on all the morally significant kinds it is an instance of’. Ross continues to explain that the phrase ‘prima facie duty’ is to some extent misleading. This is, first, because a prima facie duty is not really a duty, but rather an aspect of an act that is relevant for making the performance of that act a duty. And second, it is because its being a prima facie duty is an objective aspect of the act, and not only a seeming one. For instance, if I promised to visit my friend, I have the prima facie obligation (to use the modern terminology) to visit my friend. If a particular instance of visiting my friend involves violating a curfew, I also have the prima facie obligation not to perform that act, stemming from the general prohibition to violate the curfew. One act token belongs to two action types, one of which is obligatory and the other one of which is prohibited. Each type to which the concrete act belongs provides an aspect that is relevant for judging the deontic status of the act. A conclusion based on merely one of the two aspects is defeasible in the light of the act’s having the other aspect too. The exposition of Ross makes it clear that the prima facie character of obligations relates to action types, while being actually obligated is a characteristic of act tokens. It seems to me that an obligation can also be prima facie for another reason. There may be circumstances in a particular case that make that the deontic status of an action type to which a concrete act belongs is not inherited by the act, while these circumstances do not involve that the act belongs to a type with a different deontic status. For instance, if I promised to visit a friend, my act of visiting this friend is prima facie obligatory as an instance of promise keeping. If my friend has released me from my promise, however, or if my promise was made under duress, my act is not actually obligatory. Still, the release or the duress are not reasons why I ought not perform the act, but merely reasons that block the relation between the deontic status of the action type (promise keeping) and the act token (the actual visit) that belongs to this type. The first case of prima facie obligation has colliding reasons that plead for and against the obligatoriness of the BOOK REVIEW 77 act. If a promise was made under duress, there is an exclusionary reason that blocks the operation of the principle that promises ought to be kept. The visit was never obligatory. The release from a promise, finally, is a cancelling condition that takes away the obligatory nature which the act originally had (see Hage, 1997, pp. 15f.) 1. Contrary to Duty Obligations Another phenomenon which has given rise to the idea that deontic reasoning is especially defeasible is the occurrence of so-called CTD obligations. It takes some explanation to illustrate this. The traditional Kripke-style semantics for deontic logic defines what is obligatory as that what is the case in all deontically preferred or ideal worlds. The so-called Chisholm paradox (Chisholm, 1963) brings some problems with this approach to the light. The paradox is presented by means of four sentences, the ‘Chisholm set’, which are apparently consistent, but are inconsistent under the traditional semantics: THE CHISHOLM SET A ought to assist his neighbours. If A assists his neighbours he ought to call them. If A does not assist his neighbours he ought not to call them. A does not assist his neighbours. In an ideal world, A both assists his neighbours and calls them. That is, A ought to assist and call his neighbours. In the actual world A does not assist his neighbours, and therefore should not call them. So A both ought and ought not to call his neighbours. This inconsistency is brought about by the feature of the traditional semantics that it both validates deontic detachment (derive #(Call) from #(Assist → Call) and #(Assist)) and factual detachment (derive #(∼Call) from ∼Assist → #(∼Call) and ∼Assist). Deontic detachment is validated by the intuition that deontic reasoning deals with what is ideally the case. Clearly, in the ideal case A would call his neighbours to inform them that he will come to their assistance. Factual detachment is validated by the intuition that what ought to be done depends on what is actually the case. Actually, A does not assist his neighbours and therefore should not call them. The two intuitions presuppose a different role for deontic logic, namely, reasoning about what is ideally the case, and reasoning about what ought to be done in the real world. These two roles are hard to reconcile in one logic, unless the logic combines the two kinds of reasoning in different parts. The paper by Carmo and Jones in the present volume provides such a combination logic. Nevertheless, many have attempted to do what is, in my opinion, undoable and this has lead to many modifications of the Standard System of Deontic Logic 78 BOOK REVIEW (Hilpinen, 1971, p. 13f.; Chellas, 1980, p. 190f.). These new systems have lead to new paradoxes that deal with CTD obligations. I will mention some of them, because they play an important role in the papers in Defeasible Deontic Logic. One solution to the Chisholm paradox is to point out that an element of time is involved. The obligation to call is replaced by the obligation not to call as soon as it is fixed that A will not assist his neighbours. This change in the obligations explains the seeming inconsistency. However, the Gentle Murder paradox is similar to the Chisholm paradox, but does not involve time: THE GENTLE MURDER PARADOX One ought not to murder If one does murder, one ought to do it gently. In fact A does murder. Therefore, A ought to murder gently. In an ideal world A would not murder and therefore would not murder gently either. In the real world A does murder, however and therefore ought to do it gently. Since murdering gently involves murdering, it seems that in the real world A ought to murder, which is somewhat strange. To me this case seems quite unparadoxical. If one ought to murder gently, the obligation only refers to the aspect of gentleness of the murdering, not to the murdering itself. The derivation of the obligation to murder from the obligation to murder gently is clearly fallacious. As a consequence, the obligation to murder gently does not contradict the obligation not to murder. Nevertheless, some systems of deontic logic allow this derivation and assume that the CTD obligation contradicts its primary obligation. The reason why these system allow this is another intuition, namely that the principle of so called ‘deontic inheritance’ is acceptable. Deontic inheritance means that if some act is obligatory, and this act necessarily involves another act, this other act is obligatory too. Or, if some state of affairs is obligatory and this states of affair necessarily involves another state of affairs, this other state of affairs is obligatory too. For instance, if one ought to go to London by bike, this involves that one ought to go to London. Or, if it is obligatory that all vehicles are parked in the parking, it is obligatory that all cars are parked in the parking. Yet, as the gentle murder case illustrates, this intuition does not hold unrestrictedly. My intuition is that it does not hold if the obligatoriness refers to an aspect of an act or a state of affairs, rather than to the act or state of affairs itself. There is, however, another paradox which seems to show that the issue is even more complex. Lennart Åqvist (1967) has introduced the paradox of the knower: BOOK REVIEW 79 THE KNOWER PARADOX A ought not do X If A does X, B ought to know it. If B knows that A does X, then A does X. A does X. Since B ought to know that A does X, and since the knowledge seems to imply that A does X, it seems that it ought to be the case that A does X, which conflicts with his obligation not to do X. Although this paradox is not quite the same as the paradox of the gentle murder, it seems to me that is has a solution that is at least similar. Although B’s knowing that A does X presupposes that A does X, the act of knowing itself does not involve that A does X. It is the act that is obligatory, not its presuppositions. This analysis can also be applied to the Gentle Murder paradox, if one assumes that murdering gently presupposes that one murders. These solutions to the gentle murder paradox and the knower paradox follow essentially a suggestion made by Castañeda (1981), who distinguishes between what has deontic focus and what are merely circumstances of an action. He elaborates this distinction, which seems to me to be sound, by another distinction between practitions (action types) and propositions. Castañeda’s idea was that only practitions and not propositions can have deontic focus,. However, Prakken and Sergot (1994) have pointed out that some CTD obligations have nothing to do with actions, so that the distinction between practitions and propositions is of no avail. In this connection they introduced the paradox of the white fences, based on a real life case: THE FENCES PARADOX Holiday cottages ought to have no fences. If they have a fence, it ought to be white. Cottage A has a fence. Therefore the fence of cottage A ought to be white. That the fence of cottage A ought to be white seems to imply by deontic inheritance that cottage A ought to have a fence. Since the obligation is of the ought-to-be type, there is no practition involved. Castañeda’s solution therefore does not help. Nevertheless, I feel that it is in the spirit of Castañeda to distinguish between a state of affairs and its presuppositions, and to say that the obligatoriness of a state of affairs may transfer to its parts, but not to its presuppositions. The obligatoriness of a fence being white transfers to the obligatoriness of the fence being coloured, but not to the fence’s existence. Again there is no contradiction between the fact that there ought to be no fence and the fact that a fence ought to be white. 80 BOOK REVIEW Prakken and Sergot search for the solution in another direction, however. They take an approach which was taken before by Von Wright (1971) in response to the Chisholm paradox. This approach involves the introduction of a dyadic deontic logic in order to express contextual obligations. The obligation of the fence being white does not exist tout court, but only in the context where there is a fence. Formally: #(White(fence)/Fence). For this dyadic type of deontic logic a special kind of semantics was developed. This semantics assumes that there is an hierarchical ordering on possible worlds, where the higher worlds contain fewer norm violations than the lower ones. Intuitively a sentence as #(White(fence)/Fence) is true if fences are white in the best worlds in which there are fences (which are clearly not the best possible worlds). The limitation of the considered possible worlds to those in which there are fences reflects the contextual nature of the obligation that fences are white. Systems which make use of such a preference ordering on possible worlds are sometimes called Hansson/Lewis systems, after the pioneering work of Hansson (1969) and Lewis (1974). Now is the time to explain why the presence of CTD obligations has been seen as a reason why deontic reasoning is defeasible. A contextual obligation of the form #(B/A) is quite similar to a conditional obligation of the form A ⇒ #(B)⋆ (see Alchourrón, 1993, p. 58). (However, Prakken and Sergot argue in their paper that contextual obligation should be distinguished from conditional obligation.) One way to interpret the defeasibility of an argument from A to B is to disallow the step from A ⇒ B to (A & C) ⇒ B. This step, strengthening the antecedent, is invalid if the argument from A to B is defeasible. In many dyadic deontic logic, the step from #(B/A) to #(B/A & C) is not valid either. For instance, from the fact that one ought to visit one’s friend in the context that one has promised to do so, it may not be concluded that one ought to visit one’s friend in the context that one has promised to do so and was released from the promise. It is this line of reasoning, explicitly mentioned in the paper by Van der Torre and Tan, which connects CTD obligations to the defeasibility of deontic reasoning. Several papers in Defeasible Deontic Logic, in particular those by Åqvist, Van der Torre and Tan, Prakken and Sergot, and Carmo and Jones, deal in some way or other with this presumed connection between CTD obligations and defeasibility in the sense of the invalidity of strengthening the antecedent. 2. The Papers One purpose of a review is to inform potential readers of a book whether they should take the trouble to do so. In case of books that collect papers, this is a difficult task because of the diversity of the papers. I will try to give an impression of all papers by briefly summarising them. ⋆ The double arrow stands for a conditional as used in conditional logics, instead of the more usual material conditional. BOOK REVIEW 81 DONALD NUTE AND XIAOCHANG YU : INTRODUCTION In their introduction to the book, Nute and Yu give a brief overview of some paradoxes of deontic logic, with special emphasis on the CTD paradoxes. JOHN F. HORTY: NON - MONOTONIC FOUNDATIONS FOR DEONTIC LOGIC Horty starts with pointing out that modal approaches to deontic logic have difficulties with conflicting norms. He discusses standard deontic logic, in which conflicting norms are inconsistent, and the system EM, a variant on Chellas’ (1980) system CDK, that relativises every ought to a set of norms, so that real conflicts become impossible. As an alternative Horty elaborates a proposal by Van Fraassen (1973). This proposal comes down to the following: something is obligatory relative to a set of norms if it is prescribed by a maximal consistent subset of the norms. In elaborating this proposal, Horty uses Reiter’s (1980) default logic, by representing norms as normal defaults. Horty discusses the resulting system and some variations on it. Moreover he generalises the system to make it deal with conditional norms. He assumes in this connection that a conditional ought should be overridden in some context whenever a more specific ought is applicable that is inconsistent with it. For instance #(C/A) is overridden by #(∼C/A&B). MARVIN BELZER AND BARRY LOEWER : DEONTIC LOGICS OF DEFEASIBILITY Belzer and Loewer discuss a family of dyadic logics for defeasible deontic reasoning. According to Belzer and Loewer, a normative rule such as ‘One ought to do A given B’ is defeasible in a normative system S, if and only if S contains another rule to the effect that one ought not do A given B&C, or one is permitted not to do A given B&C. Belzer and Loewer start with a very weak logic M3D (presumably to be read as Minimal 3D, where 3D abbreviates Dyadic Deontic Detachment and designates a system of deontic logic that the authors described in their (1983)). The authors use #(A/B) to mean that B defeasibly requires A. #(A/B) is logically compatible with both #(∼A/B&C) and ∼ #(A/B&C). According to Belzer and Loewer, deontic conclusions are typically relative to a set of ‘eligible’ premises. A proposition may be taken to be eligible if it is settled at a time t in a world w. The system M3D is characterised by the following connection between #(A/B) and Ot A: If #(A/B) is true and B is eligible at t and #(A/B) is not defeated due to some C, which is both (a) eligible at t and (b) such that ∼ #(A/B&C) or #(∼A/B&C), then #t A is true. This captures the passing of a prima facie obligation into an actual (or ‘all out’) one if it is not overridden by a more specific conflicting obligation. Belzer and Loewer claim that even the weak logic M3D is rich enough to capture a number of notions that play a central part in deontic 82 BOOK REVIEW reasoning, such as, amongst others, the notions of an absolute reason, a prima facie reason, a conclusive (or all out) reason, a stronger reason, an obligation being overridden, and its being undercut. After the exposition of M3D, Belzer and Loewer continue to discuss some extensions to it. The system M3D+ adds to M3D the possibility to derive #(Q/B) from #(A/B) in case A entails Q (a kind of deontic inheritance). In M3D++ the principle of agglomeration is added to M3D+. This principle holds that for any A, B and C, if #(B/A) and #(C/A), then #(B&C/A). For instance, If one ought to assist if a person is drowning, and if one ought to warn the police if a person is drowning, one ought both to assist and to warn the police if a person is drowning. The final extension discussed by Belzer and Loewer is a principle suggested by Von Wright, namely that it is possible to derive #(B/A&C) if it both holds that #(B/A) and P(C/A). For instance, if one ought to assist if a person is drowning, and if it is permitted to smoke a cigarette if a person is drowning, one ought to assist when a person is drowning while one smokes a cigarette. The addition of this principle to M3D++ leads to the already familiar system 3D. Belzer and Loewer not only describe the variations in between the systems M3D and 3D, but also discuss characteristics of deontic reasoning that inspire these variations. LENNART Å QVIST: SYSTEMATIC FRAME CONSTANTS IN DEFEASIBLE DEONTIC LOGIC Åqvist’s paper aims to provide adequate semantic foundations for a number of extensions of the dyadic system of deontic logic DSDL3, proposed by Bengt Hansson (1969). The primarily technical paper has as its starting point a subdivision of all possible worlds into a hierarchy of world classes, where each class (a systematic frame constant) is a set of worlds that are somewhat lesser than the worlds of the class above. The worlds at the top of the hierarchy are ideal ones. The basic ideas are that the proposition #(A/B) (for reasons of uniformity I deviate from the notation of Åqvist) is true if A is true in all the best worlds in which B is true. P(A/B) is then true if A is true in some of the best worlds in which B is true. Åqvist discusses some variations on this theme, both from a model theoretic and from a proof theoretic point of view. LEENDERT, W. N . VAN DER TORRE AND YAO - HUA TAN : THE MANY FACES OF DEFEASIBILITY IN DEFEASIBLE DEONTIC LOGIC Van der Torre and Tan argue that the notion of defeasibility in connection with deontic logic is ambiguous. In fact they distinguish between factual defeasibility, strong overridden defeasibility, and weak overridden defeasibility. With factual defeasibility, the authors mean that an obligation can be ‘overshadowed’ if it is BOOK REVIEW 83 violated. For instance, the obligation to have no fence around one’s house is overshadowed by the obligation to have a white fence in case one violates the first obligation and has a fence despite the prohibition. Weak overridden defeasibility occurs in case of conflicting (prima facie) obligations, where one obligation does not cancel the other one, but merely outweighs it. For instance, the obligation to save a drowning child weakly overrides the obligation not to swim in the pond. Characteristically in cases like these, if one does not act on the overriding obligation, one still ought to act on the overridden one. So, if one decides not to save the child, one is still not allowed to swim in the pond. Strong overridden defeasibility occurs if there are exceptional circumstances that make that the original obligation is replaced by an incompatible one. For instance, the obligation not to have a fence around one’s house is strongly overridden by the obligation to have a (white) fence in case one has a dog. Van der Torre and Tan develop a series of dyadic deontic logics to deal with the several versions of defeasibility. The version they end up with is defined by means of a Hansson/Lewis model that has two preference orders, one for ideality, and one for normality. The ordering in terms of ideality deals with factual defeasibility; the ordering in terms of normality deals with overriding defeasibility. Y. U . RYU AND R . M . LEE : DEONTIC LOGIC VIEWED AS DEFEASIBLE REASONING Ryu and Lee follow Horty in treating deontic conditionals as a kind of defaults. They extend Horty’s account by dealing with conflicts between obligations and permissions, and defeat between more than two deontic conditionals. They take the notion of a competing set of deontic conditionals as their starting point. Informally, a set of conditionals is competing if against a background of necessary and contingent facts the consequents of the conditionals are inconsistent, while no subset is inconsistent against the same background. Competing deontic conditionals may lead to deontic conflicts. Such conflicts can be avoided by a preference relation over the conditionals. Ryu and Lee elaborate on this with specificity as criterion for preference. A conditional is preferable to a set of conditionals if their combination is competing and the antecedent of the conditional is more specific than the antecedents of the conditionals in the set. A set of conditionals is preferable to a conditional if their antecedents are more specific than that of the conditional. Ryu and Lee offer a proof to the effect that a CTD deontic conditional is not preferable to its primary obligation. (Apparently, they assume that a CTD obligation competes sometimes with its primary obligation.) The next step in the argument is to define the deontic base of a deontic theory as a maximal subset of the theory’s deontic conditionals that is not competing all things considered, that is taken preference into account. Such a deontic base is intuitively to be understood as a maximal set of conditional obligations together with compatible permissions that can be fulfilled without conflicts. 84 BOOK REVIEW A deontic extension of a theory is the deductive closure of the theory’s necessary and contingent facts, combined with one of the theory’s deontic bases. This notion is used to define enforceable, fulfilled and violated obligations, and a weak notion of permission. The authors conclude their paper by considering other grounds of preference than specificity, and by comparing their work to earlier work of their own and to Horty (1993), an earlier version of the paper discussed above. MICHAEL MORREAU : REASONS TO THINK AND ACT Morreau offers an integrated logical framework for reasons to believe and reasons to act. Reasons are defined by means of a dedicated conditional operator that relates two propositions. The statement that A is a reason for B is then analysed as the conjunction of the conditional A ⇒ B, and the conditional’s antecedent. A ⇒ B is to be interpreted as ‘If A, then B other things being equal’. Morreau characterises the conditional operator by model theoretic means. Central is a worlds-selection function that assigns a proposition (a set of possible worlds) to a combination of a possible world and another proposition (set of worlds). The intended intuition is that the first proposition describes what is normally the case given the facts of some possible world and the assumption that some proposition is true in it. By means of the conditional operator Morreau defines a notion of inference from reasons to justified conclusions and seeming duties. The corresponding notion of allowed consequence is both invalid (in the traditional sense), defeasible, and perplexing in the sense that inconsistent conclusions may be allowed. The definition makes use of assumptions to the effect that ‘other things are equal’. Syntactically these assumptions are made in the form of material conditionals of the following form: (A ⇒ B) → (A → B). A maximal set of such sentences is added to a theory, such that the result is consistent. A conclusion is an allowed consequence of a theory if it is entailed by this theory with some maximal set of assumptions. Morreau then goes on to define subsets of sets of assumptions. These are called focuses of attention and they are used to exclude the use of some conditionals (whose corresponding assumptions are not included in the focus) in making inferences. Another generalisation that Morreau introduces is to replace the notion of a focus of attention (a set of sentences) by the notion of a focal vector. A focal vector is a linearly ordered finite set of focuses. The idea is that the order of the vector provides an ordering on the conditionals that are taken into account in drawing conclusions. Morreau’s paper is concluded by a semantic characterisation of the resulting general logic. BOOK REVIEW 85 NICOLAS ASHER AND DANIEL BONEVAC : COMMON SENSE OBLIGATION Asher and Bonevac take as their starting point the distinction between constitutive rules (principles) and epistemic rules. The authors clearly distinguish between what is prima facie the case (epistemic) and what is ceteris paribus the case (constitutive). If somebody performs some unattractive job, it may, for instance prima facie be assumed that she ought to perform that job, because why should she do it otherwise? However, the fact that somebody performs an unattractive job is not a reason why she ought to perform it. It is only a reason for believing that she ought to perform it for some other reason. If, however, somebody promised to perform the unattractive job, this is a reason why she ought, ceteris paribus, to perform that job. Asher and Bonevac introduce two conditionals to represent both epistemic and constitutive relations between states of affairs. A > B means that normally, if A is the case, B is also the case. A >o B means that, ceteris paribus, if A is the case, B ought to be the case. By means of these two conditionals and the way they are defined, Asher and Bonevac strive to obtain an account of obligation that satisfies the following six requirements: 1. Default Detachment: Arguments of the form: If A, then it ought to be the case that B, A, therefore It ought to be the case that B should count as acceptable if no other moral considerations apply. 2. Conditional Conflict: When two prima facie principles conflict, it is in general not possible to draw conclusions. 3. Deontic Specificity: More specific prima facie obligations should take precedence over less specific ones. 4. Unwanted Implications: Unwanted implications such as in the Gentle Murderer paradox should be avoided. 5. Unconditional Actual Obligation: It should be possible to express unconditional actual obligations, and those should not be able to conflict. 6. Unconditional Prima Facie Obligation: It should be possible to express unconditional prima facie obligations, and those should be able to conflict. Asher and Bonevac use a kind of update semantics to characterise a sceptical nonmonotonic inference relation for their logic. They conclude their paper by arguing why the logic satisfies all the requirements that they posited for an adequate logic of obligation. ROBERT C . KOONS AND T. K . SEUNG : DEFEASIBLE REASONING AND MORAL DILEMMAS Koons and Seung take position against what they call the Classical Deductivist Model as applied in ethical theory. According to this model: (a) all particular ethical facts are logically deducible from some set of exceptionless universal principles, and (b) ethical facts are mutually consistent and no ethical claim is both true and false. 86 BOOK REVIEW Koons and Seung mention two problems with this classical model: 1. There are no such things as finitary exceptionless generalisations. It is, according to Koons and Seung, impossible to enumerate in finitary first order logic all the relevant conditions that may arise in the application of any moral rule. 2. The classical model cannot account for the occurrence of moral residue. Moral residue is the phenomenon that violated obligations, even if they are rightly set aside by stronger obligations, can leave duties. For example, one can have the duty to repair the damages that resulted from the violation of an overridden duty. As a solution to these problems, Koons and Seung propose the combination of two ideas. One is Horty’s idea to treat obligations as defaults, which allows a moral theory to have more extensions. The second idea is Van Fraassen’s theory that sentences can have more than one truth value (supervaluation). Koons and Seung illustrate their approach by applying it to a number of telling cases of moral and legal conflict. HENRY PRAKKEN AND MAREK SERGOT: DYADIC DEONTIC LOGIC AND CONTRARY TO DUTY OBLIGATIONS Prakken and Sergot tackle the problem how to develop a variant of dyadic deontic logic that deals adequately with the several variants of CTD obligations. In particular, they address the question under which circumstances it is allowed to extend the context of a contextual obligation. For instance, under which circumstances is it allowed to conclude from the fact that if one kills, one ought to do it gently, to the fact that if one kills and smokes a cigarette, one ought to kill gently? This question generalises to the question what should be filled in for ǫ to make the principle ǫ → (#(A/B) → #(A/B & C) into a valid one. Prakken and Sergot take dyadic logics of the Hansson-Lewis type, which work with a preference ordering on possible worlds, as their starting point. They defend this choice by opposing contextual obligations to prima facie obligations, conditional obligations and ideal obligations. Prakken and Sergot do not consider the invalidity of factual detachment for contextual obligations as problematic. But they see an inadequacy in the way in which Hansson-Lewis systems deal with cases like the following: 1. There must be no dog. 2. If there is a dog, there must be a sign. 3. There must be no sign. If 2 is not considered as an exception to 3, these propositions should in the view of Prakken and Sergot be considered inconsistent. However, in Hansson-Lewis systems they would be consistent. Their meaning would be that in ideal worlds there would be neither dogs nor signs, and in worlds in which there are dogs, there should also be signs. According to Prakken and Sergot, this example illustrates that BOOK REVIEW 87 Hansson-Lewis systems do not capture ‘that sub-ideal worlds should still measure up to the ideal worlds as much as possible’. To repair this inadequacy, the authors try to adapt the Hansson-Lewis framework. The main idea is to first make an ordering on possible worlds to reflect the primary obligations. Then the secondary obligations are used to refine this ordering for the CTD cases. The results of this approach turn out to be disappointing, however. It turns out that it is impossible to find a sensible condition ǫ that allows extension of a context. According to the authors, the reason why this is impossible is that the possibility of extending the context depends on other obligations that may also hold and that may interfere with the obligation the context of which is to be extended. This disappointing result leads Prakken and Sergot to pay attention to another approach. They propose to disregard consequential closure of obligations (deontic inheritance) in determining the ordering on possible worlds although they want to retain it for determining what is obligatory. The final part of their paper is devoted to a brief elaboration of this idea. LAMBÈR ROYAKKERS AND FRANK DIGNUM : DEFEASIBLE REASONING WITH LEGAL RULES Royakkers and Dignum address the issue of reasoning with inconsistent rules. In particular, they attempt to deal with three issues that were in their opinion inadequately handled by earlier approaches. These issues are the absence of a notion of permission, that only pairs of statements are considered to check consistency, and that most earlier approaches only deal with deontic defeasible conditionals and not with non-deontic ones. The approach of Royakkers and Dignum is an elaboration of argument based theories of defeasible reasoning as developed by, amongst others, Pollock (e.g., 1987) and popularised in the Law and AI community by the work of Prakken and Sartor (e.g., 1996). The authors distinguish between rules, which they treat as Reiter defaults, and norms. One difference is that norms can be violated, while rules cannot be violated. The second difference, which the authors consider to be the most important one, concerns the defeasibility of rules and of norms. The authors assume a priority of rules over norms in the sense that rules can only be defeated by other rules, and that the outcome of rule conflicts is assumed as fixed while determining whether there is a conflict of norms. Royakkers and Dignum define arguments as sets of rules that are applicable in combination with a given set of facts. They assume an ordering defined over the rules, and define a defeat relation over arguments by means of this ordering. In particular argument 1 is defeated by argument 2 if the two arguments in combination with the facts have inconsistent conclusions, and the rule in argument 1 on which the conclusion is based is not higher in the hierarchy than the conflicting rule in argument 2. 88 BOOK REVIEW The set of arguments that is possible given a theory consisting of rules and facts is in the familiar way divided into three categories: justified, overruled and defensible. The conclusions of the justified and the defensible arguments are defined as the outcome of the arguments of a theory. Norms are treated just like rules. That is, the authors define arguments based on norms, and norm conflicts and defeat amongst norms. The definition of defeat amongst norms differs from the definition of defeat amongst rules, however. Where the latter definition makes use of conflict of individual rules that belong to competing arguments, the former only makes use of the hierarchy between norms in conflicting arguments. That is, a normative argument is defeated if it has the weakest norm, even if this weakest norm itself does not conflict with a norm in the overruling argument. The authors conclude their paper with a characterisation of norm violation. DONALD NUTE : APPARENT OBLIGATION Nute aims to contrast three notions of obligation, namely the notions of prima facie obligation, actual obligation, and apparent obligation. Coarsely stated an actual obligation is an obligation that holds on the basis of all relevant circumstances. A prima facie obligation is an obligation that holds because of some circumstances, but which turn out not to be an actual obligation because there are relevant circumstances that were not taken into account. An apparent obligation is what an actor – given his other beliefs rationally believes to be an actual obligation. Nute proposes a formalism for representing and using the defeasible rules that guide moral reasoning, and that captures the above mentioned distinctions. This formalism is a deontic extension of a proof theory for defeasible reasoning. It allows both factual and deontic detachment, and deontic inheritance. The original proof theory for defeasible reasoning is defined for a stripped down version of predicate logic, that only has the negation as operator, which is extended with rules. The basic notion is that of a defeasible theory, that consists of a set F of formulas, a set R of rules, a conflicts set C, and a preference relation defined over the set of rules. There are three kinds of rules, strict ones, defeasible ones, and undercutters. The conflicts set consists of sets of formulas that are considered to be in conflict amongst each other. It is used to determine when defeasible inference must make use of priorities. Nute discusses a number of characteristics that a conflicts set might have. For instance a conflicts set will normally contain the pair {P, ¬P} for any formula P. Moreover, if a theory contains the strict rule {P, Q} → R, it might contain the set {P, Q, ¬R} in its conflicts set. Nute also discusses a number of characteristics which the preference relation over the rules might have. He assigns a central place to specificity, but also makes room for other preference relations that might be added to specificity and even given priority above it. The author describes a number of characteristics that are desirable in a defeasible proof theory and gives a proof theory that satisfies these desires. Typical BOOK REVIEW 89 characteristics of this theory are that derivation based on strict rules and strictly proven facts is not defeasible and takes precedence over semi-strict derivation, based on strict rules and defeasibly proven facts. Semi-strict derivation takes in turn precedence over defeasible derivation based on defeasible rules and defeasibly proven facts. This proof theory is given a deontic extension by adding strict and defeasible deontic inheritance and strict and defeasible deontic detachment. In both cases the strict versions take precedence over the defeasible ones. Nute illustrates his theory by discussing a number of classical contrary-to-duty cases. His theory easily deals with the Chisholm case. Given suitable formalisations of the premises, it can also deal with Gentle murder case. However, the Knower paradox escapes the present capabilities of his theory. JOSÉ CARMO AND ANDREW JONES : A NEW APPROACH TO CONTRARY TO DUTY OBLIGATIONS Carmo and Jones exploit the distinction between actual and ideal obligations to develop a logic that meets the following requirements: With regard to the Chisholm set it must allow a formalisation in which 1. the set is consistent; 2. the members of the set are logically independent; 3. the two conditional sentences have analogous (presumably: the same) logical structures. Moreover, the logic should have the capacity 4. to derive actual obligations; 5. to derive ideal obligations; 6. to represent norm violations; 7. to avoid the pragmatic oddity (this is the oddity that if a norm violation has occurred, both the original obligation and the contrary to duty obligation, which presupposes the violation) hold. For example, it should not be derivable (in the same sense of ‘ought’) that both there ought to be no fence and there ought to be a white fence. The basic idea behind the logic proposed by Carmo and Jones is to distinguish between what is actually possible and what is potentially possible. What is actually possible depends on what an actor has (firmly) decided to do, while what is potentially possible does not. For example, if I have firmly decided to commit a murder, it is potentially possible that I do not murder, while actually it is not possible anymore. Corresponding to this distinction is the distinction between actual and ideal obligation. Coarsely stated, ideal obligation is what is ideally the case given what is potentially possible, while actual obligation is what is ideally the case given what is actually possible. (Apparently the murderer can, by fixing his mind, replace the actual obligation not to murder by a merely ideal one, combined with an actual obligation to murder gently.) 90 BOOK REVIEW Based on these intuitions, Carmo and Jones define three deontic operators, for dyadic obligation, monadic actual obligation, and monadic ideal obligation. These operators are semantically characterised by means of three relations over possible worlds, representing ideal worlds relative to some proposition, and worlds that are actually or potentially possible relative to some world. The authors demonstrate by means of, amongst others the Chisholm set and an adapted version of the fence example how their formalism provides solutions for a number of CTD situations. RON LOUI : ALCHOURRÓN AND VON WRIGHT ON CONFLICT AMONG NORMS An alternative for defeasible reasoning is belief revision. If a logically forcing argument leads to an unacceptable conclusion, there are in principle three solutions: accept the unacceptable, change the logic to make the argument logically nonforcing, or reject one or more of the premises. Defeasible logic takes the second approach. Loui critically discusses the third approach. He uses quotations from the work of the philosophers/logicians Alchourrón and Von Wright to illustrate how both of them rejected defeasible reasoning in favour of some variant of belief revision. In the case of Alchourrón this is really belief revision, in the case of Von Wright it is revision of the norms that lead to inconsistency if applied. Conclusion The papers in Defeasible Deontic Logic reflect an ongoing debate on the conceptualisation of some central issues in the ontology of normative systems, including the law. It is possible to discern three main approaches to defeasible deontic reasoning. One approach, taken by Horty, Ryu and Lee, Koons and Seung, and Nute, treats deontic sentences as Reiter-like defaults. This approach focuses primarily on conflicting obligations. A second approach uses a dyadic deontic logic to deal with CTD obligations. This approach is taken by Åqvist, Van der Torre and Tan, Prakken and Sergot, and Carmo and Jones. The third approach uses a form of conditional logic to represent norms. It is both suitable to deal with conflicting obligations and with exceptions to norms, but is not particularly suited to CTD obligations. This approach is taken in the papers by Belzer and Loewer, Morreau, and Asher and Bonevac. Together the papers in Defeasible Deontic Logic provide a useful overview of the state of the art in central parts of both deontic and legal logic. Everybody who is trying to develop legal ontologies or attempts to improve on the present theories of legal reasoning is advised to study at least some of the papers in this volume. BOOK REVIEW 91 References Alchourrón, C.E. (1993). Philosophical Foundations of Deontic Logic and the Logic of Defeasible Conditionals. In: Meijer, J.-J. Ch. & Wieringa, R.J. (eds.) Deontic Logic in Computer Science, 43–84. John Wiley, London. Allen, L.E. & Saxon, C.S. (1993). A-Hohfeld: A Language for Robust Structural Representation of Knowledge in the Legal Domain to Build Interpretation-Assistance Expert Systems. In: Meyer, J-J. Ch. &Wieringa, R.J. (eds.) Deontic Logic in Computer Science. Normative System Specification, 205–224. John Wiley, London. Åqvist, L. (1967). Good Samaritans, Contrary-to-Duty Imperatives, and Epistemic Obligations. Noûs 1, 361–379. Castañeda, H.N. (1981). The Paradoxes of Deontic Logic: The Simplest Solution to All of Them in One Fell Swoop. In: Hilpinen, R. (ed.) New Studies in Deontic Logic, 37–86. D. Reidel, Dordrecht. Chellas, B.F. (1980). Modal Logic; An Introduction. Cambridge University Press, Cambridge. Chisholm, R.M. (1963). Contrary-to-Duty Imperatives and Deontic Logic, Analysis 24, 33–36. Hage, J.C. (1997). Reasoning with Rules, Kluwer Academic Publishers, Dordrecht. Hansson, B. (1969). An Analysis of Some Deontic Logics. In: Hilpinen, R. (ed.) Deontic Logic: Introductory and Systematic Readings, 121–147. D. Reidel, Dordrecht. Hilpinen, R. (ed.) (1971), Deontic Logic: Introductory and Systematic Readings, D. Reidel, Dordrecht. Hohfeld, W.N. (1913). Fundamental Legal Conceptions as Applied in Judicial Reasoning, Yale Law Journal 23, 16. Horty, J. (1993). Deontic Logic as Founded in Nonmonotonic Logic. Annals of Mathematics and Artificial Intelligence 9, 69–91. Jones, A.J.I. & Sergot, M. (1992). Deontic Logic in the Representation of Law: Towards a Methodology. Artificial Intelligence and Law 1, 45–64. Lewis, D. (1974). Semantic Analyses for Dyadic Deontic Logic. In: Stendlund, S. (ed.) Logical Theory and Semantic Analysis, 1–14. D. Reidel, Dordrecht. Lindahl, L. (1977). Position and Change; A Study in Law and Logic. D. Reidel, Dordrecht. Loewer, B. & Belzer, M. (1983). Dyadic Deontic Detachment. Synthese 54, 295–319. Pollock, J.L. (1987). Defeasible Reasoning. Cognitive Science 11, 481–518. Prakken, H. & Sartor, G. (1996). A Dialectical Model of Assessing Conflicting Arguments in Legal Reasoning. Artificial Intelligence and Law, 4(3/4), 331–368. Also in Prakken, H. & Sartor, G. (eds.) (1997). Logical Models of Legal Argumentation. Kluwer Academic Publishers, Dordrecht. Prakken, H. & Sergot, M. (1994). Contrary-to-Duty Imperatives, Defeasibility and Violability In: Jones, A.J.I. & Sergot, M. (eds.) Deon ’94, Proceedings of the Second International Workshop on Deontic Logic in Computer Science, pp. 296–318. Reiter, R. (1980). A Logic for Default Reasoning. Artificial Intelligence 13, 81–132. Ross, W.D. (1930). The Right and the Good. Clarendon Press, Oxford. Van Fraassen, B. (1973). Values and the Heart’s Command. The Journal of Philosophy 70, 5–19. Von Wright, G.H. (1971). A New System of Deontic Logic. In: Hilpinen, R. (ed.) Deontic Logic: Introductory and Systematic Readings, 105–120. D. Reidel, Dordrecht. Department of Metajuridica University of Maastricht Maastricht The Netherlands Jaap Hage