Centered around the analysis of the prescriptive portion of the Vedas, the Sanskrit philosophical school of Mīmāṃsā provides a treasure trove of normative investigations. We focus on the leading Mīmāṃsā authors Prabhākara, Kumārila and Maṇḍana, and discuss three modal logics that formalize their deontic theories. In the first part of this paper, we use logic to analyze, compare and clarify the various solutions to the _śyena_ controversy, a two-thousand-year-old problem arising from seemingly conflicting commands in the Vedas. In the (...) second part, the formalized Mīmāṃsā theories are analyzed and employed to provide alternative perspectives on well-known paradoxes from the contemporary field of deontic logic. Thus, we go from logic to Mīmāṃsā and back again. (shrink)

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

In an earlier paper by the author, Åqvist , I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two-dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two-dimensionality, its being based on discrete and finite time, and its use of so-called systematic frame constants in order to enable us to indicate (...) longitudes and latitudes of any points in the co-ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two-dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense logic; and to deal with a curious puzzle known as the so-called epistemic obligation paradox – a well known stumbling-block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two-dimensional modalities. (shrink)

In a recent paper, Sven Danielsson argued that the ‘original paradoxes' of deontic logic, in particular Ross's paradox and Prior's paradox of derived obligation, can be solved by restricting the modal inheritance rule. I argue that this does not solve the paradoxes.

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)

This paper generalizes the (epistemic) preface paradox beyond the principle of belief aggregation and constructs a similar paradox for deontic reasoning. The analysis of the deontic case yields a solution strategy---restricting belief/obligation aggregation rather than giving it up altogether---that can be transferred to the epistemic case. Our proposal amounts to a reasonable compromise between two goals: (i) sticking to bridge principles between evidence and belief, such as the Lockean Thesis, and (ii) obtaining a sufficiently strong logic of doxastic (...) and deontic reasoning. (shrink)

It is argued that Ross's Paradox in deontic logic is a problem which should be taken seriously, and which can be given a solution which also solves some other wellknown paradoxes and the traditional problems with conditional obligation.

A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. “if you have hurt your friend, you should apologise”, “if he is guilty, he should confess”, and “if she will not keep her promise to you, she ought to call you”. It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic (...) class='Hi'>deontic systems, i.e., systems that include temporal, alethic and dyadic deontic operators. We will then show how it is possible to use our formal apparatus to symbolise contrary-to-duty obligations and to solve the so-called contrary-to-duty (obligation) paradox, a problem well known in deontic logic. We will argue that this response to the puzzle has many attractive features. Semantic tableaux are used to characterise our systems proof theoretically and a kind of possible world semantics, inspired by the so-called T× W semantics, to characterise them semantically. Our models contain several different accessibility relations and a preference relation between possible worlds, which are used in the definitions of the truth conditions for the various operators. Soundness results are obtained for every tableau system and completeness results for a subclass of them. (shrink)

In this paper, I will discuss some examples of the so-called contrary-to-duty paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us what ought to be the case if something forbidden is true, for example: ‘If she is guilty, she should confess’. Contrary-to-duty obligations are important in our moral and legal thinking. Therefore, we want to be able to find an adequate symbolisation of such obligations in some logical system, a task that has turned (...) out to be difficult. This is shown by the so-called contrary-to-duty paradox. I will investigate and evaluate one kind of solution to this problem that has been suggested in the literature, which I will call the ‘counterfactual solution’. I will use some recent systems that combine not only counterfactual logic and deontic logic, but also temporal logic, in my analysis of the paradox. I will argue that the counterfactual solution has many attractive features and that it can give a fairly satisfactory answer to some examples of the contrary-to-duty paradox, but that it nevertheless has some serious problems. The conclusion is that, notwithstanding the many attractive features of the solution, there seem to be other approaches to the paradox that are more promising. (shrink)

Overview of fundamental work in deontic logic.

In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the (...) restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions. (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.

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)

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.

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)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the (...) restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (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)

Actualists hold that contrary-to-duty scenarios give rise to deontic dilemmas and provide counterexamples to the transmission principle, according to which we ought to take the necessary means to actions we ought to perform. In an earlier article, I have argued, contrary to actualism, that the notion of ‘ought’ that figures in conclusions of practical deliberation does not allow for deontic dilemmas and validates the transmission principle. Here I defend these claims, together with my possibilist account of contrary-to-duty scenarios, (...) against Stephen White’s recent criticism. (shrink)

The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, which fixes (...) the types of action that are abstractly prescribed, and what is ideal with respect to the specific situation in which the agent acts, and (ii) the transitions associated with actions and the results of actions, which can obtain even without the action being performed. (shrink)

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a (...) detailed case study illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985. (shrink)

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a (...) detailed case study illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985. (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)

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)

Deontic logic is the logic of normative concepts such as obligation, permission, and prohibition. This non-technical overview of the area has a strong emphasis on the connections between deontic logic and problems discussed in moral philosophy. Major issues treated are the distinction between ought-to-be and ought-to-do, the various meanings of permissive expressions, the logical relations among norms, the paradoxes of deontic logic, and the nature of moral conflicts and moral dilemmas. It is concluded that deontic (...) logic has resources for precise treatment of important issues in moral philosophy, but in order to make full use of these resources, more co-operation between logicians and moral philosophers is needed. (shrink)

In this paper I argue that deontic modals are hyperintensional, i.e. logically equivalent contents cannot be substituted in their scope. I give two arguments, one deductive and the other abductive. First, I show that the contrary thesis leads to falsity; second, I argue that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity and explanatory power. I then propose a philosophical analysis of this thesis and outline some consequences. In Section (...) 1 I introduce and define deontic modality and hyperintensionality. In Section 2 I give a reductio for the hyperintensionality of deontic modals. If the argument is sound, a useful corollary is that deontic modals are also non-intensional, and therefore possible-world semantics accounts are illfitted for them. I then show how the main result can be strengthened or weakened by varying the definition of logical validity. In Section 3 I give an abductive argument for the hyperintensionality of deontic modals, arguing that with a single move we are able to solve many paradoxes and puzzles traditionally troubling deontic logic. I present a version of a hyperintensional deontic logic in an appendix, which I prove is sound and complete with respect to a version of truthmaker semantics. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

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)

Traditional approaches in deontic logic have focused on the so-called reportative reading of obligation sentences, by providing truth-functional semantics based on a primitive ideality order between possible worlds. Those approaches, however, do not take into account that, in natural language, obligation sentences primarily carry a prescriptive effect. The paper focuses precisely on that prescriptive character, and shows that the reportative reading can be derived from the prescriptive one. A dynamic, non truth-functional semantics for necessity deontic modals is developed, (...) in which the ideality relations among possible worlds can be updated. Finally, it is proven that the semantics solves several of the classic deontic paradoxes. (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)

A new deontic logic, Action Type Deontic Logic, is presented. To motivate this logic, a number of benchmark cases are shown, representing inferences a deontic logic should validate. Some of the benchmark cases are singled out for further comments and some formal approaches to deontic reasoning are evaluated with respect to the benchmark cases. After that follows an informal introduction to the ideas behind the formal semantics, focussing on the distinction between action types and action tokens. (...) Then the syntax and semantics of Action Type Deontic Logic is presented and it is shown to meet the benchmarks. Finally, possibilities for further research are indicated. In the appendix, decidability of the satisfiability of formulas is proved via a technique known from monadic First Order Logic. (shrink)

This paper explores the idea that a semantics for ‘ought’ should be neutral between different ways of deciding what an agent ought to do in a situation. While the idea is, I argue, well-motivated, taking it seriously leads to surprising, even paradoxical, problems for theorizing about the meaning of ‘ought’. This paper describes and defends one strategy—a form of Expressivism for the modal ‘ought’—for navigating these problems.

Niko Kolodny and John MacFarlane claim that a situation involving some trapped miners involves a deontic paradox the resolution of which requires rejecting the logical law of modus ponens. I show that the appearance of paradox results from confusion and that the miners case supplies no cogent reason for impugning modus ponens.

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)

In response to the charge that deontic ("argent-centered") restrictions are paradoxical, several recent writers suggest that such restrictions find support within T.M. Scanlon's contractualism. I suggest that this claim is only interesting if these restrictions are stronger than those supported by indirect consequentialism. I argue that contractualism cannot support restrictions any stronger than those supported by indirect consequentialism. The contractualists have mislocated the source of the paradox, which arises under any theory that defines right action in patient-focused terms. Consequentialism (...) and contractualism share this feature, so contractualism cannot support stronger deontic restrictions than consequentialism supports. (shrink)

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a (...) detailed case study illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985. (shrink)

Since it was presented in 1963, Chisholm’s paradox has attracted constant attention in the deontic logic literature, but without the emergence of any definitive solution. We claim this is due to its having no single solution. The paradox actually presents many challenges to the formalization of deontic statements, including (1) context sensitivity of unconditional oughts, (2) formalizing conditional oughts, and (3) distinguishing generic from nongeneric oughts. Using the practical interpretation of ‘ought’ as a guideline, we propose a linguistically (...) motivated logical solution to each of these problems, and explain the relation of the solution to the problem of contrary-to-duty obligations. (shrink)