What really makes the concepts of obligation or permission so important for practical philosophy? What if we could find a better concept, one that, despite the simplicity, could show itself as intuitive and rich as possible? Could justifications be used in common language and practice as a sign of ethical judgment and as a strong motive for action? In most scenarios, for example, it really doesn’t matter if a given action is obliged, permitted or forbidden, one may perform the action (...) as long as a justification for doing it is present. In this sense, the notion of justification seems to be more basic and powerful than other concepts used in the philosophical discourse. The existence of formal systems based on the epistemological side of justification, created by Artemov, led us primarily to think that justification could make the formal discourse much more accurate for ethics than the ones using deontological concepts. In the semantical and syntactical aspects, almost all of Artemov’s systems directly proved to be fruitful for ethical purposes. We also developed combinations between the standard deontic logic and logics of justification, resulting in what whe called the Logics of Normative Justification. These systems were able to change the object of the justification formulas and shed some light in ethics as a whole, normative and metaethics. Metaethics were a forgotten subject in formal ethics. We were also able to deal with some known problems in deontic logic, like the famous Ross’s paradox and the expressiveness of prima facie and all-things-considered obligations. (shrink)

Abstract.The author gives a short survey of the different methods which have been proposed to deal with the logic of norm sentences on the basis of logical systems of descriptive language: deontic logic, logic of norms as an isomorphism of propositional logic, restriction of logical relations to the propositional content of norm sentences, transformation of norms into sanction sentences, preference interpretation of norm sentences, double interpretation of ought‐sentences and the use of the descriptive (...) interpretation as a tool for establishing the logic of norms, proposition about norms in the place of normative logic, the logic of admissible worlds, postulates addressed to the rational lawgiver and technical ought as a substitute for nor‐mological considerations. A critical analysis of these attempts may prove them inappropriate, but it is not sufficient to prove the impossibility of any method of founding normative logic on systems of a descriptive language. Therefore the author adds a general consideration on the chances of such approaches. (shrink)

This is the latest volume in the Workshops in Computing series and contains papers to be presented at the Third International Workshop on Deontic Logic in Computer Science (DEON '96) to be held in Sesimbra, Portugal 11 - 13 January 1996. It contains a variety of contributions covering the relationship between deontic logics, logics of action and normative systems (i.e. systems of or about interacting agents whose behaviour is subject to ideal constraints that may not always be (...) fulfilled in practice). The papers range from the theoretical studies of the logical and conceptual tools needed, to studies of various applications. The resulting volume will be of interest to researchers working in a variety of fields from philosophy, logic and legal theory, through to artificial intelligence and computer/management sciences. (shrink)

A useful logic in which to specify normative system behaviour, deontic logic has a broad spectrum of possible applications within the field: from legal expert systems to natural language processing, database integrity to electronic contracting and the specification of fault-tolerant software.

Abstract.The paper offers a critical survey of two main sorts of problems hindering the possibility of conceiving deontic logic as a suitable account of the logical behaviour of (sentences expressing) legal norms. The notion of “legal norm” is viewed as the main source of the first sort of problems: (a) the typological variety of legal norms requires an account both of the differing logical behaviour of (sentences expressing) differing legal norms, and of the relations which (...) might hold amon them; (b) the ontologic, semantic, and epistemic features of legal norms shed doubt on the very attempt to figure out a logical analysis of (sentences expressing) legal norms. The notion of “systemic legal validity” is viewed as the main source of the second sort of problems: Deontic logic does not provide suitable logical tools to account for legal phenomena like enactment, derogation, and conflicts between legal norms which rely on systemic legal validity. (shrink)

In this thesis, I develop and investigate various novel semantic frameworks for deontic logic. Deontic logic concerns the logical aspects of normative reasoning. In particular, it concerns reasoning about what is required, allowed and forbidden. I focus on two main issues: free-choice reasoning and the role of norms in deontic logic. -/- Free-choice reasoning concerns permissions and obligations that offer choices between different actions. Such permissions and obligations are typically expressed by a disjunctive (...) clause in the scope of a deontic operator. For instance, the sentence "Jane may take an apple or a pear" intuitively offers Jane a choice between two permitted courses of action: she may take an apple, and she may take a pear. In the first part of the thesis, I develop semantic frameworks for deontic logic that account for free-choice reasoning. I show that the resulting logics avoid problems that arise for other logical accounts of free-choice reasoning. The main technical contributions are completeness results for axiomatizations of the different logics. -/- Semantic frameworks for deontic logic typically only talk about norms implicitly. In the second part of the thesis, I clarify the role of norms in deontic logic. I develop a formal model of normative systems where norms are represented explicitly. The model takes into account both the hierarchical structure of normative systems, and the function of norms to regulate agent behavior. I show how the model can be used to clarify issues in the study of normative systems. I also develop a norm-based semantics for deontic action logic based on the model. (shrink)

Review of the book mentioned in the title.

Abstract.If norms are neither true nor false, can logical relations such as contradiction and entailment obtain between them? Earlier logical positivists and also Hans Kelsen in his later years have answered the question with No. While appreciating the seriousness of the problem, the author of the present paper makes a fresh attempt to answer the question with Yes. His answer presupposes that norms can be judged from the point of view of their rationality. The deontic loic or (...) logic of norms built on this foundation is much more restricted, however, than tae “classical” systems. This again is a consequence of the author's opinion that the sentential connectives (negation, conjunction, disjunction, etc.) apply to norms only on condition that they can be “shifted” from joining norm‐formulations to the descriptive contents of the norms themselves. (shrink)

In this paper, the set-theoretic approach in the logical theory of normative systems is extended using Broome’s definition of the normative code function. The syntax and semantics for first order metanormative language is defined, and metanormative language is applied in the formalization of the basic principles in Broome’s approach and in the construction of a logical typology of normative systems. Special attention is given to the types of normative systems which are not definable in terms of the properties of singular (...) sets of requirements (e.g. the realization equivalence of codes, the social compatibility of codes, and the compatibility of codes issued by different normative sources). Examples are given of the application of the typology in the interpretation of philosophical texts. Von Wright’s hypothesis on the connection of logical properties of normative systems, conceived set-theoretically, with standard deontic logic is proved by introducing the translation function between the metanormative language and the restricted language of standard deontic logic. The translation reveals that von Wright’s hypothesis must be appended. The problems of narrow and wide scope readings of the deontic conditionals and of the meaning of iterated deontic operators are addressed using the distinction between relative and absolute normative codes. The theorem on the existence of a realization equivalent absolute code for any relative code is proved. (shrink)

Abstract.If norms are neither true nor false, can logical relations such as contradiction and entailment obtain between them? Earlier logical positivists and also Hans Kelsen in his later years have answered the question with No. While appreciating the seriousness of the problem, the author of the present paper makes a fresh attempt to answer the question with Yes. His answer presupposes that norms can be judged from the point of view of their rationality. The deontic loic or (...) logic of norms built on this foundation is much more restricted, however, than tae “classical” systems. This again is a consequence of the author's opinion that the sentential connectives (negation, conjunction, disjunction, etc.) apply to norms only on condition that they can be “shifted” from joining norm‐formulations to the descriptive contents of the norms themselves. (shrink)

The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of (...) class='Hi'>deontic logic with the language of the extended set-theoretical approach are introduced, and used in proving the correspondence between the deontic theorems, on one side, and the perfection properties of the norm-set and the ``counter-set'', on the other side. In this way the possibility of reinterpretation of standard deontic logic as the theory of perfection properties that ought to be achieved in norm-giving activity has been formally proved. The extended set-theoretic approach is applied to the problem of rationality of principles of completion of normative systems. The paper concludes with a plaidoyer for logical pragmatics turn envisaged in the late phase of Von Wright's work in deontic logic. (shrink)

Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative (...) system or to the system of values under which we predicate the deontic qualifications. By taking this aspect into account, we arrive at a logical system which preserves laws proper to a deontic logic but where the standard paradoxes of deontic logic do not arise. It is a logic of strictly-deontic modalities DR. (shrink)

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning (...) in order to meet (ii). This results in the adaptive logics LNPr and LNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPr and LNPm are equipped with a preferential semantics and a dynamic proof theory. (shrink)

Deontic logic is standardly conceived as the logic of true statements about the existence of obligations and permissions. In his last writings on the subject, G. H. von Wright criticized this view of deontic logic, stressing the rationality of norm imposition as the proper foundation of deontic logic. The present paper is an attempt to advance such an account of deontic logic using the formal apparatus of update semantics and dynamic (...) class='Hi'>logic. That is, we first define norm systems and a semantics of norm performatives as transformations of the norm system. Then a static modal logic for norm propositions is defined on that basis. In the course of this exposition we stress the performative nature of (i) free choice permission, (ii) the sealing legal principle and (iii) the social nature of permission. That is, (i) granting a disjunctive permission means granting permission for both disjuncts; (ii) non-prohibition does not entail permission, but the authority can declare that whatever he does not forbid is thereby permitted; and (iii) granting permission to one person means that all others are committed to not prevent the invocation of that permission. (shrink)

We present the inconsistency-adaptive deontic logic DP r , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets (...) a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r. (shrink)

In the paper we present a formal system motivated by a specific methodology of creating norms. According to the methodology, a norm-giver before establishing a set of norms should create a picture of the agent by creating his repertoire of actions. Then, knowing what the agent can do in particular situations, the norm-giver regulates these actions by assigning deontic qualifications to each of them. The set of norms created for each situation should respect (1) generally valid (...) deontic principles being the theses of our logic and (2) facts from the ontology of action whose relevance for the systems of norms we postulate. (shrink)

The biennial DEON conferences are designed to promote interdisciplinary cooperation amongst scholars interested in linking the formal-logical study of normative concepts and normative systems with computer science, artificial intelligence, linguistics, philosophy, organization theory and law. In addition to these general themes, DEON 2016 encouraged a special focus on the topic "Reasons, Argumentation and Justification.".

In this paper, I will discuss boulesic and deontic logic and the relationship between these branches of logic. By ‘boulesic logic,’ or ‘the logic of the will,’ I mean a new kind of logic that deals with ‘boulesic’ concepts, expressions, sentences, arguments and systems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be the case that’ and ‘individual x accepts that it is the case that.’ These expressions will (...) be symbolised by two sentential operators that take individuals and sentences as arguments and give sentences as values. Deontic logic is a relatively well-established branch of logic. It deals with normative concepts, sentences, arguments and systems. In this paper, I will show how deontic logic can be grounded in boulesic logic. I will develop a set of semantic tableau systems that include boulesic and alethic operators, possibilist quantifiers and the identity predicate; I will then show how these systems can be augmented by a set of deontic operators. I use a kind of possible world semantics to explain the intended meaning of our formal systems. Intuitively, we can think of our semantics as a description of the structure of a perfectly rational will. I mention some interesting theorems that can be proved in our systems, including some versions of the so-called hypothetical imperative. Finally, I show that all systems that are described in this paper are sound and complete with respect to their semantics. (shrink)

Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des (...) normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

Situationist deontic logic is a model of that fraction of normative discourse which refers to only one situation and one set of alternatives. As we can see from a whole series of well-known paradoxes, standard deontic logic (SDL) is seriously mistaken even at the situationist level. In this paper it is shown how a more realistic deontic logic can be based on the assumption that prescriptive predicates satisfy the property of contranegativity. A satisfactory account (...) of situation-specific norms is a necessary prerequisite for a successful treatment of more complex normative structures. (shrink)

Abstract.The authors concentrate on the analysis of the concept of permission. After a general account of differing concepts of permission both with regard to different legal theories and to different legal ideologies, they argue in favour of a “radical” imperativism which leaves no place for permissive norms. Thus, in contrast with the logic of normative language (LNL) purported by Alchourrón and Bulygin, the authors figure out a system of deontic logic ‐ supplemented by devices of the (...) possible world semantics ‐ according to which a normative system (N) is conceived as a set of logical consequences of a certain finite set of basic obligations and no room is left either for the concept of weak permission or for the concept of strong permission. Finally the authors raise some criticisms concerning the view maintained by Alchourron and Bulygin on strong permission.*. (shrink)

The paper tackles two problems. The first one is to grasp the real meaning of Jerzy Kalinowski’s theory of normative sentences. His formal system K 1 is a simple logic formulated in a very limited language . While presenting it Kalinowski formulated a few interesting philosophical remarks on norms and actions. He did not, however, possess the tools to formalise them fully. We propose a formulation of Kalinowski’s ideas with the use of a set-theoretical frame similar to the (...) one presented by Krister Segerberg in his A Deontic Logic of Action. At the same time we enrich the language used by Kalinowski with more operators on actions and present an adequate axiomatisation of the resulting system. That allows us to disclose some unrevealed aspects of Kalinowski’s theory. The most important one is a relation between acts which we call moral indiscernibility. Our second problem is a proper understanding of moral indiscernibility. We show how a repertoire of agent’s actions, defined with the use of simple observable elements of actions, can be filtrated by the relation of moral indiscernibility. That allows us to understand the consequences of Kalinowski’s claim that not doing something good is always bad. (shrink)

The present volume is a sequel to Deontic Logic: Introductory and Systematic Readings : its purpose is to offer a view of some of the main directions of research in contemporary deontic logic. Most of the articles included in Introductory and Systematic Readings represent what may be called the standard modal approach to deontic logic, in which de on tic logic is treated as a branch of modal logic, and the normative concepts (...) of obligation, permission and prohibition are regarded as analogous to the "alethic" modalities necessity, possibility and impossibility. As Simo Knuuttila shows in his contribution to the present volume, this approach goes back to late medieval philosophy. Several 14th century philosophers observed the analogies between deontic and alethic modalities and discussed the deontic interpretations of various laws of modal logic. In contemporary deontic logic the modal approach was revived by G. H. von Wright's classic paper 'Deontic Logic'. Certain analogies between deontic and alethic modalities are obvious and uncontroversial, but the standard approach has often been criticized on the ground that it exaggerates the analogies and tends to ignore those features of normative concepts which distinguish them from other modalities. (shrink)

There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of (...) a methodology for its use in the analysis and representation of law.The essential point for which we argue is that deontic logic — in some form or other —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, or as we also say, between the ideal and the actual. We take the library regulations at Imperial College as the main illustration, and small examples from genuinely legal domains to introduce specific points. In conclusion, we touch on the role of deontic logic in the development of the theory of normative positions. (shrink)

A considerable number of books and papers have analyzed normative concepts using new techniques developed by logicians; however, few have bridged the gap between the English legal culture and the Continental tradition in legal philosophy. This book addresses this issue by offering an introductory study on the many possibilities that logical analysis offers the study of legal systems. The volume is divided into two sections: the first covers the basic aspects of classical and deontic logic and its connections, (...) advancing an explanation of the most important topics of the discipline by comparing different systems of deontic logic and exploring some of the most important paradoxes in its domain. The second section deals with the role of logic in the analysis of legal systems by discussing in what sense deontic logic and the logic of norm-propositions are useful tools for a proper understanding of the systematic structure of law. (shrink)

In this paper, I set out some basic elements of a deontic logic with an implementation appropriate for handling conflicting legal obligations for purposes of programming autonomous machine agents. Kantian justice demands that the prescriptive system of enforceable public laws be consistent, yet statutes or case holdings may often describe legal obligations that contradict; moreover, even fundamental constitutional rights may come into conflict. I argue that a deontic logic of the law should not try to work (...) around such conflicts but, instead, identify and expose them so that the rights and duties that generate inconsistencies in public law can be explicitly qualified and the conflicts resolved. I then argue that a credulous, non-monotonic deontic logic can describe inconsistent legal obligations while meeting Kant’s demand for consistency in the prescriptive system of public law. Finally, I propose an implementation of this logic via a modified form of “answer set programming,” which I demonstrate with some simple examples. (shrink)

The knowledge norm of assertion is the subject of a lively debate on when someone is in a position to assert something. However, not much has been said about the logic that underlies such debate. In this paper, I propose a formalisation of the knowledge norm in a deontic logic that aims to be explanatory and conceptually sound. Afterwards, I investigate some problems that this formalisation makes visible. This reveals some significant limitations of the underlying logic: (...) it can neither contain Axiom 4 nor Axiom C4. Moreover, sentences of the form p and I have not asserted that p appear to licence a violation of deontic rules. (shrink)

(See also the separate entry for the volume itself.) This introduction has three parts. The first providing an overview of some main lines of research in deontic logic: the emergence of SDL, Chisholm's paradox and the development of dyadic deontic logics, various other puzzles/challenges and areas of development, along with philosophical applications. The second part focus on some actual and potential fruitful interactions between deontic logic, computer science and artificial intelligence. These include applications of (...) class='Hi'>deontic logic to AI knowledge representation in legal systems, to modelling computer systems where it is expected that sub-ideal states will emerge and require countermeasures, to norm-governed human interactions with computer systems, and to the representation of some features of multi-agent systems where different agent-like computer systems interact with one another. The third and final part briefly groups and previews the papers in the anthology. (shrink)

This paper presents and discusses Henri Poincaré’s view on the logical non-derivability of imperatives from indicatives. Firstly, his point of view is compared with David Hume’s. Then Poincaré’s thesis is shown to have been implicitly or explicitly essential to attempts to build a logic of imperatives (norms) as a special linguistic category as well as a deontic logic. The paper shows deontic logic enables us to formulate general principles concerning the logical separability of deonticals (...) (sentences with deontic operators) and non-deontic sentences. Finally, the paper includes remarks on the reception of Poincaré’s discussed ideas in later logical and philosophical literature with the second issue illustrated by legal philosophy. (shrink)

This volume contains the proceedings of DEON2020/2021, the 15th International Conference on Deontic Logic and Normative Systems that was organized by the Munich Center for Mathematical Philosophy at LMU Munich (Germany) on 21st-24th July, 2021. The biennial DEON conferences are designed to promote interdisciplinary cooperation amongst scholars interested in linking the formal-logical study of normative concepts, normative language and normative systems with computer science, artificial intelligence, linguistics, philosophy, organization theory, and law.

This anthology contains revised versions of selected papers presented at the fourth bi-annual international deontic logic conference, DEON’98. This volume includes our substantial introduction, and an article from me as a contributor. The volume includes papers from all four distinguished invited speakers, David Makinson, Donald Nute, Claudio Pizzi, and the founder of deontic logic, Georg Von Wright. Other notables among the authors are Dov Gabbay (co-editor of the Handbook on Philosophical Logic vols.1-4, and editor of (...) a number of logic book series); Lars Lindahl (author of Position and Change: A Study in Law and Logic); Andrew Jones (past editor of the Norwegian Journal of Philosophical Logic, and the co-author of the entry “Deontic Logic and Contrary-to-Duties” in the 2nd edition of Handbook on Philosophical Logic); and Marek Sergot (a leading researcher at the interface of deontic logic and computer science.). (shrink)

This chapter contains sections titled: Introduction On Law and Morality Legal Rights and Legal Principles Law and Legal Systems Deontic Logic and Legal Philosophy Philosophical Doctrines in Latin America Conclusion References.

Deontic logic is devoted to the study of logical properties of normative predicates such as permission, obligation and prohibition. Since it is usual to apply these predicates to actions, many deontic logicians have proposed formalisms where actions and action combinators are present. Some standard action combinators are action conjunction, choice between actions and not doing a given action. These combinators resemble boolean operators, and therefore the theory of boolean algebra offers a well-known athematical framework to study the (...) properties of the classic deontic operators when applied to actions. In his seminal work, Segerberg uses constructions coming from boolean algebras to formalize the usual deontic notions. Segerberg’s work provided the initial step to understand logical properties of deontic operators when they are applied to actions. In the last years, other authors have proposed related logics. In this chapter we introduce Segerberg’s work, study related formalisms and investigate further challenges in this area. (shrink)

On the face of it, normative conflicts are commonplace. Yet standard deontic logic declares them to be logically impossible. That prompts the question, What are the proper principles of normative reasoning if such conflicts are possible? This paper examines several alternatives that have been proposed for a logic of 'ought' that can accommodate normative conflicts, and finds all of them unsatisfactory as measured against three criteria of adequacy. It then introduces a new logic that does meet (...) all three criteria, and so allows for the possibility of genuine normative conflicts. (shrink)

The book under review consists of two parts closely related to its title: I Introduction to Deontic Logic, II Logic and Legal Systems. Each part is divided into chapters. Part I brings the following units: 1. The Language of Logic and the Possibility of Deontic Logic; 2. Paradoxes and Shortcomings of Logic; 3. Norm-propositions, Conditional Norms, and Defeasibility, and Part II the following: 4. Legal Systems and Legal Validity; 5. Legal Indeterminacy: Normative (...) Gaps and Conflicts of Norms; 6... (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for (...) the studies of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well‐known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two‐level approach to obligations is tested first against standard scenarios of contrary‐to‐duty obligations, leading also to a generalization for the Kanger‐Anderson reduction of deontic logic. Next, the priority (...) framework is applied to model two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two‐level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners. (shrink)

If deontic logic is to cast light on any of the normative sciences, such as legal reasoning, then certain problems regarding its logical constants must be faced. Recent studies in the area of deontic logic have tended to assume that it is our responses to the “paradoxes” of deontic implication which are fundamental to resolving problems with the use of deontic logic to investigate various branches of normative reasoning. In this paper I wish (...) to show that the paradoxes are of secondary importance; that they are merely by‐products of the central issue, namely the ability of certain syntactic forms to embody natural language structures used in reasoning about norms. An investigation of modal syntax is proffered as the best starting‐point from which to tackle the questions that still dog the legitimacy of deontic logic. Part I provides some philosophical background to the discussion of deontic logical constants. Part II addresses in greater detail issues concerning the representation of normative concepts; and Part III offers a few remarks on the general issue of deontic logic's fruitfulness as an analytical tool. (shrink)

This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well-known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two-level approach to obligations is tested first against standard scenarios of contrary-to-duty obligations, leading also to a generalization for the Kanger-Anderson reduction of deontic logic. Next, the priority (...) framework is applied to model two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two-level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners. (shrink)