This paper offers a critical analysis of the logical structure of principles proposed by Robert Alexy and, in particular, of their structure as optimisation commands. Its first part dwells on the question whether the optimisation element in the logical structure should be understood as part of modalisation, as part of the consequent, or as an independent element. In the second part, the author analyses possible forms of inter-definability of deontic operators. Finally, some questions are raised on the conditional structure (...) proposed by Alexy for principles. (shrink)

This article deals with the problem of justification of war in the light of Leibnizian natural right and deontic definitions. From an analysis of the principles of rationality on which, according to Leibniz, the justification of an act is based, it proposes “deontic types of war” - namely: justifiable wars (whether just or facultative), just wars (defensive war, war of cooperation), facultative wars (preventive war, humanitarian intervention), unjust wars (war of aggression, war of extermination, terrorism) -, which express (...) the modality according to which their agents are constrained to act, namely: authorized, necessarily justified, contingently justified or unjustified to the military action. This modalisation is illustrated by a “war casuistry”, mostly taken from Leibniz’s reflections on the wars of his time. As it will be seen, our hypothesis states that the sufficient reason for a war is at bottom identified with the principle of the best, whose application requires an examination of the consequences of action in different possible scenarios. (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)

A paper by Schulz (Philos Stud 149:367–386, 2010) describes how the suppositional view of indicative conditionals can be supplemented with a derived view of epistemic modals. In a recent criticism of this paper, Willer (Philos Stud 153:365–375, 2011) argues that the resulting account of conditionals and epistemic modals cannot do justice to the validity of certain inference patterns involving modalised conditionals. In the present response, I analyse Willer’s argument, identify an implicit presupposition which can plausibly be denied and show that (...) accepting it would blur the difference between plain assumptions and their epistemic necessitations. (shrink)

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)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic (...) structure that interacts directly with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...) showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (Necinc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO-f which does not validate (Necinc). An Appendix discusses (Necinc) in relation to counterpart theory. Of course, it would be a mistake to think that the rules for "multiple pointing" follow automatically from the rules for pointing proper. Max Black—The Elusiveness of Sets In some influential articles during the 1980s George Boolos proposed an interpretation of monadic second-order logic in terms of plural quantification [4, 5]. One objection to this proposal, pressed by Williamson [22, 456-7], focuses on the modal behaviour of plural variables, arguing that the proposed interpretation yields the wrong results in respect of the modal status of atomic predications. In the present paper I will present this objection and argue against it. In the course of developing the argument, I will have cause to consider the under-investigated question of how a logic for plurals should be extended to incorporate modal operators. (shrink)

Overview of fundamental work in deontic logic.

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.

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)

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)

Since the middle of the last century, normative language has been much studied. In particular, the normative function performed by certain sentences and by certain speech acts has been investigated in depth. Still, the normative function performed by certain physical artifacts designed and built to regulate human behaviors has not yet been thoroughly investigated. We propose to call this specific type of artifacts with normative intent ‘deontic artifacts’. This article aims to investigate this normative phenomenon that is so widespread (...) in our daily reality, but so often forgotten by scholars of norms and normativity. (shrink)

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)

Deontic constraints prohibit an agent performing acts of a certain type even when doing so will prevent more instances of that act being performed by others. In this article I show how deontic constraints can be interpreted as either maximizing or non-maximizing rules. I then argue that they should be interpreted as maximizing rules because interpreting them as non-maximizing rules results in a problem with moral advice. Given this conclusion, a strong case can be made that consequentialism provides (...) the best account of deontic constraints. (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.

Computational systems are traditionally approached from control-oriented perspectives; however, as soon as we move from centralized to decentralized computational infrastructures, direct control needs to be replaced by distributed coordination mechanisms that are on par with institutional constructs observable in human societies (contracts, agreements, enforcement mechanisms, etc.). This paper presents a formalization of Hohfeld's framework building upon a logic whose language includes primitive operators of ability and parametric deontic operators. The proposal is meant to highlight the fundamental interaction between (...) class='Hi'>deontic and potestative concepts and contains proofs of soundness and completeness with respect to a class of relational models. (shrink)

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

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)

In his recent article “Deontic Cycling and the Structure of Commonsense Morality,” Tim Willenken argues that commonsense ethics allows for rational agents having both ranked reasons (A > B, B > C, and A > C) and cyclical reasons (A < B, B < C, and A > C). His goal is to show that not all plausible views are variations of consequentialism, as consequentialism requires ranked reasons. Here I argue apparent instances of deontic cycling in commonsense morality (...) are the byproducts of an incomplete characterizations of the cases in question. (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)

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)

According to a recent challenge to Kratzer's canonical contextualist semantics for deontic modal expressions, no contextualist view can make sense of cases in which such a modal must be information-sensitive in some way. Here I show how Kratzer's semantics is compatible with readings of the targeted sentences that fit with the data. I then outline a general account of how contexts select parameter values for modal expressions and show, in terms of that account, how the needed, contextualist-friendly readings might (...) plausibly get selected in the challenge cases. (shrink)

This paper offers an account of deontic normativity in terms of attributive goodness. An action is permissible for S in C just in case there is a good practical inference available to S in C that results in S performing (or intending to perform) the action. The standards of goodness for practical inferences are determined by what is a good or bad exercise of the human capacity of practical reason, which is an attributive (and not a deontic) assessment.

The article offers an overview of the deontic theory developed by the philosophical school of Mīmāṃsā, which is, and has been since the last centuries BCE, the main source of normative concepts in Sanskrit thought. Thus, the Mīmāṃsā deontics is interesting for any historian of philosophy and constitutes a thought-provoking occasion to rethink deontic concepts, taking advantage of centuries of systematic reflections on these topics. Some comparison with notions currently used in Euro-American normative theories and metaethical principles is (...) offered in order to show possible points of contact and deep divergences. In more detail, after an introduction explaining the methodology and aims of our work, we discuss how Mīmāṃsā authors distinguished and defined some fundamental deontic concepts, such as different types of prescriptions and prohibitions. We then discuss how Mīmāṃsā authors approached the problem of conflicts among commands without jeopardising the validity of the normative text issuing them. In the second part of the article we introduce our formal apparatus, which is construed around the main taxonomic and conceptual distinctions used in the first part. Our formal rendering captures the most important features of the Mīmāṃsā theory and can thus serve as a concise and rigorous presentation of it for scholars working in deontic logic. (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)

According to deontic justice theory, individuals often feel principled moral obligations to uphold norms of justice. That is, standards of justice can be valued for their own sake, even apart from serving self-interested goals. While a growing body of evidence in business ethics supports the notion of deontic justice, skepticism remains. This hesitation results, at least in part, from the absence of a coherent framework for explaining how individuals produce and experience deontic justice. To address this need, (...) we argue that a compelling, yet still missing, step is to gain further understanding into the underlying neural and psychological mechanisms of deontic justice. Here, we advance a theoretical model that disentangles three key processes of deontic justice: The use of justice rules to assess events, cognitive empathy, and affective empathy. Together with reviewing neural systems supporting these processes, broader implications of our model for business ethics scholarship are discussed. (shrink)

Deontic reasoning is thinking about whether actions are forbidden or allowed, obligatory or not obligatory. It is proposed that social norms, imposing constraints on individual actions, constitute the fundamental concept for the system of these four deontic modalities, and that people reason from such norms flexibly according to deontic core principles. Two experiments are presented, one on deontic conditional reasoning, the other on “pure” deontic reasoning. Both experiments demonstrate people's high deontic competence and confirm (...) the proposed representational and inferential principles. Experiment 1 additionally shows small effects of the conditional formulations. These findings support the dual source approach (Beller & Spada, 2003) that distinguishes between domain-specific and domain-general inferences. Implications for other theories of deontic reasoning are discussed. (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.

Many philosophers think the distinctive function of deontic evaluation is to guide action. This idea is used in arguments for a range of substantive claims. In this paper, we entirely do one completely destructive thing and partly do one not entirely constructive thing. The first thing: we argue that there is an unrecognized gap between the claim that the function of deontic evaluation is to guide action and attempts to put that claim to use. We consider and reject (...) four arguments intended to bridge this gap. The interim conclusion is thus that arguments starting with the claim that the function of deontic evaluation is to guide action have a lacuna. The second thing: we consider a different tack for making arguments of this sort work. We sketch a methodology one could accept that would do the trick. Unfortunately, as we’ll explain, although this methodology would bridge the gap in arguments that put claims about the function of deontic evaluation to work, it would do so in a way that vitiates any interest we might have in such arguments. As an aside, we’ll also point out how epistemologists, who have recently become interested in the function of epistemic evaluation, appear to already recognize this fact. The conclusion is hence a dilemma: either arguments from deontic function to substance have a lacuna or such arguments lack teeth. (shrink)

Illustrates the prevalence of implicit quantification in deontic assertions in ordinary language.

Modality and negation, as two important linguistic features used to realise subjectivity, have been investigated within various disciplines, such as logic, linguistics and philosophy, and law. The interaction between modality and negation, as a relatively new and undeveloped domain, has however not been paid due attention in scholarship. This corpus-based study investigates three aspects of their interaction: the differentiation of the deontic value by negation, the categorization of deontic modality in Hong Kong legislation via negation, and distribution patterns (...) of deontic modality, especially distribution patterns of the negation of modality, in Hong Kong legislation. This study shows that negation is a powerful linguistic mechanism not only for determining the nature and functions of modality, but also for determining the value of modality. This study also reveals that negation helps us to investigate the distribution of deontic modality in Hong Kong legislation and hence revisit the legal framework in Hong Kong. A study taking into account the discursive and professional aspects of the interaction between deontic modality and negation will provide a theoretical basis for the natural language processing of modality and negation in legislation and also offer important implications for the study of negation and modality in general contexts. (shrink)

The evaluative categories (goodness, badness, betterness, and the like) and the deontic categories (requiredness, permittedness, forbiddenness, and the like) are separate families of normative categories, each with its own distinctive logic, structure, and basis. The aim of this chapter is to argue that there is a third family of normative categories beyond these familiar two, with its own special logic, structure, and basis, namely the fitting. This family includes properties and relations picked out by terms such as ‘fitting’, ‘apt’, (...) ‘merited’, ‘warranted’, and ‘justified’, as well as certain adjectives ending in ‘-able’ (e.g. ‘admirable’), ‘-ing’ (e.g. ‘annoying’), ‘-ive’ (e.g. ‘persuasive’), ‘-some’ (e.g. ‘fearsome’), and ‘-worthy’ (e.g. ‘blameworthy’). Acknowledging the distinctiveness of fittingness as a type of normative category changes how we think about the foundations of ethics and other normative disciplines. Instead of asking, “Is the good prior to the right, or the right prior to the good?” we should be asking, “What are the priority relations among the right, the good, and the fitting?”. (shrink)

The Deontic Transfer Principle states that if it is permissible for a person A to cause another person B harm H then, other things being equal, it is permissible for A to impose a risk of harm H on B. In this article we show that the Deontic Transfer Principle is vulnerable to counterexamples, and that the same is true of a range of closely related principles. We conclude that the deontic status of a risk imposition is (...) not directly inherited from the deontic properties of deterministic acts. (shrink)

The aim of the paper is to extend the calculus DSC1 in such a way as to satisfy all the requirements listed in [2] as well as a further stipulation { called `the principle of unionvolvement' { to the eect that neither deontic compatibility nor deontic incompatibility of codes should be presupposed in deontic logic. The observation that sentences of the form PKuw are stronger than it was suggested in [1] has been the point of departure.

In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics (DPM) that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of our normative (...) reasoning by their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts. (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)

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)

We investigate an extension of the formalism of interpreted systems by Halpern and colleagues to model the correct behaviour of agents. The semantical model allows for the representation and reasoning about states of correct and incorrect functioning behaviour of the agents, and of the system as a whole. We axiomatise this semantic class by mapping it into a suitable class of Kripke models. The resulting logic, KD45n i-j, is a stronger version of KD, the system often referred to as Standard (...) Deontic Logic. We extend this formal framework to include the standard epistemic notions defined on interpreted systems, and introduce a new doubly-indexed operator representing the knowledge that an agent would have if it operates under the assumption that a group of agents is functioning correctly. We discuss these issues both theoretically and in terms of applications, and present further directions of work. (shrink)

Torbjörn Tännsjö has written a clear and thought-provoking book on healthcare priority setting. He argues that different branches of ethical theory—utilitarianism, egalitarianism, and prioritarianism—are in general agreement on real-world healthcare priorities, and that it is human irrationality that stands in the way of complying with their recommendations. While I am generally sympathetic to the overall project and line of argumentation taken by the book, this paper raises two concerns with Tännsjö’s argument. First, that he is wrong to set aside (...) class='Hi'>deontic constraints as irrelevant or as pointing in the same direction as consequentialism. Secondly, that his argument against prioritarianism in favor of utilitarianism is insufficient and under-developed. Given these problems, I conclude that we should welcome Tännsjö’s contribution but with these qualifications in mind. (shrink)

This study draws on deontic justice theory to examine an unexplored socioemotional micro-foundation of corporate social responsibility (CSR), namely anticipated guilt, in an effort to improve our understanding of employees’ moral reactions to their organization’s CSR. We empirically investigate whether environmental CSR induces anticipated guilt (i.e., concerns about future guilt for not contributing to organizational CSR) leading to organizational environmental citizenship behavior. We also consider two boundary conditions related to the social nature of anticipated guilt: line manager support for (...) the environment and negative environmental group norms. To test our hypotheses, we analyzed data from a convenience sample of 503 managers working in Mexican organizations, using Latent Moderated Structural equation modeling. Overall, our results support the deontic argument that employees care about CSR because CSR embodies moral concerns. Specifically, our findings show that efforts to avoid a guilty conscience increase when the line manager provides increased resources and control to act for the environment, and when group members do not care for the environment, suggesting that employees feel they have to compensate for their group’s moral failure. (shrink)

Three experiments investigated the contrasting predictions of the evolutionary and decision-theoretic approaches to deontic reasoning. Two experiments embedded a hazard management (HM) rule in a social contract scenario that should lead to competition between innate modules. A 3rd experiment used a pure HM task. Threatening material was also introduced into the antecedent, p, of a deontic rule, if p then must q. According to the evolutionary approach, more HM responses (Cosmides & Tooby, 2000) are predicted when p is (...) threatening, whereas decision theory predicts fewer. All 3 experiments were consistent with decision theory. Other theories are discussed, and it is concluded that they cannot account for the behavior observed in these experiments. (shrink)

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)