Artificial Intelligence and Law

, Volume 23, Issue 1, pp 43–102 | Cite as

Situated legal systems and their operational semantics

  • Antônio Carlos da Rocha CostaEmail author


This work adopts H. Kelsen’s concept of legal system, proposes a formal definition for such notion, and introduces an operational semantical framework for legal systems that are (structurally and operationally) situated in agent societies. Agent societies are defined. Relevant formal properties of situated legal systems (action-based dynamics; orthogonality between the operational semantics and the processes of legal reasoning and decision-making; validity of norms; and completeness) are discussed; the way they are exposed in the operational semantical framework is explained, and their truth formally proved. Also, for the sake of a better understanding of the legal-theoretic assumptions of the paper, recurring issues regarding Kelsen’s theory of law (namely, his “positivism”, the attribution of a plain deductive nature to legal reasoning and decision-making, and the notions of basic norm, authorization, and discretion) are briefly reviewed. They are put in confrontation with the points of view of R. Dworkin, H. Hart, and J. Raz, and an attempt is made to clarify them from the perspective of the provided formalization. A brief case study in agent-based modeling and simulation of public policy processes is presented, as an illustration of the way of using situated legal systems, and the proposed operational semantical framework, in a practical application.


Situated legal systems Kelsen’s theory of legal systems Agent societies Operational semantics of situated legal systems Formal analysis of the Kelsen-Dworkin-Hart-Raz debate 



To Maria Francisca Carneiro, who first introduced me to the logical problems of law. CAPES, FAPERGS and CNPq provided partial financial support for this work. The author is grateful to the anonymous referees, for their careful review of the first version of the paper, and for their most useful criticisms and suggestions.


  1. Alchourrón CE (1969) Logic of norms and logic of normative propositions. Log Anal 12(47):242–268 zbMATHGoogle Scholar
  2. Alchourrón CE, Bulygin E (1971) Normative systems. Springer, Berlin zbMATHGoogle Scholar
  3. Austin J (1995) The province of jurisprudence determined. Cambridge University Press, CambridgeGoogle Scholar
  4. Bentham J (1970a) The limits of jursiprudence defined. Greenwood Publishing Group, WestportGoogle Scholar
  5. Bentham J (1970b) Of laws in general. Athlone Press, LondonGoogle Scholar
  6. Boella G, van der Torre L, Verhagen H (2006) Introduction to normative multiagent systems. Comput Math Organ Theory 12:71–79CrossRefGoogle Scholar
  7. Burrell G, Morgan G (1979) Sociological paradigms and organisational analysis: elements of the sociology of corporate life. Ashgate Publishing, SurreyGoogle Scholar
  8. Chomsky N (2002) Syntatic structures. De Gruyter Mouton, BerlinGoogle Scholar
  9. Costa ACR (2014a) Proposal for a notion of modularity in multiagent systems. In: Birna van Riemskijk  M, Dalpiaz F, Dix J (eds) Informal proceedings of EMAS 2014. AAMAS@ParisGoogle Scholar
  10. Costa ACR (2014b) On the legal aspects of agent societies. Open publication on doi: 10.13140/2.1.4345.7923
  11. Costa ACR (2014c) On the bases of an architectural style for agent societies: concept and core operational structure. Open publication on doi: 10.13140/2.1.4583.8720
  12. Costa ACR (2014d) Toward a formal reconstruction of Kelsen’s theory of legal systems. In: WEIT 2013 - 2nd workshop-school on theoretical computer science, IEEE, New YorkGoogle Scholar
  13. Costa ACR, Dimuro GP (2009) A minimal dynamical organization model. In: Dignum V (ed) Hanbook of multi-agent systems: semantics and dynamics of organizational models. IGI Global, pp 419–445Google Scholar
  14. Costa ACR, Santos IAS (2012) Toward a framework for simulating agent-based models of public policy processes on the Jason-CArtAgO platform. In: AMPLE@ECAI 2012 - 2nd international workshop on agent-based modeling for policy engineering. ECAI, MontpellierGoogle Scholar
  15. Costa ACR, Hübner JF, Bordini RH (1994) On entering an open society. In: Proceedings of the XI Brazilian symposium on artificial intelligence. Sociedade Brasileira de Computação, Fortaleza, pp 535–546Google Scholar
  16. Davis KC (1976) Discretionary justice: a preliminary inquiry. University of Illinois Press, ChampaignGoogle Scholar
  17. Demazeau Y, Costa ACR (1996) Populations and organizations in open multi-agent systems. In: 1st national symposium on parallel and distributed artificial intelligence (PDAI’96). Hyderabad, IndiaGoogle Scholar
  18. Dworkin R (1977) Taking rights seriously. Harvard University Press, CambridgeGoogle Scholar
  19. Dworkin R (1985) A matter of principle. Harvard University Press, CambridgeGoogle Scholar
  20. Dworkin R (1986) Law’s empire. Harvard University Press, CambridgeGoogle Scholar
  21. Fernández M (2014) Programming languages and operational semantics: a concise overview. Springer, BerlinGoogle Scholar
  22. Fox MS (1979) Organization structuring: designing large complex software. Technical report, Carnegie-Mellon University (Technical Report CMU-CS-79-155), PittsburghGoogle Scholar
  23. Gilbert N, Troitzsch K (2005) Simulation for the social scientist. Open University Press, LondonGoogle Scholar
  24. Governatori G, Rotolo A (2008) A computational framework for institutional agency. AI Law 16(1):25–52Google Scholar
  25. Governatori G, Rotolo A (2010) Changing legal systems: legal abrogations and annulments in Defeasible Logic. J IGPL 18(1):157–194CrossRefzbMATHMathSciNetGoogle Scholar
  26. Governatori G, Sartor G (eds) (2011) Special issue: deontic logic and normative systems. AI Law 19(2–3)Google Scholar
  27. Grossi D, Rotolo A (2011) Logic in the law: a concise overview. In: Gupta A, van Benthem J (eds) Logic and philosophy today. College Publications, London, pp 251–274Google Scholar
  28. Hart HLA (1958) Positivism and the separation of law and morals. Harv Law Rev 71(4):593–629CrossRefGoogle Scholar
  29. Hart HLA (1962–1963) Kelsen visited. UCLA Law Rev 10:709–728Google Scholar
  30. Hart HLA (2012) The concept of law. Oxford University Press, OxfordGoogle Scholar
  31. Hoare CAR (1985) Communicating sequential processes. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  32. Hood C (1983) The tools of government. Macmillan, LondonGoogle Scholar
  33. Hübner JF, Boissier O, Kitio R, Ricci A (2010) Instrumenting multi-agent organisations with organisational artifacts and agents: giving the organisational power back to the agents. J Auton Agents Multi-Agent Syst 20(3):369–400CrossRefGoogle Scholar
  34. Kelsen H (1991) General theory of norms. Oxford University Press, OxfordCrossRefGoogle Scholar
  35. Kelsen H (2007) General theory of law and state. The Law Book Exchange, New JerseyGoogle Scholar
  36. Kelsen H (2009) Pure theory of law. The Law Book Exchange, New JerseyGoogle Scholar
  37. Kelsen H, Klug U (1981) Rechtsnormen und Logishe Analyse. Ein Briefwechsel 1959 bis 1965. Deuticke (Brazilian translation: Normas Jurídicas e Análise Lógica - Correspondência 1959–1965. Editora Forense, 1984)Google Scholar
  38. Ladyman J (2001) Understanding philosophy of science. Routledge, LondonGoogle Scholar
  39. Lehmann J, Breuker J, Brouwer B (2004) Causation in AI and law. AI Law 12:279–315Google Scholar
  40. Luhmann N (2008) Law as a social system. Oxford University Press, OxfordGoogle Scholar
  41. MacCormick N, Weinberger O (2010) An institutional theory of law: new approaches to legal positivism. Springer, BerlinGoogle Scholar
  42. Milner R (1980) A calculus of communicating systems. Springer, BerlinzbMATHGoogle Scholar
  43. Paulson SL, Paulson BL (eds) (2007) Normativity and norms—critical perspectives on Kelsenian themes. Claredon Press, OxfordGoogle Scholar
  44. Plotkin G (1981) A structural approach to operational semantics. Technical report, University of AarhusGoogle Scholar
  45. Porter BF (1968) Deity and morality—with regard to the naturalistic fallacy. Routledge, LondonGoogle Scholar
  46. Raz J (1970) Concept of a legal system: an introduction to the theory of legal system. Oxford University Press, OxfordGoogle Scholar
  47. Raz J (1971) The identity of legal systems. Calif Law Rev 59(3):795–815CrossRefGoogle Scholar
  48. Ricci A, Viroli M, Omicini A (2006) Programming MAS with artifacts. In: Bordini RP, Dastani M, Dix J, El Fallah Seghrouchni A (eds) Programming multi-agent systems, vol 3862., LNAI Springer, pp 206–221. Springer, 2006. 3rd International workshop (PROMAS 2005), AAMAS 2005, Utrecht, The Netherlands, 26/jul/2005. Revised and Invited PapersGoogle Scholar
  49. Santos IAS, Mota FP, Costa ACR, Dimuro GP (2012) Um framework para simulação de políticas públicas aplicado ao caso da piracema, sob o olhar da teoria dos jogos. In Encontro Nacional de Inteligência Artificial - ENIA 2012, Sociedade Brasileira de Computação, Porto AlegreGoogle Scholar
  50. Searle JR (1995) The construction of social reality. The Free Press, New YorkGoogle Scholar
  51. Turner JH (2010) Theoretical principles of sociology. Springer, BerlinGoogle Scholar
  52. Wegner P (1968) Programming languages, information structures and machine organization. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Programa de Pós-Graduação em Computação, Centro de Ciências ComputacionaisUniversidade Federal do Rio Grande (FURG)Rio GrandeBrazil

Personalised recommendations