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Situated legal systems and their operational semantics

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Abstract

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.

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Notes

  1. In Costa (2014d), we introduced a first version of the formalization of Kelsen’s concept of legal system, which we use, slightly revised, in the present paper.

  2. See Davis (1976), or Sect. 10, for the concept of discretion.

  3. Compare with the XYZ model in e.g., (Costa and Dimuro 2009), from which it developed.

  4. See Lehmann et al. (2004) for an analysis of the import of the material environment of agent societies for their legal systems, a subject we don’t treat explicitly here.

  5. Kelsen (2009) uses the term legal norm both in this wider sense (including the idea of authorizations) and in a narrower sense, distinguishing the former senses (obligation, prohibition, and permission) from that of authorization. In the formalization introduced in the next sections, we use the term legal norm in its narrower sense, captured in the formal concept of imputation. That is, the formal concept of imputation does not capture the idea of authorization, which receives a separate formal treatment.

  6. Section 5 presents our formalization of Kelsen’s concept of legal system, detailing the main aspects of the notion of imputation and other related notions.

  7. Kelsen’s expressions for these two types of presentations of legal norms are, respectively, “figure of speech” and “unambiguous description” (Kelsen 2009). Raz (1970), on the other hand, frames this distinction in terms of what he calls the problem of the individuation of legal norms (see also Sect. 12).

  8. Or else, one can understand it in the terms of a similar distinction made in the realm of programming languages, between the concrete syntax and the abstract syntax of a programming language expression (Fernández 2014).

  9. Compare the simple form of Kelsen’s abstract syntax of legal norms with the complex form resulting from Bentham’s (1970a) logical analysis of the concrete syntax of legal norms, as formally presented by Raz (1970). See also Alchourrón and Bulygin (1971), where Alchourrón and Bulygin also aim to formalize the complex logical structure of the concrete language of law.

  10. See (Costa and Dimuro 2009)  for the detailed formal operational requirements for the proper realization of a functional implementation.

  11. We use the expression legal fact to denote either a record of the performance of a legal or social act, or a record of a factual ascertainment that a legal organ may make, when trying a concrete legal case, but with the formal requirement that such records be performed only when legally authorized, see Sect. 8.

  12. See Sect. 12 for a brief comment on alternative possibilities of formalization of situated legal systems, based on process-theoretic approaches.

  13. The presentation is based on the formalization of Kelsen’s notion of legal system that we have introduced in Costa (2014d). We revise such formalization here, specially regarding authorizations (see Sect.10) and the concept of temporal evolution of situated legal systems.

  14. \(\wp (X)\) is the powerset of the set \(X\).

  15. Following the notation in Raz (1970).

  16. Kelsen (1991, 2009) was one of the first to make clear the distinction between norms (expressions of norms themselves) and norm propositions (statements about the existence and properties of norms), a conception largely amplified by C. Alchourrón in the 1960’s, and later, through the distinction between the logic of norms and the logic of normative propositions (Alchourrón 1969; Alchourrón and Bulygin 1971).

  17. For more on the relation between legal norms and authorizations, and specially about the difference between explicit and implicit authorizations, see the discussion in Sect. 10.

  18. Note that \(\Downarrow\) aims to capture Kelsen’s idea that imputations are not logical implications, since they do not connect propositions, but two types of conducts, thus being unsuitable to an assignment of truth-values: imputations can not be true or false, only valid or non valid, in a given legal system (see Kelsen 1991, and Sect. 9).

  19. That \(Ag_2\) should be a type of legal organ is a requirement imposed by the fact that legal systems restrict the performance of legal sanctions, in a monopolistic way, to their legal organs (i.e., to the state Kelsen 2009).

  20. Which represents a significant departure from J. Bentham and J. L. Austin’s view of legal systems as systems of norms directly commanding their subjects (Bentham 1970b; Austin 1995), a point rightly indicated by Hart (2012).

  21. A difference that, according to Hart (1962–1963), can not be clarified within the Kelsenian conceptual framework.

  22. Notice how the operational semantics allows to account for the derogation of legal norms in terms of the performance of legal acts, not in terms of the validity of derogation norms. From the operational point of view, Kelsen’s account of norm derogation in terms of the validity of derogation norms (Kelsen 2009), is—still—given in terms of the surface structure of law (see Sect. 3).

  23. Kelsen himself makes little or no theoretical use at all of the notion of legal fact in the way we are using it here (Kelsen 2009). His account of the operation of legal systems is given mainly in terms of the conducts of legal organs, that is, in terms of the performance of legal actions (or, legal events), thus in purely process-theoretic terms, as suggested in Sect. 12.

  24. The use of a time-indexed structure allows us to capture, in one single formal construct, the synchronic and the diachronic aspects of the historical evolution of legal systems, an idea that (e.g., Raz 1970) considered in terms of two distinct informal concepts: legal systems and momentary legal systems.

  25. Clearly, \(D_{\mathrm {S}}\) can be deduced from \((\varGamma ,\longrightarrow )\). It is made explicit here for convenience.

  26. General methods for defining the operational semantics of action systems over transition systems were introduced (Plotkin 1981), but their exposition is out of the scope of the present paper.

  27. See Kelsen (2009) for the clarification of the relation between legal organs and the individuals and organizational units (Kelsen says corporations) that implement them in a society.

  28. Distinguished by the legal function they perform in the system, not by their form or content. See the example distinction between tax and fine, in Sect. 5, where both acts have the same form and content (charge of an amount of money), but different legal functions.

  29. Adequacy regarding the function that the legal system is to perform in the agent society where it is situated.

  30. That is why the main result in the conclusion of the derivation rule for the basic norm is the legal authorization for the founder agent to create the initial configuration of the legal system (determining such creation as a legal act), which initial configuration should include legal authorizations for the initial legal organs to perform their inital legal acts (otherwise the thus created legal system will not be able to start to operate legally).

  31. There are legal acts implicit in other derivation rules, like the rule for the imputation of sanctions, that also affect the record of legal facts.

  32. But the obligation of their execution can be determined by sanctioning their omission.

  33. Figure 3 builds on the general idea of the small-steps semantics of action systems (Plotkin 1981).

  34. Of course, if the norm also makes explicit its temporal and spatial spheres of validity, additional facts concerning such spheres of validity have to be determined and taken into account in the legal reasoning, thus giving rise to additional points of discretion, within this deliberation process.

  35. Dworkin (1977) made extensive use, in his argumentations, of the expression hard case. The meaning he assigns to that expression is identical to that which (Hart 2012) assigns, namely, a case to which no legislation applies in a straightforward way, either because of the plain absence of a pertinent legislation, or because of a lack of clarity in the extant legislation, regarding the concrete circumstance involved in the case.

  36. Notice the double point of view required by this account of the founding act of a legal system: a combination of a socially causal element (the political authorization for the founding act), and a normative element (the assumed validity of the basic norm). From this perspective, Kelsen’s solution to the problem of the founding of legal systems is analogous to that by Hart, who similarly states that the ultimate rule of recognition, which determines the identity of the legal system, has to be seen from this double, political and normative, point of view (Hart 2012).

  37. In either case, the conduct must be admitted by the legal system in its material sphere.

  38. See Kelsen and Klug (1981), specially the chapter with Kelsen’s manuscript about Law and Logic.

  39. An idea that, in fact, can be thought to be implicitly assumed by Hart, in his notion of the ultimate rule of recognition (Hart 2012).

  40. Interestingly enough, that characterization of “positivism” would put Hart himself outside the field of “positivism”, due to his strong concern with the definite minimal content that he thinks every legal system should have (Dworkin 1977, e.g., says Hart is a “moral philosopher”). On the other hand, Hart explictly classifies himself as “positivist”, in the usual sense of someone who admits the possibility of independence between descriptive and evaluative (or, justificatory) points of view toward an object of study (Hart 2012).

  41. In fact, there seems to be a strong similarity, if not plain identity, between what Dworkin calls individual rights and what Hart requires as the minimum content of law, when taken in concrete terms.

  42. At the end, Dworkin effectively rules out legal orders as the main components of legal systems, and plainly treats “principles as law” (Dworkin 1977, Chap. 2), that is, construes legal systems essentially as systems of legal principles and legal policies.

  43. Kelsen calls “authentic” (i.e., creative of new valid legal norms), not only an interpretation that instantiates for the concrete case being tried (as a new, individual norm) one of the possibilities within the frame of possibilities determined by the legal norm appropriate for the case, but also, in the trial of a hard case, an interpretation that solves the case by creating a new norm, specific for the case, if it happens that the legal organ responsible for the trial is legally authorized to create such a norm, and this even if it happens that there is no valid legal norm that can determine the scope of content of the new norm, which means that this content is wholly determined by the discretion of the legal organ that creates it.

  44. In Dworkin’s terms Dworkin (1977), the solution of hard cases is achieved by “reaching beyond the law for some other sort of standard to guide him [the judge] in manufacturing a fresh legal rule or supplementing an old one.” (our emphasis).

  45. Kelsen’s expression about this problem is that it is not a “problem of legal theory but of legal politics” (Kelsen 2009).

  46. Notice that the problem of the validity of the legal norms, and of the legal system as a whole, is not made explicit by that list of four problems. One may conceive that it is implict in the combination of the problems of existence and identity. That, however, is in direct opposition to Kelsen’s approach, which emphasizes the importance of the explicit treatment of the problem of the validity of legal norms.

  47. At the price of having to make crucial use of an auxiliary set, the record of legal facts \({\mathrm {RLFact}}\), which is an ad-hoc addition to Kelsen’s theory.

  48. http://www.ibama.gov.br.

  49. http://www.ibama.gov.br/servicos-recursos-pesqueiros/defeso-aguas-continentais.

  50. On the basis of this type of formalization, an agent-based model for this public policy for fishing activity was developed, and preliminary simulation studies relating costs of norm enforcing and positive results for the sustainability of fishing activities were presented in Santos et al. (2012).

  51. That this action-based view of legal systems is compatible with Kelsen’s own view of law is shown by his general conception of norms as meanings of acts of will directed toward the conducts of others, and of legal norms as the meanings of such acts, when legally authorized (Kelsen 2009).

References

  • Alchourrón CE (1969) Logic of norms and logic of normative propositions. Log Anal 12(47):242–268

    MATH  Google Scholar 

  • Alchourrón CE, Bulygin E (1971) Normative systems. Springer, Berlin

    MATH  Google Scholar 

  • Austin J (1995) The province of jurisprudence determined. Cambridge University Press, Cambridge

    Google Scholar 

  • Bentham J (1970a) The limits of jursiprudence defined. Greenwood Publishing Group, Westport

    Google Scholar 

  • Bentham J (1970b) Of laws in general. Athlone Press, London

    Google Scholar 

  • Boella G, van der Torre L, Verhagen H (2006) Introduction to normative multiagent systems. Comput Math Organ Theory 12:71–79

    Article  Google Scholar 

  • Burrell G, Morgan G (1979) Sociological paradigms and organisational analysis: elements of the sociology of corporate life. Ashgate Publishing, Surrey

    Google Scholar 

  • Chomsky N (2002) Syntatic structures. De Gruyter Mouton, Berlin

    Google Scholar 

  • 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@Paris

  • Costa ACR (2014b) On the legal aspects of agent societies. Open publication on www.ResearchGate.net. doi:10.13140/2.1.4345.7923

  • Costa ACR (2014c) On the bases of an architectural style for agent societies: concept and core operational structure. Open publication on www.ResearchGate.net. doi:10.13140/2.1.4583.8720

  • 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 York

  • 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 419–445

  • 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, Montpellier

  • 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 535–546

  • Davis KC (1976) Discretionary justice: a preliminary inquiry. University of Illinois Press, Champaign

    Google Scholar 

  • 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, India

  • Dworkin R (1977) Taking rights seriously. Harvard University Press, Cambridge

    Google Scholar 

  • Dworkin R (1985) A matter of principle. Harvard University Press, Cambridge

    Google Scholar 

  • Dworkin R (1986) Law’s empire. Harvard University Press, Cambridge

    Google Scholar 

  • Fernández M (2014) Programming languages and operational semantics: a concise overview. Springer, Berlin

    Google Scholar 

  • Fox MS (1979) Organization structuring: designing large complex software. Technical report, Carnegie-Mellon University (Technical Report CMU-CS-79-155), Pittsburgh

  • Gilbert N, Troitzsch K (2005) Simulation for the social scientist. Open University Press, London

    Google Scholar 

  • Governatori G, Rotolo A (2008) A computational framework for institutional agency. AI Law 16(1):25–52

    Google Scholar 

  • Governatori G, Rotolo A (2010) Changing legal systems: legal abrogations and annulments in Defeasible Logic. J IGPL 18(1):157–194

    Article  MATH  MathSciNet  Google Scholar 

  • Governatori G, Sartor G (eds) (2011) Special issue: deontic logic and normative systems. AI Law 19(2–3)

  • 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 251–274

    Google Scholar 

  • Hart HLA (1958) Positivism and the separation of law and morals. Harv Law Rev 71(4):593–629

    Article  Google Scholar 

  • Hart HLA (1962–1963) Kelsen visited. UCLA Law Rev 10:709–728

  • Hart HLA (2012) The concept of law. Oxford University Press, Oxford

    Google Scholar 

  • Hoare CAR (1985) Communicating sequential processes. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Hood C (1983) The tools of government. Macmillan, London

    Google Scholar 

  • 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):369–400

    Article  Google Scholar 

  • Kelsen H (1991) General theory of norms. Oxford University Press, Oxford

    Book  Google Scholar 

  • Kelsen H (2007) General theory of law and state. The Law Book Exchange, New Jersey

    Google Scholar 

  • Kelsen H (2009) Pure theory of law. The Law Book Exchange, New Jersey

    Google Scholar 

  • 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)

  • Ladyman J (2001) Understanding philosophy of science. Routledge, London

    Google Scholar 

  • Lehmann J, Breuker J, Brouwer B (2004) Causation in AI and law. AI Law 12:279–315

    Google Scholar 

  • Luhmann N (2008) Law as a social system. Oxford University Press, Oxford

    Google Scholar 

  • MacCormick N, Weinberger O (2010) An institutional theory of law: new approaches to legal positivism. Springer, Berlin

    Google Scholar 

  • Milner R (1980) A calculus of communicating systems. Springer, Berlin

    MATH  Google Scholar 

  • Paulson SL, Paulson BL (eds) (2007) Normativity and norms—critical perspectives on Kelsenian themes. Claredon Press, Oxford

    Google Scholar 

  • Plotkin G (1981) A structural approach to operational semantics. Technical report, University of Aarhus

  • Porter BF (1968) Deity and morality—with regard to the naturalistic fallacy. Routledge, London

    Google Scholar 

  • Raz J (1970) Concept of a legal system: an introduction to the theory of legal system. Oxford University Press, Oxford

    Google Scholar 

  • Raz J (1971) The identity of legal systems. Calif Law Rev 59(3):795–815

    Article  Google Scholar 

  • 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 Papers

  • 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 Alegre

  • Searle JR (1995) The construction of social reality. The Free Press, New York

    Google Scholar 

  • Turner JH (2010) Theoretical principles of sociology. Springer, Berlin

    Google Scholar 

  • Wegner P (1968) Programming languages, information structures and machine organization. McGraw-Hill, New York

    Google Scholar 

Download references

Acknowledgments

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.

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  1. Programa de Pós-Graduação em Computação, Centro de Ciências Computacionais, Universidade Federal do Rio Grande (FURG), Rio Grande, RS, 96.201-900, Brazil

    Antônio Carlos da Rocha Costa

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da Rocha Costa, A.C. Situated legal systems and their operational semantics. Artif Intell Law 23, 43–102 (2015). https://doi.org/10.1007/s10506-015-9164-z

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