Abstract
General obligations such as ‘every driver has to give way to a driver coming from the right’ are central in legal reasoning, but have been mostly overlooked in deontic logic. We claim that a simple extension of Standard Deontic Logic to the predicative level is insufficient to capture general obligations. Instead, we argue for an explicit representation of bearers (and counterparties) of obligations as terms in a quantified deontic logic. To achieve this we develop a term-modal counterpart of Standard Deontic Logic and give a sound and strongly complete axiomatization for it. We go on to show that this logic is not only suitable for capturing reasoning with general obligations, but also with (multital and paucital) Hohfeldian rights relations and rules of rights.
The research on this paper was enabled by subventions from the Research Foundation—Flanders, through the project “Towards a more integrated formal account of actual ethical reasoning, with applications in medical ethics.” (G0D2716N). The authors are indebted to Thijs De Coninck, Federico Faroldi, Pawel Pawlowski, and Nathan Wood for comments on an earlier version of this paper. Frederik Van De Putte is a Marie Skłodowska-Curie Fellow at the University of Bayreuth and a Postdoctoral Fellow of the Research Foundation—Flanders.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
In legal reasoning, deriving consequences from general statements is not restricted to simple applications of so-called legal syllogisms. In view of the legal principle “like cases should be treated alike”, it is commonly accepted that all legal decisions should be founded on general rules (see, for instance, Feteris 2017, p. 25).
- 2.
Within a logical approach to legal reasoning, logical validity is seen as a necessary requirement for the acceptability of legal arguments, see Feteris (2017), p. 25.
- 3.
Achen et al. (2019) also uses a Hilbert-style axiomatisation.
- 4.
A notable exception to the limitation to paucital rights is Markovich (2020).
- 5.
There is no consensus in the literature on the terminology. Therefore our use of terminology might differ slightly from that found in other work.
- 6.
- 7.
Herrestad and Krogh claim that they have “few clear and convincing intuitions” regarding directed permissions and argue that directed permissions are not the duals of directed obligations (Herrestad and Krogh 1995, p. 504).
- 8.
“Elke bestuurder moet voorrang verlenen aan de bestuurder die van rechts komt, behalve indien hij op een rotonde rijdt of indien de bestuurder die van rechts komt uit een verboden rijrichting komt.” Artikel 12.3.1. van het Koninklijk besluit houdende algemeen reglement op de politie van het wegverkeer en van het gebruik van de openbare weg.
- 9.
- 10.
In all of our citations we will change the notation used for constants and variables (ranging over persons) to ensure a uniform notation and easy reading experience. We will use a, b, … for individual persons and x, y, … for variables ranging over persons.
- 11.
The emphasis in this and further quotations is Hohfeld’s own.
- 12.
The full quote is “A has an indefinite number of legal privileges of entering on the land, using the land, harming the land, etc” (Hohfeld 1917, p. 746). The phrase ‘indefinite number of privileges’ refers to an indefinite number of privileges to enter on the land, an indefinite number of privileges of using the land, etc. This is illustrated by the fact that Hohfeld later refers to these privileges as “multital, or in rem, ‘privilege-no-right’ relations” (Hohfeld 1917, p. 747).
- 13.
Kanger’s theory of ‘atomic types of rights’ differs from the Hohfeldian theory of rights, but the point about the existence of ‘rules of rights’ holds regardless of the specific theory of rights one accepts.
- 14.
Going even further: “A few states have held that in narcotics cases knowledge is not an essential element of possession” (Whitebread and Stevens 1972, p. 753).
- 15.
Whether such a law is just is a different discussion.
- 16.
Cfr. also Hohfelds indefinite classes of multital rights (Hohfeld 1917, p. 718).
- 17.
This problem was already noted by Hansson (1970).
- 18.
Equivalently, one can obtain constant domain semantics by assigning the same domain to every world.
- 19.
It is also possible to expand the domain to also include other objects, like the apples from the introduction. See for example Achen et al. (2019).
- 20.
Note that \(\{{\mathsf {O}}_a^b \varphi , {\mathsf {O}}_a^c \neg \varphi \}\) is inconsistent in TMDL, but not in this new logic.
- 21.
- 22.
The converse is not valid.
- 23.
This asymmetry was also noted by Hohfeld, see Sect. 13.3.
- 24.
Note that Hohfeld himself also laments the fact that there is no single term available to express the correlative of a permission (Hohfeld 1913, p. 33).
- 25.
A broad class of non-normal, classical term modal logics is studied in Frijters and Van De Putte (2020).
References
Achen, A., Liberman, A. O., & Rendsvig, R. K. (2019). Dynamic term-modal logics for epistemic planning. arXiv preprint arXiv:1906.06047.
Ankersmit, F. R. (2006). Wat er mis is met de ministeriële verantwoordelijkheid. Rechtsfilosofie & Rechtstheorie, 35, 134–153.
Beirlaen, M., Heyninck, J., & Straßer, C. (2018). Structured argumentation with prioritized conditional obligations and permissions. Journal of Logic and Computation, 29(2), 187–214.
Corsi, G., & Orlandelli, E. (2013). Free quantified epistemic logics. Studia Logica, 101(6), 1159–1183.
Corsi, G., & Tassi, G. (2014). A new approach to epistemic logic. In Logic, reasoning, and rationality (pp. 27–44). Berlin: Springer.
Dong, H., & Roy, O. (2020). Dynamic logic of legal competences. (unpublished).
Feteris, E. T. (2017). Fundamentals of legal argumentation (vol. 1). Berlin: Springer.
Fitting, M. (2007). Modal proof theory. In P. Blackburn, J. F. A. K. van Benthem, F. Wolter (Eds.), Handbook of modal logic. Amsterdam: Elsevier.
Fitting, M., Thalmann, L., & Voronkov, A. (2001). Term-modal logics. Studia Logica, 69(1), 133–169.
Frijters, S., & Van De Putte, F. (2020). Classical term-modal logics. Journal of Logic and Computation, exaa053. https://doi.org/10.1093/logcom/exaa053
Goble, L. (2013). Prima facie norms, normative conflicts, and dilemmas. In D. Gabbay, J. Horty, X. Parent, R. van der Meyden, & L. van der Torre (Eds.), Handbook of deontic logic and normative systems (vol. 1, pp. 241–351). Rickmansworth: College Publications.
Hage, J. (2018). Of norms. In G. Bongiovanni, G. Postema, A. Rotolo, G. Sartor, C. Valentini, & D. Walton (Eds.), Handbook of legal reasoning and argumentation (pp. 103–138). Dordrecht: Springer.
Hansson, B. (1970). Deontic logic and different levels of generality. Theoria, 36(3), 241–248.
Hansson, S. O. (2013). The varieties of permission. In D. Gabbay, J. Horty, X. Parent, R. van der Meyden, & L. van der Torre (Eds.), Handbook of deontic logic and normative systems (pp. 195–240). Rickmansworth: College Publications.
Herrestad, H., & Krogh, C. (1995). Deontic logic relativised to bearers and counterparties. Anniversary Anthology in Computers and Law, 453–522.
Hilpinen, R. (1974). On the semantics of personal directives. In C. H. Heidrich (Ed.), Semantics and Communication (pp. 162–179). Amsterdam: North Holland Publishing Company.
Hohfeld, W. N. (1913). Some fundamental legal conceptions as applied in judicial reasoning. The Yale Law Journal, 23, 16–59.
Hohfeld, W. N. (1917). Fundamental legal conceptions as applied in judicial reasoning. The Yale Law Journal, 26(8), 710–770.
Horty, J. F. (2012). Reasons as defaults. Oxford: Oxford University Press.
Hughes, G. E., & Creswell, M. J. (1996). A New Introduction to Modal Logic. London: Routledge.
Humberstone, I. L. (1971). Two sorts of ‘ought’s. Analysis, 32(1), 8–11.
Kanger, S. (1970). New foundations for ethical theory. In Deontic logic: Introductory and systematic readings (pp. 36–58). Berlin: Springer.
Kanger, S. (2001). Law and logic. In G. Holmström, S. Hintikka, & R. Sliwinski (Eds.), Collected papers of Stig Kanger with essays on his life and work (vol. I, pp. 146–169). Amsterdam: Kluwer.
Kanger, S., & Kanger, H. (1966). Rights and parliamentarism. Theoria, 32(2), 85–115.
Kooi, B. (2007). Dynamic term-modal logic. In J. Van Benthem, S. Ju, & F. Veltman (Eds.), Proceedings of the Workshop on Logic, Rationality and Interaction. Texts in Computing Computer Science (vol. 8, pp. 173–185). Rickmansworth: College Publications.
Krogh, C., & Herrestad, H. (1996). Getting personal: Some notes on the relationship between personal and impersonal obligation. In Deontic logic, agency and normative systems (pp. 134–153). Berlin: Springer.
Lindahl, L. (2012). Position and change: A study in law and logic. Synthese Library (vol. 112). Berlin: Springer.
Makinson, D. (1986). On the formal representation of rights relations. Journal of Philosophical Logic, 15(4), 403–425.
Markovich, R. (2020). Understanding hohfeld and formalizing legal rights: The Hohfeldian conceptions and their conditional consequences. Studia Logica, 108(1), 129–158.
McNamara, P. (2004). Agential obligation as non-agential personal obligation plus agency. Journal of Applied Logic, 2(1), 117–152.
Navarro, P. E., & Rodríguez, J. L. (2014). Deontic logic and legal systems. Cambridge: Cambridge University Press.
Sartor, G. (2018). Defeasibility in law. In G. Bongiovanni, G. Postema, A. Rotolo, G. Sartor, C. Valentini, D. Walton (Eds.), Handbook of legal reasoning and argumentation (pp. 315–364). Dordrecht: Springer.
Sergot, M. (2013). Normative positions. In D. Gabbay, J. Horty, X. Parent, R. van der Meyden, & L. van der Torre (Eds.), Handbook of deontic logic and normative systems (pp. 353–406). Rickmansworth: College Publications.
Tan, Y.-H., & Thoen, W. (1998). A logical model of directed obligations and permissions to support electronic contracting. International Journal of Electronic Commerce, 3(2), 87–104.
Thalmann, L. (2000). Term-modal logic and quantifier-free dynamic assignment logic. Ph.D. Thesis, Acta Universitatis Upsaliensis.
Thomason, R. H. (1970). Some completeness results for modal predicate calculi. In K. Lambert (Ed.), Philosophical problems in logic. Synthese library (vol. 29, pp. 56–76). Dordrecht: Springer.
Van De Putte, F., Beirlaen, M., & Meheus, J. (2019). Adaptive deontic logics. In Handbook of deontic logic (vol. 2). Rickmansworth: College Publications.
Walton, D. (2018). Legal reasoning and argumentation. In G. Bongiovanni, G. Postema, A. Rotolo, G. Sartor, C. Valentini, & D. Walton (Eds.), Handbook of legal reasoning and argumentation (pp. 47–75). Dordrecht: Springer.
Whitebread, C. H., & Stevens, R. (1972). Constructive possession in narcotics cases: To have and have not. Virginia Law Review, 58(5), 751–775.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Frijters, S., Meheus, J., Putte, F.V.D. (2022). Reasoning with Rules and Rights: Term-Modal Deontic Logic. In: Rahman, S., Armgardt, M., Kvernenes, H.C.N. (eds) New Developments in Legal Reasoning and Logic. Logic, Argumentation & Reasoning, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-030-70084-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-70084-3_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-70083-6
Online ISBN: 978-3-030-70084-3
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)