Deontic Logic

Edited by Matteo Pascucci (Slovak Academy of Sciences, Central European University)
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Summary Deontic logic can be described as the rigorous study of the deductive and semantic behaviour of normative concepts.
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  1. De la ingeniosa disolución que dio el gobernador Sancho Panza a la paradoja del suicida.Luis Felipe Bartolo Alegre - manuscript
    This is the story of how the noble squire Sancho Panza, while governing what he thought to be an insula, ingeniously solved a paradox not unlike those of modern logic.
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  2. A Spurious Paradox.Danny Frederick - manuscript
    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.
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  3. David Lewis' semantics for deontic logic.Holly Smith - manuscript
    Mind, Vol. LXXXVI (April, 1977) pp. 242-248.
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  4. An inconsistency-adaptive deontic logic for normative conflicts.Mathieu Beirlaen, Christian Strasser & Joke Meheus - forthcoming - Journal of Philosophical Logic.
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  5. Deontic Logic and Natural Language.Fabrizio Cariani - forthcoming - In Dov Gabbay, Ron van der Meyden, John Horty, Xavier Parent & Leandert van der Torre (eds.), The Handbook of Deontic Logic (Vol. II). College Publications.
    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.
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  6. Deontic Logics based on Boolean Algebra.Pablo F. Castro & Piotr Kulicki - forthcoming - In Robert Trypuz (ed.), Krister Segerberg on Logic of Actions. Springer.
    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 (...)
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  7. Contextual Factors in Deontic Reasoning.Keith J. Holyoak & Patricia W. Cheng - forthcoming - Thinking and Reasoning.
  8. The Explanatory Problem for Cognitivism about Practical Reason.Errol Lord - forthcoming - In Conor McHugh Jonathan Way & Daniel Whiting (eds.), Normativity: Epistemic and Practical.
    Cognitivists about practical reason hold that we can explain why certain wide-scope requirements of practical rationality are true by appealing to certain epistemic requirements. Extant discussions of cognitivism focus solely on two claims. The first is the claim that intentions involve beliefs. The second is that whenever your intentions are incoherent in certain ways, you will be epistemically irrational. Even if the cognitivist successfully defends these claims, she still needs to show that they entail certain practical requirements. That is, she (...)
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  9. A Two-Dimensional Logic for Two Paradoxes of Deontic Modality.Fusco Melissa & Kocurek Alexander - forthcoming - Review of Symbolic 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 (...)
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  10. Deontic Logic and Ethics.Shyam Nair - forthcoming - In Gabbay, John Horty, Xavier Parent, Ron van der Meyden & Leon van der Torre (eds.), Handbook of Deontic Logic and Normative System, Volume 2. College Publications.
    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 (...)
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  11. Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics.Eugenio Orlandelli - forthcoming - Logic and Logical Philosophy:1.
    G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they are (...)
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  12. A legal grounding for deontic logic.Clayton Peterson - forthcoming - (Soumis).
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  13. Iterated modalities and the parallel between deontic and modal logic.E. J. Szewak - forthcoming - Logique Et Analyse.
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  14. On deontic action logics based on Boolean algebra.Robert Trypuz & Piotr Kulicki - forthcoming - Journal of Logic and Computation.
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  15. Disease as a Deontic Construct.Kazem Sadegh-Zadeh - 2nd ed. 2015 - In Handbook of Analytic Philosophy of Medicine. Springer Verlag.
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  16. Medicine Is a Deontic Discipline.Kazem Sadegh-Zadeh - 2nd ed. 2015 - In Handbook of Analytic Philosophy of Medicine. Springer Verlag.
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  17. Solving the Ross and Prior Paradoxes. Classical Modal Calculus..Pociej Jan - 2024 - Https://Doi.Org/10.6084/M9.Figshare.25257277.V1.
    Resolving the Ross and Prior paradoxes proved to be a difficult task. Its first two stages, involving the identification of the true natures of the implication and truth values, are described in the articles "Solving the Paradox of Material Implication – 2024" and "Solving Jörgensen's Dilemma – 2024". This article describes the third stage, which involves the discovery of missing modal operators and the Classical Modal Calculus. Finally, procedures for solving both paradoxes are provided.
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  18. Beyond reasons and obligations: A dual-role approach to reasons and supererogation.Knoks Aleks & Streit David - 2023 - In Juliano Maranhão, Clayton Peterson, Christian Straßer & van der Torre Leendert (eds.), Deontic Logic and Normative Systems: 16th International Conference (DEON2023, Trois-Rivières). London: College Publications. pp. 119-137.
    Dual-role approaches to reasons say, roughly, that reasons can relate to actions in two fundamentally different ways: they can either require conformity, or justify an action without requiring that it be taken. This paper develops a formal dual-role approach, combining ideas from defeasible logic and practical philosophy. It then uses the approach to shed light on the phenomenon of supererogation and resolve a well-known puzzle about supererogation, namely, Horton’s All or Nothing Problem.
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  19. The Validity of the Argument from Inductive Risk.Matthew J. Brown & Jacob Stegenga - 2023 - Canadian Journal of Philosophy 53 (2):187-190.
    Havstad (2022) argues that the argument from inductive risk for the claim that non-epistemic values have a legitimate role to play in the internal stages of science is deductively valid. She also defends its premises and thus soundness. This is, as far as we are aware, the best reconstruction of the argument from inductive risk in the existing literature. However, there is a small flaw in this reconstruction of the argument from inductive risk which appears to render the argument invalid. (...)
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  20. Truthmaker Foundations for Deontic Logic’: Response to Rothchild’s and Yablo’s ‘Permissive Updates.Kit Fine - 2023 - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Springer Verlag. pp. 663-689.
    I attempt to provide a general account of deontic context, equally applicable within and an intensional and a hyperintensional framework; I compare Rothschild's and Yablo's accounts of the semantics for deontic logic, deontic updating and denotic duality with my own accounts; and I conclude with some general remarks on negation.
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  21. The Simplest Solution to the Deepest Paradox of Deontic Logic.Jeremiah Joven Joaquin - 2023 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 30 (4):312-322.
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  22. Deontic Logic and Normative Systems: 16th International Conference (DEON2023, Trois-Rivières).Juliano Maranhão, Clayton Peterson, Christian Straßer & van der Torre Leendert (eds.) - 2023 - College Publications.
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  23. Three Forms of Actualist Direct Consequentialism.Shyam Nair - 2023 - Utilitas 35 (1):1-24.
    One family of maximizing act consequentialist theories are actualist direct theories. Indeed, historically there are at least three different forms of actualist direct consequentialism (due to Bentham, Moore, and contemporary consequentialists). This paper is about the logical differences between these three actualist direct theories and the differences between actualist direct theories and their competitors. Three main points emerge. First, the sharpest separation between actualist direct theories and their competitors concerns the so-called inheritance principle. Second, there are a myriad of other (...)
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  24. Free Choice in Modal Inquisitive Logic.Karl Nygren - 2023 - Journal of Philosophical Logic 52 (2):347-391.
    This paper investigates inquisitive extensions of normal modal logic with an existential modal operator taken as primitive. The semantics of the existential modality is generalized to apply to questions, as well as statements. When the generalized existential modality is applied to a question, the result is a statement that roughly expresses that each way of resolving the question is consistent with the available information. I study the resulting logic both from a semantic and from a proof-theoretic point of view. I (...)
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  25. A formal, diagrammatic, and operational study of normative relations.Matteo Pascucci & Giovanni Sileno - 2023 - Journal of Logic and Computation 33 (4):764-795.
    In this work, we provide an extensive analysis of Hohfeld’s theory of normative relations, focusing in particular on diagrammatic structures. Our contribution is threefold. First, we specify an extensional formal language to represent the main notions in the two families of normative relations identified by Hohfeld (i.e. the deontic and the potestative family). Our primary focus is on the part of the theory concerning potestative relations. In this regard, we assign a key role to the concept of ability, which is (...)
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  26. Contrastive Consent and Secondary Permissibility.Theron Pummer - 2023 - Philosophy and Phenomenological Research 106 (3):677-691.
    Consider three cases: -/- Turn: A trolley is about to kill five innocent strangers. You can turn the trolley onto me, saving the five and killing me. -/- Hurl: A trolley is about to kill five innocent strangers. You can hurl me at the trolley, saving the five and paralyzing me. -/- TurnHurl: A trolley is about to kill five innocent strangers. You can turn the trolley onto me, saving the five and killing me. You can instead hurl me at (...)
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  27. Do formal objections to the error theory overgeneralize?Bart Streumer & Daniel Wodak - 2023 - Analysis 83 (4):732-741.
    We argued that formal objections to the error theory overgeneralize and therefore fail. Christine Tiefensee and Gregory Wheeler deny this. We argue that they are wrong, for two reasons. The first concerns how we should adjudicate conflicts between formal and substantive commitments. The second concerns an overlooked tension between formal objections and non-error-theoretic views. Our discussion shows that the commitments behind formal objections to the error theory, such as the dual schema, should be regarded as much more contentious than is (...)
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  28. From Ideal Worlds to Ideality.Craig Warmke - 2023 - Journal of the American Philosophical Association 9 (1):114-134.
    In common treatments of deontic logic, the obligatory is what is true in all deontically ideal possible worlds. In this article, I offer a new semantics for Standard Deontic Logic with Leibnizian intensions rather than possible worlds. Even though the new semantics furnishes models that resemble Venn diagrams, the semantics captures the strong soundness and completeness of Standard Deontic Logic. Since, unlike possible worlds, many Leibnizian intensions are not maximally consistent entities, we can amend the semantics to invalidate the inference (...)
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  29. A Deontic Logic for Programming Rightful Machines: Kant’s Normative Demand for Consistency in the Law.Ava Thomas Wright - 2023 - Logics for Ai and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence (Lingai) and the International Workshop on Logic, Ai and Law (Lail).
    In this paper, I set out some basic elements of a deontic logic with an implementation appropriate for handling conflicting legal obligations for purposes of programming autonomous machine agents. Kantian justice demands that the prescriptive system of enforceable public laws be consistent, yet statutes or case holdings may often describe legal obligations that contradict; moreover, even fundamental constitutional rights may come into conflict. I argue that a deontic logic of the law should not try to work around such conflicts but, (...)
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  30. In Search of Modal Hypodoxes using Paradox Hypodox Duality.Peter Eldridge-Smith - 2022 - Philosophia 50 (5):2457-2476.
    The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis of the duality and I search (...)
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  31. A Two-Dimensional Logic for Two Paradoxes of Deontic Modality.Melissa Fusco & Alexander W. Kocurek - 2022 - Review of Symbolic Logic 15 (4):991-1022.
    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 (...)
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  32. Generalizing Deontic Action Logic.Alessandro Giordani & Matteo Pascucci - 2022 - Studia Logica 110 (4):989-1033.
    We introduce a multimodal framework of deontic action logic which encodes the interaction between two fundamental procedures in normative reasoning: conceptual classification and deontic classification. The expressive power of the framework is noteworthy, since it combines insights from agency logic and dynamic logic, allowing for a representation of many kinds of normative conflicts. We provide a semantic characterization for three axiomatic systems of increasing strength, showing how our approach can be modularly extended in order to get different levels of analysis (...)
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  33. Supererogation and Conditional Obligation.Daniel Muñoz & Theron Pummer - 2022 - Philosophical Studies 179 (5):1429–1443.
    There are plenty of classic paradoxes about conditional obligations, like the duty to be gentle if one is to murder, and about “supererogatory” deeds beyond the call of duty. But little has been said about the intersection of these topics. We develop the first general account of conditional supererogation, with the power to solve familiar puzzles as well as several that we introduce. Our account, moreover, flows from two familiar ideas: that conditionals restrict quantification and that supererogation emerges from a (...)
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  34. Norms and Alternatives : Logical Aspects of Normative Reasoning.Karl Nygren - 2022 - Dissertation, Stockholm University
    In this thesis, I develop and investigate various novel semantic frameworks for deontic logic. Deontic logic concerns the logical aspects of normative reasoning. In particular, it concerns reasoning about what is required, allowed and forbidden. I focus on two main issues: free-choice reasoning and the role of norms in deontic logic. -/- Free-choice reasoning concerns permissions and obligations that offer choices between different actions. Such permissions and obligations are typically expressed by a disjunctive clause in the scope of a deontic (...)
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  35. Normatively determined propositions.Matteo Pascucci & Claudio E. A. Pizzi - 2022 - In V. Giardino, S. Linker, S. Burns, F. Bellucci, J. M. Boucheix & P. Viana (eds.), Diagrammatic Representation and Inference. Proceedings of Diagrams 2022. Cham: Springer. pp. 78-85.
    In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposition. Finally, we show how the two resulting squares can be combined (...)
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  36. Deontic Logic, Weakening and Decisions Concerning Disjunctive Obligations.Michael J. Shaffer - 2022 - Logos and Episteme 13 (1):93-102.
    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 (...)
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  37. The Paradox of Epistemic Obligation Avoided.Michael J. Shaffer - 2022 - The Reasoner 16:49-50.
    This short paper offers a skeptical solution to Åqvist's paradox of epistemic obligation. The solution is based on the contention that in SDL/KDT logics the externalist features of knowledge, about which we cannot have obligations, are obscured.
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  38. Inheritance: Professor Procrastinate and the logic of obligation1.Kyle Blumberg & John Hawthorne - 2021 - Philosophy and Phenomenological Research 106 (1):84-106.
    Inheritance is the principle that deontic `ought' is closed under entailment. This paper is about a tension that arises in connection with Inheritance. More specifically, it is about two observations that pull in opposite directions. One of them raises questions about the validity of Inheritance, while the other appears to provide strong support for it. We argue that existing approaches to deontic modals fail to provide us with an adequate resolution of this tension. In response, we develop a positive analysis, (...)
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  39. Deontic Concepts and Their Clash in Mīmāṃsā: Towards an Interpretation.Elisa Freschi & Matteo Pascucci - 2021 - Theoria 87 (3):659-703.
    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 (...)
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  40. The good, the bad and the right. Formal reductions among deontic concepts.Daniela Glavaničová & Matteo Pascucci - 2021 - Bulletin of the Section of Logic 50 (2):151-176.
    The present article provides a taxonomic analysis of bimodal logics of normative ideality and normative awfulness, two notions whose meaning is here explained in terms of the moral values pursued by a given community. Furthermore, the article addresses the traditional problem of a reduction among deontic concepts: we explore the possibility of defining other relevant normative notions, such as obligation, explicit permission and Hohfeldian relations, in terms of ideality and awfulness. Some proposals in this respect, which have been formulated in (...)
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  41. Axiomatizing norms across time and the 'Paradox of the Court'.Daniela Glavaničová & Matteo Pascucci - 2021 - In Fenrong Liu, Alessandra Marra, Paul Portner & Frederik Van de Putte (eds.), Deontic Logic and Normative Systems. Proceedings of DEON 2020/2021. College Publications. pp. 201-218.
    In normative reasoning one typically refers to intervals of time across which norms are intended to hold, as well as to alternative possibilities representing hypothetical developments of a given scenario. Thus, deontic modalities are naturally intertwined with temporal and metaphysical ones. Furthermore, contemporary debates in philosophy suggest that a proper understanding of fundamental ethical principles, such as the Ought-Implies-Can thesis, requires a simultaneous analysis of these three families of concepts. In the present article we propose a general formal framework which (...)
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  42. Alternative semantics for normative reasoning with an application to regret and responsibility.Daniela Glavaničová & Matteo Pascucci - 2021 - Logic and Logical Philosophy 30 (4):653-679.
    We provide a fine-grained analysis of notions of regret and responsibility (such as agent-regret and individual responsibility) in terms of a language of multimodal logic. This language undergoes a detailed semantic analysis via two sorts of models: (i) relating models, which are equipped with a relation of propositional pertinence, and (ii) synonymy models, which are equipped with a relation of propositional synonymy. We specify a class of strictly relating models and show that each synonymy model can be transformed into an (...)
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  43. How Knowledge Triggers Obligation.Davide Grossi, Barteld Kooi, Xingchi Su & Rineke Verbrugge - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 201-215.
    Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and all-things-considered obligations. Finally, in the dynamic epistemic logic tradition, we (...)
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  44. Modeling legal conflict resolution based on dynamic logic.Fengkui Ju, Karl Nygren & Tianwen Xu - 2021 - Journal of Logic and Computation 31 (4):1102-1128.
    Conflicts between legal norms are common in reality. In many legislations, legal conflicts between norms are resolved by applying ordered principles. This work presents a formalization of the conflict resolution mechanism and introduces action legal logic (⁠ALL) to reason about the normative consequences of possibly conflicting legal systems. The semantics of ALL is explicitly based on legal systems consisting of norms and ordered principles. Legal systems specify the legal status of transitions in transition systems and the language of ALL describes (...)
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  45. Moral Principles: Hedged, Contributory, Mixed.Aleks Knoks - 2021 - In Deontic Logic and Normative Systems 2020/21.
    It's natural to think that the principles expressed by the statements "Promises ought to be kept" and "We ought to help those in need" are defeasible. But how are we to make sense of this defeasibility? On one proposal, moral principles have hedges or built-in unless clauses specifying the conditions under which the principle doesn't apply. On another, such principles are contributory and, thus, do not specify which actions ought to be carried out, but only what counts in favor or (...)
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  46. Deontic Logic and Normative Systems: 15th International Conference, DEON 2020/2021.Fenrong Liu, Alessandra Marra, Paul Portner & Frederik Van De Putte (eds.) - 2021 - College Publications.
    This volume contains the proceedings of DEON2020/2021, the 15th International Conference on Deontic Logic and Normative Systems that was organized by the Munich Center for Mathematical Philosophy at LMU Munich (Germany) on 21st-24th July, 2021. The biennial DEON conferences are designed to promote interdisciplinary cooperation amongst scholars interested in linking the formal-logical study of normative concepts, normative language and normative systems with computer science, artificial intelligence, linguistics, philosophy, organization theory, and law.
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  47. A Framework for Intuitionistic Grammar Logics.Tim Lyon - 2021 - In Pietro Baroni, Christoph Benzmüller & Yὶ N. Wang (eds.), Lecture Notes in Computer Science. 93413 Cham, Germany: pp. 495-503.
    We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.
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  48. Normative parties in subject position and in object position.Tereza Novotná & Matteo Pascucci - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications. pp. 147-164.
    We analyze some normative relations as instances of a general schema of relations among a finite number of parties; in this schema parties can play various roles grouped into two main conceptual layers, called 'subject position' and 'object position'. Relying on the theoretical apparatus introduced, we develop a new symbolic representation for normative reasoning which constitutes an alternative to approaches available in the literature. Our contribution includes a semantic characterization for a series of logical systems built over the proposed framework.
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  49. Deontic Logic Based on Inquisitive Semantics.Karl Nygren - 2021 - In Fenrong Liu, Alessandra Marra, Paul Portner & Frederik Van De Putte (eds.), Deontic Logic and Normative Systems: 15th International Conference, DEON 2020/2021. London: College Publications. pp. 339-357.
    This paper introduces deontic logic based on inquisitive semantics. A semantics for action formulas is introduced where each action formula is associated with a set of alternatives. Deontic operators are then interpreted as quantifying over all alternatives associated with the action formulas within their scope. It is shown how this construction provides solutions to problems related to free choice permissions and obligations, including issues concerning Hurford disjunctions. The main technical result is a complete axiomatization of the logic.
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  50. The search for symmetry in Hohfeldian modalities.Matteo Pascucci & Giovanni Sileno - 2021 - In Amrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo & Petrucio Viana (eds.), Diagrammatic Representation and Inference. Proceedings of Diagrams 2021. Springer. pp. 87-102.
    In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition and exploit (...)
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