I identify and develop a solution to the puzzles of anankastic conditionals that is novel in the sense that it has gone largely unnoticed, but also well-worn in that the materials for it have long been available. The solution involves an integration of the classical Kratzerian premise semantics and a default theory of reasons (such as the one presented in Horty, 2012, leveraging several decades of research on default logic). To stress-test the proposal I also investigate how (...) it might be applied to the variety of anankastic-adjacent data discussed by Condoravdi and Lauer (2016). The resulting approach is not just an exceptional fit for the problem of anankastic conditionals, but also an independently promising upgrade on the classical account of modals. (shrink)

I begin by reviewing classical semantics and the problems presented by normative conflicts. After a brief detour through default logic, I establish some connections between the treatment of conflicts in each of these two approaches, classical and default, and then move on to consider some further issues: priorities among norms, or reasons, conditional oughts, and reasons about reasons.

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)

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)

John Horty has proposed an approach to reasoning with ought-propositions which stands in contrast to the standard modal approach to deontic logic. Horty’s approach is based on default theories as known from the framework of Default Logic. It is argued that the approach cannot be extended beyond the most simple kinds of default theories and that it fails in particular to account for conditional obligations. The most plausible ways of straightening out the defects of the approach (...) conform to a simple theory of default reasoning in standard deontic language. (shrink)

A compositional semantics for anankastic conditionals (‘If you want p, you must φ’) has been elusive. Condoravdi and Lauer (2016) decisively object to all semantics that precede their own. CL's view rests on a response to *the problem of conflicting goals*; CL use an interpretation of 'want' on which an agent's desires don't conflict with her beliefs. But a proper response requires lack of conflict with the facts. CL's view fails. Anankastic conditionals are still a mystery.

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' (...) uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation"--Publisher. (shrink)

In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including (...) default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the admissibility semantics for all these formalisms has a natural argumentation-theoretic interpretation and proof procedure, which seem to correspond well with informal argumentation. (shrink)

Lou Goble proposed powerful conditional deontic logics (CDPM) that are able to deal with deontic conflicts by means of restricting the inheritance principle. One of the central problems for dyadic deontic logics is to properly treat the restricted applicability of the principle “strengthening the antecedent”. In most cases it is desirable to derive from an obligation A under condition B, that A is also obliged under condition B and C. However, there are important counterexamples. Goble proposed a (...) weakened rational monotonicity principle to tackle this problem. This solution is suboptimal as it is for some examples counter-intuitive or even leads to explosion. The paper identifies also other problems of Goble’s systems. For instance, to make optimal use of the restricted inheritance principle, in many cases the user has to manually add certain statements to the premises. An adaptive logic framework based on CDPM is proposed which is able to tackle these problems. It allows for certain rules to be applied as much as possible. In this way counter-intuitive consequences as well as explosion can be prohibited and no user interference is required. Furthermore, for non-conflicting premise sets the adaptive logics are equivalent to Goble’s dyadic version of standard deontic logic. (shrink)

Abstract.The paper outlines the approach to the analysis of deontic conditionals taken in earlier work by Jones and Pörn, compares it very briefly with two main trends within dyadic deontic logic, and then discusses problems associated with the augmentation principle and the factual detachment principle. The author then modifies Jones and Pörn's previous system, using a classical but not normal (in the sense of Chellas) deontic modality to provide the basis for an alternative analysis of deontic (...) conditionals. This new analysis validates neither the factual detachment nor the augmentation principles. However, influenced by the approach of James Delgrande to default reasoning, the author tries to show how a restricted form of factual detachment may be accommodated within the revised system. (shrink)

​This volume brings together a group of philosophically oriented logicians and logic-minded philosophers, mainly from Asia, to address a variety of logical and philosophical topics, such as modal logic and related directions (e.g. temporal logic, epistemic logic, deontic logic, logic of conditionals, and modal proof theory), theory of truth, paradoxes, intentionality, and social networks. New approaches are also proposed, such as extended modal logic with planarity of graphs, extended branching time temporal logic with conditional operators, and a relational treatment (...) of language and logical systems, to name but a few.Given the variety of topics and issues discussed here, the book will appeal to readers from a broad range of disciplines, from mathematical/philosophical logic, computing science, cognitive science and artificial intelligence, to linguistics, game theory and beyond. (shrink)

The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty’s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides (...) with Horty’s one, this is not true in more complicated or “realistic” settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones. (shrink)

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output (...) system, considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourr6n/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step. (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)

Normal systems of modal logic, interpreted as deontic logics, are unsuitable for a logic of conflicting obligations. By using modal operators based on a more complex semantics, however, we can provide for conflicting obligations, as in [9], which is formally similar to a fragment of the logic of ability later given in [2], Having gone that far, we may find it desirable to be able to express and consider claims about the comparative strengths, or degrees of urgency, (...) of the conflicting obligations under which we stand. This paper, building on the formalism of the logic of ability in [2], provides a complete and decidable system for such a language. (shrink)

This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this (...) method the language of Reiter's default logic is extended to include modal expressions, after which the argumentation framework in default logic of [20, 22] is used to give a plausible logical analysis of moral dilemmas and prima facie obligations. (shrink)

Realism for agents with unconditional beliefs, desires and intentions has been analyzed in modal logic. This paper provides a logical analysis of realism for agents with conditional beliefs and desires in a rule based approach analogous to Reiter's default logic. We distinguish two types of realism, which we call ‘a priori' and ‘a posteriori' realism. We analyze whether these two new properties are compatible with other properties discussed in the literature, such as existence of extensions. We show that Reiter's (...) default logic is too strong, in the sense that a weaker notion of maximality of extensions is needed to satisfy realism. Finally we show that several existing approaches do not satisfy the new realism properties, and we introduce a new construction that does satisfy them. (shrink)

From a philosophical standpoint, the work presented here is based on van Fraassen [26]. The bulk of that paper is organized around a series of arguments against the assumption, built into standard deontic logic, that moral dilemmas are impossible; and van Fraassen only briefly sketches his alternative approach. His paper ends with the conclusion that “the problem of possibly irresolvable moral conflict reveals serious flaws in the philosophical and semantic foundations of ‘orthodox’ deontic logic, but also suggests a (...) rich set of new problems and methods for such logic.” My goal has been to suggest that some of these methods might be found in current research on nonmonotonic reasoning, and that some of the problems may have been confronted there as well.I have shown that nonmonotonic logics provide a natural framework for reasoning about moral dilemmas, perhaps even more useful than the ordinary modal framework, and that the issues surrounding the treatment of exceptional information within these logics run parallel to some of the problems posed by conditional oughts. However, there is also another way in which deontic logic might benefit from a connection to nonmonotonic reasoning. A familiar criticism among ethicists of work in deontic logic is that it is too abstract, and too far removed from the kind of problems confronted by real agents in moral deliberation. It must be said that similar criticisms of abstraction and irrelevance are often lodged against work in nonmonotonic reasoning by more practically minded researchers in artificial intelligence; but here, at least, the criticisms are taken seriously. Nonmonotonic logic aims at a qualitative account of commonsense reasoning, which can be used to relate planning and action to defeasible goals and beliefs; and at least some of the theories developed in this area have been tested in realistic situations. By linking the subject of deontic logic to this research, it may be possible also to relate the idealized study of moral reasoning typical of the field to a more robust treatment of practical deliberation. (shrink)

This chapter contains sections titled: Modal Concepts The Semantics of Modalities and Systems of Modal Logic Modality and Quantification Deontic, Epistemic, and Temporal Modalities Epistemic Logic Deontic Logic Temporal Frames Conditional Obligations and Rules of Detachment.

An extraordinary amount of recent work by philosophers of language, meta-ethicists, and semanticists has focused on the meaning and function of language expressing concepts having to do with what is allowed, forbidden, required, or obligatory, in view of the requirements of morality, the law, one's preferences or goals, or what an authority has commanded: in short, deontic modality. This volume presents new work on the much-discussed topic of deontic modality by leading figures in the philosophy of language, meta-ethics, (...) and linguistic semantics. The papers tackle issues about the place of decision and probability theory in the semantics of deontic modality, the viability of standard possible worlds treatments of the truth conditions of deontic modal sentences, the possibility of dynamic semantic treatments of deontic modality, the methodology of semantics for deontic modals, and the prospects for representationalist, expressivist, and inferentialist treatments of deontic modality. (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.

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...

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)

This chapter provides a selective survey of prominent theories of the semantics of deontic modals in logic and natural language. We focus on Kratzer’s (1977; 1981; 1991) semantics and extensions to this analysis. Kratzer’s semantics has been far and away the most influential theory of deontic modals, which provide a base case for the interpretation of normative language in general. Understanding the logic and truth-conditions of normative language is one of the core areas of metaethics. It (...) informs our understanding of normative arguments and normative reasoning. As this chapter will emphasize, some forms of normative language don’t allow for the inferences that classical logic trains philosophers to expect. Understanding what inferences are valid for normative language should impact our under-standing of how we reason, and should reason, about the normative. We will first look at how deontic modals are understood in the context of modal logic and natural language. Then we’ll survey some recent debates and discoveries in the literature on deontic modals in natural language. We close with some considerations about the relevance of natural language to metaethics. (shrink)

This is a note from an AMC session on Jeff Horty's (2012) book *Reasons as Defaults*.

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)

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)

A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions. In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities.

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.

Kolodny and MacFarlane have made a pioneering contribution to our understanding of how the interpretation of deontic modals can be sensitive to evidence and information. But integrating the discussion of information-sensitivity into the standard Kratzerian framework for modals suggests ways of capturing the relevant data without treating deontic modals as “informational modals” in their sense. I show that though one such way of capturing the data within the standard semantics fails, an alternative does not. (...) Nevertheless I argue that we have good reasons to adopt an information-sensitive semantics of the general type Kolodny and MacFarlane describe. Contrary to the standard semantics, relative deontic value between possibilities sometimes depends on which possibilities are live. I develop an ordering semantics for deontic modals that captures this point and addresses various complications introduced by integrating the discussion of information-sensitivity into the standard semantic framework. By attending to these complexities, we can also illuminate various roles that information and evidence play in logical arguments, discourse, and deliberation. (shrink)

This paper concerns a thorny problem posed by conditional requirements: we expect some modal conditionals of the form ‘if p, then it must be that p’ to be false, yet they all come out true given two basic assumptions needed to account for ordinary conditional requirement like ‘If the light turns red, then cars must stop’. The first assumption is a semantic expectation linking conditional requirements with absolute ones, the second is the possible-worlds-based definition of modal sentences. Keeping the former (...) means giving up the latter, a result with profound implications for Kratzer’s formal semantics, modifications thereof, as well as deontic logics. (shrink)

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)

Deontic necessity modals (e.g. 'have to', 'ought to', 'must', 'need to', 'should', etc.) seem to vary in how they interact with negation. According to some accounts, what forces modals like 'ought' and 'should' to outscope negation is their polarity sensitivity -- modals that scope over negation do so because they are positive polarity items. But there is a conflict between this account and a widely assumed theory of if-clauses, namely the restrictor analysis. In particular, the conflict (...) arises for constructions containing a bound pronoun in the if-clause. This note spells out the core conflict. (shrink)

Within legal contexts, a claim to knowledge requires that the evidence appealed to fulfills conditions established by legal norms that belong to the so-called Evidence Law. In addition, the epistemic justification presupposed by this kind of knowledge is temporally affected by the changing character of the evidence and the judicial discretion usually exercised in the applications of the Evidence Law. As such, these two scenarios involve three modalities: temporal, epistemic, and deontic. The present paper philosophically discusses the links between (...) these modal dimensions in the above legal context. Based on the discussion, a formal tense-epistemic-deontic logic is developed. That is, the paper characterizes a formal language formally representing the three dimensions through specific logical operators, constructs a formal semantics for the language, and specifies a formal logical system. Finally, the soundness and completeness of the system with respect to the semantics is proved. (shrink)

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of (...) this paper is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concerns Åqvist’s system F supplemented with the principle of cautious monotony. It is established that, under the maximality rule, F + is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth . From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F + is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth . Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity. (shrink)

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...) obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. -/- I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis' V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. -/- My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like "If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated" is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations. (shrink)

We consider an infinite hierarchy of systems of Alethic Modal Logic with so-called Levels of Perfection, and add to them suitable definitions of such interesting deontic categories as those of supererogation, offence, conditional obligation and conditional permission. We then state three problems concerning the proper characterization of the resulting logic(s) for our defined notions, and discuss two of these problems in some detail.

Our goal here is to help identify the contextualist’s most worthy competitor to relativism. Recently, some philosophers of language and linguists have argued that, while there are contextualist-friendly semantic theories of deontic modals that fit with the relativist’s challenge data, the best such theories are not Lewis-Kratzer-style semantic theories. If correct, this would be important: It would show that the theory that has for many years enjoyed the status of the default view of modals in English (...) and other languages is in need of revision. Here we defend the default view by showing how a Kratzer-style semantics is able to make available readings of the relevant utterances that fit with the pretheoretical judgments opponents purport it cannot fully capture. Having established this, we turn to considering the more theoretical grounds proponents have offered for preferring their rival contextualist views. Here the question is to what extent such grounds favor semantic over what Korta and Perry call “near-side pragmatic” explanations of our judgments. In particular, we argue that our favored readings figure in near-side pragmatic explanations of those judgments that possess the methodological and theoretical advantages of systematicity and unity at least as well as, if not to a greater extent than, those of opponents who argue for their revised semantic theories on the basis of these advantages. (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)

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)

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 this paper we present an executable approach to model interactions between agents that involve sensitive, privacy-related information. The approach is formal and based on deontic, epistemic and action logic. It is conceptually related to the Belief-Desire-Intention model of Bratman. Our approach uses the concept of sphere as developed by Waltzer to capture the notion that information is provided mostly with restrictions regarding its application. We use software agent technology to create an executable approach. Our agents hold beliefs about (...) the world, have goals and commitment to the goals. They have the capacity to reason about different courses of action, and communicate with one another. The main new ingredient of our approach is the idea to model information itself as an intentional agent whose main goal it is to preserve the integrity of the information and regulate its dissemination. We demonstrate our approach by applying it to an important process in the insurance industry: applying for a life insurance. In this paper we will: (1) describe the challenge organizational complexity poses in moral reasoning about informational relationships; (2) propose an executable approach, using software agents with reasoning capacities grounded in modal logic, in which moral constraints on informational relatio nships can be modeled and investigated; (3) describe the details of our approach, in which information itself is modeled as an intentional agent in its own right; (4) test and validate it by applying it to a concrete ‘hard case’ from the insurance industry; and (5) conclude that our approach upholds and offers potential for both research and practical application. (shrink)

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (cf. Hansson [10]) (...) studies formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can “deconstruct” standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power.. (shrink)

Two groups of agents, G1 and G2, face a *moral conflict* if G1 has a moral obligation and G2 has a moral obligation, such that these obligations cannot both be fulfilled. We study moral conflicts using a multi-agent deontic logic devised to represent reasoning about sentences like "In the interest of group F of agents, group G of agents ought to see to it that phi". We provide a formal language and a consequentialist semantics. An illustration of our semantics (...) with an analysis of the Prisoner’s Dilemma follows. Next, necessary and sufficient conditions are given for (1) the possibility that a single group of agents faces a moral conflict, for (2) the possibility that two groups of agents face a moral conflict within a single moral code, and for (3) the possibility that two groups of agents face a moral conflict. (shrink)

This paper presents a justification counterpart for dyadic deontic logic, which is often argued to be better than Standard Deontic Logic at representing conditional and contrary-to-duty obligations, such as those exemplified by the notorious Chisholm’s puzzle. We consider the alethic-deontic system (E) and present the explicit version of this system (JE) by replacing the alethic Box-modality with proof terms and the dyadic deontic Circ-modality with justification terms. The explicit representation of strong factual detachment (SFD) is given (...) and finally soundness and completeness of the system (JE) with respect to basic models and preference models is established. (shrink)

Statements containing epistemic modals (e.g., “by spring 2023 most European countries may have the Covid-19 pandemic under control”) are common expressions of epistemic uncertainty. In this paper, previous published findings (Knobe & Yalcin, 2014; Khoo & Phillips, 2018) on the opposition between Contextualism and Relativism for epistemic modals are re-examined. It is found that these findings contain a substantial degree of individual variation. To investigate whether participants differ in their interpretation of epistemic modals, an experiment with multiple (...) phases and sessions is used to classify participants according to the three semantic theories of Relativism, Contextualism, and Objectivism. Through this study, some of the first empirical evidence for the kind of truth-value shifts postulated by semantic Relativism is presented. It is furthermore found that participants’ disagreement judgments match their truth evaluations and that participants are capable of distinguishing between truth and justification. In a second experimental session, it is investigated whether participants thus classified follow the norm of retraction which Relativism uses to account for argumentation with epistemic modals. Here the results are less favorable for Relativism. In a second experiment, these results are replicated and the normative beliefs of participants concerning the norm of retraction are investigated following work on measuring norms by Bicchieri (2017). Again, it is found that on average participants show no strong preferences concerning the norm of retraction for epistemic modals. Yet, it was found that participants who had committed to Objectivism and had training in logics applied the norm of retraction to might-statements. These results present a substantial challenge to the account of argumentation with epistemic modals presented in MacFarlane (2014), as discussed. Keywords: Epistemic Modals, Relativism, Norm Conflicts, Retraction, Semantics, Truth Conditions, Argumentation. (shrink)

This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) (...) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms. (shrink)