Overview of fundamental work in deontic logic.

This paper introduces deontic logic based on inquisitive semantics. A semantics for action formulas is introduced where each action formula is associated with a set of alternatives. Deontic operators are then interpreted as quantifying over all alternatives associated with the action formulas within their scope. It is shown how this construction provides solutions to problems related to free choice permissions and obligations, including issues concerning Hurford disjunctions. The main technical result is a complete axiomatization of the (...) class='Hi'>logic. (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 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.

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)

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)

There has been a recent surge of work on deontic modality within philosophy of language. This work has put the deontic logic tradition in contact with natural language semantics, resulting in significant increase in sophistication on both ends. This chapter surveys the main motivations, achievements, and prospects of this work.

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent (...) deontic action logic and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

Deontic logic is an area of logic which investigates normative concepts, systems of norms, and normative reasoning. The word ‘deontic’ is derived from the Greek expression ‘déon’, which means ‘what is binding’ or ‘proper’. Thus, Jeremy Bentham used the word ‘deontology’ for “the science of morality,” and the Austrian philosopher Ernst Mally, who developed in the 1920s a system of the “fundamental principles the logic of ought,” called his theory ‘Deontik’. Normative concepts include the concepts (...) of obligation (ought), permission (may), prohibition (may not), and related notions, such as the concept of right. Systems of deontic logic contain, in addition to the usual sentential connectives and quantifiers, logical constants which represent some of these normative concepts. (shrink)

It is well known that systems of action deontic logic emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law are subject to paradoxes. In general, paradoxes are acknowledged as such if we have intuitions telling us that things should be different. The aim of this paper is to introduce a paradox-free deontic action system by (i) identifying the basic intuitions leading to the emergence (...) of the paradoxes and (ii) exploiting these intuitions in order to develop a consistent deontic framework, where it can be shown why some phenomena seem to be paradoxical and why they are not so if interpreted in a correct way. (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)

The purpose of this paper is to develop a class of semantic tableau systems for some dyadic deontic logics. We will consider 16 different pure dyadic deontic tableau systems and 32 different alethic dyadic deontic tableau systems. Possible world semantics is used to interpret our formal languages. Some relationships between our systems and well known dyadic deontic logics in the literature are pointed out and soundness results are obtained for every tableau system. Completeness results are obtained (...) for all 16 pure dyadic deontic systems and for 16 alethic dyadic deontic systems. (shrink)

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed (...) from a uniform point of view. (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.

When a conflict of duties arises, a resolution is often sought by use of an ordering of priority or importance. This paper examines how such a conflict resolution works, compares mechanisms that have been proposed in the literature, and gives preference to one developed by Brewka and Nebel. I distinguish between two cases – that some conflicts may remain unresolved, and that a priority ordering can be determined that resolves all – and provide semantics and axiomatic systems for accordingly defined (...) dyadic deontic operators. (shrink)

Though there have been productive interactions between moral philosophers and deontic logicians, there has also been a tradition of neglecting the insights that the fields can offer one another. The most sustained interactions between moral philosophers and deontic logicians have notbeen systematic but instead have been scattered across a number of distinct and often unrelated topics. This chapter primarily focuses on three topics. First, we discuss the “actualism/possibilism” debate which, very roughly, concerns the relevance of what one will (...) do at some future time to what one ought to do at present (§2). This topic is also used to introduce various modal deontic logics. Second we discuss the particularism debate which, very roughly, concerns whether there can be any systematic general theory of what we ought to do (§3). This topic is also used to introduce various non-modal deontic logics. Third, we discuss collective action problems which concern the connection between the obligations of individuals and the behavior and obligations of groups of individuals (§4).This topic is also used to discuss formal systems that allow us to study the relationship between individuals and groups. The chapter also contains a general discussion of the relation between ethical theory and deontic logic (§1) and a brief consideration of other miscellaneous topics (§5). (shrink)

Relevant to philosophy, law, management, and artificial intelligence, these papers explore the applicability of nonmonotonic or defeasible logic to normative reasoning. The resulting systems purport to solve well-known deontic paradoxes and to provide a better treatment than classical deontic logic does of prima facie obligation, conditional obligation, and priorities of normative principles.

This article contains an overview of the author's long‐standing involvement with deontic logic, both from a technical and from a wider philosophical point of view. As far as the formal aspects of deontic logic are concerned, the author describes his intellectual development from the original discovery of the analogy between modal (and deontic) notions on the one hand, and quantifiers on the other, through the formulation of a systematic theory of dyadic deontic concepts, to (...) the proposal of a formal logic of action as a foundation for deontic logic. In a more philosophical vein, the author discusses such questions as the very possibility of deontic logic if norms have no truth‐value, the relation between the descriptive interpretation of classical deontic logic and the logic of norm‐propositions, the correct representation of conditional or hypothetical norms, the distinction between moral obligation and practical necessity, and the interdefinability of permission and obligation. (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 deontic (...) class='Hi'>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)

We provide a description and informal analysis of the commonalities in moral discourse concerning issues in the field of information and communications technology, present a logic model (DEAL) of this type of moral discourse that makes use of recent research in deontic, epistemic, and action logic, and indicate – drawing upon recent research in computer implementations of modal logic – how information systems may be developed that implement the proposed formalization.

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)

In Meyer’s promising account [7] deontic logic is reduced to a dynamic logic. Meyer claims that with his account “we get rid of most (if not all) of the nasty paradoxes that have plagued traditional deontic logic.” But as was shown by van der Meyden in [4], Meyer’s logic also contains a paradoxical formula. In this paper we will show that another paradox can be proven, one which also effects Meyer’s “solution” to contrary to (...) duty obligations and his logic in general. (shrink)

A problem related to theWason selection task is that only some thematic versions of it are executed correctly. Fodor raises the thesis that the versions that are adequately solved are those that refer to deontic situations. In his opinion, there is a deontic logic that is different to classical logic and that allows reasoning appropriately in deontic contexts. In this paper, I review Fodor’s arguments, question his assumptions, and propose an alternative explanation, based on the (...) mental models theory, of why only some versions of the selection task with thematic content offer optimal results. (shrink)

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)

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and (...) an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games. (shrink)

. The current literature in the Artificial Intelligence and Law field reveals uncertainty concerning the potential role of deontic logic in legal knowledge representation. For instance, the Logic Programming Group at Imperial College has shown that a good deal can be achieved in this area in the absence of explicit representation of the deontic notions. This paper argues that some rather ordinary parts of the law contain structures which, if they are to be represented in (...) class='Hi'>logic, will call for use of a reasonably sophisticated deontic logic. (shrink)

This paper introduces two new paradoxes for standard deontic logic (SDL). They are importantly related to, but distinct from Ross' paradox. These two new paradoxes for SDL are the simple weakening paradox and the complex weakening paradox. Both of these paradoxes arise in virtue of the underlaying logic of SDL and are consequences of the fact that SDL incorporates the principle known as weakening. These two paradoxes then show that SDL has counter-intuitive implications related to disjunctive obligations (...) that arise in virtue of deontic weakening and in virtue of decisions concerning how to discharge such disjunctive obligations. The main result here is then that theorem T1 is a problematic component of SDL that needs to be addressed. (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)

The purpose of this paper is to e»tahlish some connections between precedent-based reasoning as it is studied in the field of Artificial Intelligence and Law, particularly in the work of Ashley, and two other fields: deontic logic and nonmonotonic logic. First, a deontic logic is described that allows lor sensible reasoning in the presence of conflicting norms. Second, a simplified version of Ashley's account of precedent-based reasoning is reformulated within the framework of this deontic (...) logic. Finally, some ideas from the theory of nonmonotonic inheritance are employed to show how Ashley's account might be elaborated to allow for a richer representation of the process of argumentation. (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.".