Skip to main content

Advertisement

Log in

Formalizing GDPR Provisions in Reified I/O Logic: The DAPRECO Knowledge Base

  • Published:
Journal of Logic, Language and Information Aims and scope Submit manuscript

Abstract

The DAPRECO knowledge base is the main outcome of the interdisciplinary project bearing the same name (https://www.fnr.lu/projects/data-protection-regulation-compliance). It is a repository of rules written in LegalRuleML, an XML formalism designed to be a standard for representing the semantic and logical content of legal documents. The rules represent the provisions of the General Data Protection Regulation (GDPR), the new Regulation that is significantly affecting the digital market in the European Union and beyond. The DAPRECO knowledge base builds upon the Privacy Ontology (PrOnto) (Palmirani et al in Proceedings of the 7th international conference on electronic government and the information systems perspective: technology-enabled innovation for democracy, government and governance, 2018c), which provides a model for the legal concepts involved in the GDPR, by adding a further layer of constraints in the form of if-then rules, referring either to standard first order logic implications or to deontic statements. If-then rules are formalized in reified Input/Output logic (Robaldo and Sun in J Log Comput 7, 2017) and then codified in LegalRuleML. Reified Input/Output logic is an application of standard Input/Output logic for legal reasoning, in which Input/Output logic is combined with the reification-based approach in Hobbs and Gordon (A formal theory of commonsense psychology, how people think people think. Cambridge University Press, Cambridge, 2017). The DAPRECO knowledge base is then a case study for reified Input/Output logic, and it shows that the formalism indeed appears to be a good candidate to effectively formalize, via uniform and simple (flat) representations, complex linguistic/deontic phenomena that may be found in legal texts. To date, the DAPRECO knowledge base is the biggest knowledge base in LegalRuleML and Input/Output logic freely available online (https://github.com/dapreco/daprecokb/blob/master/gdpr/rioKB_GDPR.xml).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. http://www.mirelproject.eu.

  2. https://www.last-jd-rioe.eu.

  3. FinTech (Financial Technology) refers to the use of artificial intelligence and computer science to support or enable banking and financial services. The main functions of FinTech software include regulatory monitoring, reporting, and compliance. RegTech (Regulatory Technology) is a more general term referring to computer technology applied to any kind of regulated business, not only finance.

  4. https://www.w3.org/OWL.

  5. http://www.akomantoso.org.

  6. See Sect. 5.5 of http://docs.oasis-open.org/legaldocml/akn-core/v1.0/akn-core-v1.0-part1-vocabulary.html.

  7. https://www.oasis-open.org/committees/legalruleml/.

  8. https://www.oasis-open.org/.

  9. http://wiki.ruleml.org/.

  10. https://plato.stanford.edu/entries/logic-deontic/#2.

  11. Regulation (EU) 2016/679 of the European Parliament and of the Council of 27 April 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing Directive 95/46/EC.

  12. https://github.com/dapreco/daprecokb/blob/master/gdpr/rioKB_GDPR.xml.

  13. https://www.fnr.lu/projects/data-protection-regulation-compliance/.

  14. A particularly representative example is the “Délibération SAN-2019-001 du 21 janvier 2019”, issued by the Commission nationale de l’informatique et des libertés (CNIL), the Supervisory Authority of France, which sanctioned Google LLC for 50 million euros.

  15. http://www.mirelproject.eu.

  16. https://www.w3.org/TR/owl2-overview.

  17. As discussed in Robaldo and Sun (2017), consider the obligations “If someone kills a dog, s/he has to spend two years in prison” and “If someone robs a bank s/he has to spend two years in prison”. Suppose also that John did one of the two, but there is no way to come to know which one, i.e. whether he killed a dog or robbed a bank. Logically, John must spend two years in prison. But on the perspective of legal reasoning, he must not: only if concrete evidence of what he did is found, obligations apply. The example considered marks an interesting border between legal reasoning and standard logical reasoning.

  18. The example of paradox discussed in Parent and Leendert (2014b) is: given the obligations “You ought to exercise hard everyday” (\(\top \), Ex) and “If you exercise hard everyday, you ought to eat heartily” (Ex, Eh), we derive via CT that also the obligation “You ought to eat heartily” (\(\top \), Eh) holds. However, this is not clearly the case: you are obliged to eat heartily only if you exercise hard everyday.

  19. See also the manuscripts at http://www.isi.edu/~hobbs/csk.html and http://www.isi.edu/~hobbs/csknowledge-references/csknowledge-references.html for a quick introduction to the logical framework.

  20. States, facts, and events are reified into FOL individuals, from the Latin word “re(s)” for “thing”: we take states, facts, and events to be things.

  21. Note that in the formulæ, all terms are FOL constants. They could be FOL variables, provided that we quantify them, e.g., ‘\(\exists _{e_b}[(blond'\,e_b\) John\()]'\).

  22. In the DAPRECO knowledge base, special LegalRuleML prefixes allow to distinguish the predicates corresponding to concepts in PrOnto from the others. See Sect. 4 below.

  23. See https://www.isi.edu/~hobbs/bgt-logic.text for details.

  24. https://github.com/dapreco/daprecokb/blob/master/gdpr/rioKB_GDPR.xml

  25. Indeed, the formula in (16) lacks a predicate referring to an exception to Article 6, paragraph 1, point 1. The handling of exceptions in reified Input/Output logic will be illustrated below in Sect. 4.2, so that we avoid that predicate in (16).

  26. We assume, for simplicity, that each eventuality may be described in a single way, i.e., that only a single description “descr(e)” (functionally) corresponds to an eventuality e.

  27. See http://www.isi.edu/~hobbs/bgt-modality.text.

  28. LegalRuleML includes a special tag to mark the bearers of obligations and permissions: \(<\texttt {lrml:Bearer/}>\). The DAPRECO knowledge base omits this tag to avoid redundancies: the bearers need to be already specified at the level of the underlying logical formalism, in order to enable nested obligations and nested permissions.

  29. Idelberger et al. (2016) recently showed that nested obligations and nested permissions may also occur in the formalization of smart contracts.

  30. In reality, formula (23) is a simplification of the formula stored in the DAPRECO knowledge base and associated with (22), as it does not specify the exceptions of Article 17, paragraph 2. Section 4.2 below illustrates how reified Input/Output logic deals with exceptions.

  31. As it will be clarified below in Sect. 4.3, the truth value of the predicate ‘reasonable’ depends on context-specific legal interpretations of the corresponding adjective.

  32. See https://plato.stanford.edu/entries/self-reference.

  33. See https://www.isi.edu/~hobbs/bgt-evstruct.text.

  34. Taken from https://www.isi.edu/~hobbs/bgt-defeasibility.text.

  35. In footnote 30 above, we noted that the two elements x and y of a pair (x, y) belonging to either O or P are always made up of conjunctions of atomic predications, with an important exception. The exception is represented by ‘naf’, which indeed introduces one level of nesting in the formulæ.

  36. In (39), we formalized “the relevant cloud service customer” occurring in (37) via the predicate PIIController. According to ISO 27018, Article 0.1: “The cloud service customer, who has the contractual relationship with the public cloud PII processor, can range from a natural person, a ‘PII principal’, processing his or her own PII in the cloud, to an organization, a ‘PII controller’, processing PII relating to many PII principals”.

  37. https://www.legislation.gov.au/Details/C2012B00077/ExplanatoryMemorandum/Text.

  38. Note that, in (55), \(\mathtt {e}_\mathtt {caj}\), \(\mathtt {e}_\mathtt {cbj}\), \(\mathtt {e}_\mathtt {daj}\), \(\mathtt {t}_\mathtt {1}\), \(\mathtt {t}_\mathtt {2}\), John, y, and z are FOL constants.

  39. https://eur-lex.europa.eu/legal-content/IT/ALL/?uri=CELEX:32014L0065&qid=1435045139484.

  40. \(\hbox {BH}_2\) is the class of languages which are the intersection of a language in NP and a language in coNP.

  41. Personal communication with Leon van der Torre.

References

  • Ajani, G., Boella, G., Di Caro, L., Robaldo, L., Humphreys, L., Praduroux, S., et al. (2017). The European legal taxonomy syllabus: A multi-lingual, multi-level ontology framework to untangle the Web of European legal terminology. Applied Ontology, 2(4).

  • Amgoud, L., & Nouioua, F. (2015). Undercutting in argumentation systems. In C. Beierle & A. Dekhtyar, (Eds.), Scalable uncertainty management - 9th international conference, SUM 2015, Québec City, QC, Canada, September 16–18, 2015. Proceedings, volume 9310 of Lecture Notes in Computer Science (pp. 267–281). Berlin: Springer.

  • Antoniou, G., Billington, D., Governatori, G., & Maher, M. J. (2001). Representation results for defeasible logic. ACM Transactions on Computational Logic, 2(2), 255–287.

    Google Scholar 

  • Arner, D. W., Barberis, J., & Buckey, R. P. (2016). FinTech, RegTech, and the reconceptualization of financial regulation. Northwestern Journal of International Law & Business, 37, 371–414.

    Google Scholar 

  • Athan, T., Boley, H., Governatori, G., Palmirani, M., Paschke, A., & Wyner, A. (2013). LegalRuleML: From metamodel to use cases (pp. 13–18). Berlin: Springer.

    Google Scholar 

  • Athan, T., Governatori, G., Palmirani, M., Paschke, A., & Wyner, A. Z. (2014). Legal interpretations in legalruleml. In Semantic Web for Law 2014 workshop, collocated at the 27th international conference on legal knowledge and information systems (JURIX 2014), CEUR workshop proceedings.

  • Athan, T., Governatori, G., Palmirani, M., Paschke, A., & Wyner, A. (2015). LegalRuleML: Design principles and foundations (pp. 151–188). Berlin: Springer.

    Google Scholar 

  • Bach, E. (1981). On time, tense, and aspect: An essay in English metaphysics. In P. Cole (Ed.), Radical pragmatics (pp. 63–81). New York: Academic Press.

    Google Scholar 

  • Bandeira, J., Bittencourt, I. I., Espinheira, P., & Isotani, S. (2016). FOCA: A methodology for ontology evaluation. https://arxiv.org/abs/1612.03353.

  • Bartolini, C., Giurgiu, A., Lenzini, G., & Robaldo, L.. (2016). Towards legal compliance by correlating standards and laws with a semi-automated methodology. In BNCAI, volume 765 of Communications in Computer and Information Science (pp. 47–62). Berlin: Springer.

  • Bochman, A. (2004). A causal approach to nonmonotonic reasoning. Artificial Intelligence, 160(1–2), 105–143.

    Google Scholar 

  • Boella, G., Di Caro, L., Humphreys, L., Robaldo, L., Rossi, R., & van der Torre, L. (2016). Eunomos, a legal document and knowledge management system for the web to provide relevant, reliable and up-to-date information on the law. Artificial Intelligence and Law, 24, 245.

    Google Scholar 

  • Boella, G., di Caro, L., Humphreys, L., Robaldo, L., & van der Torre, L. (2012). NLP challenges for Eunomos, a tool to build and manage legal knowledge. In Proceeding of “Lexical Resources and Evaluation Conference” (LREC2012). Istanbul, Turchia. https://www.aclweb.org/anthology/L12-1617/.

  • Boella, G., Di Caro, L., Rispoli, D., & Robaldo, L. (2013a). Semantic relation extraction from legislative text using generalized syntactic dependencies and support vector machines (pp. 218–225). Berlin: Springer.

    Google Scholar 

  • Boella, G., Di Caro, L., Rispoli, D., & Robaldo, L. (2013b) A system for classifying multi-label text into Eurovoc. In Proceedings of the fourteenth international conference on artificial intelligence and law, ICAIL ’13 (pp. 239–240). ACM, New York, NY, USA.

  • Boella, G., Governatori, G., Rotolo, A., & van der Torre, L. (2010). Lex Minus Dixit Quam Voluit, Lex Magis Dixit Quam Voluit: A formal study on legal compliance and interpretation (pp. 162–183). Berlin: Springer.

    Google Scholar 

  • Boella, G., & van der Torre, L. W. N. (2004a). Fulfilling or violating obligations in normative multiagent systems. IEEE/WIC/ACM international conference on intelligent agent technology (IAT 2004) (pp. 483–486), Beijing, China.

  • Boella, G., & van der Torre, L. W. N. (2004b) Regulative and constitutive norms in normative multiagent systems. In Principles of knowledge representation and reasoning: Proceedings of the ninth international conference (KR2004) (pp. 255–266).

  • Bonatti, P. A., Lutz, C., & Wolter, F. (2009). The complexity of circumscription in description logic. Journal of Artificial Intelligence Research, 35(1), 717–773.

    Google Scholar 

  • Brank, J., Grobelnik, M., & Mladenić, D. (2005). A survey of ontology evaluation techniques. In Proceedings of 8th international multi-conference information society.

  • Brozek, B. (2014). Law and defeasibility. Revus, 23, 165–170.

    Google Scholar 

  • Cadoli, M., & Lenzerini, M. (1994). The complexity of propositional closed world reasoning and circumscription. Journal of Computer and System Sciences, 48(2), 255–310.

    Google Scholar 

  • Casellas, N. (2009). Ontology evaluation through usability measures. In R. Meersman, P. Herrero, & T. Dillon (Eds.), On the move to meaningful internet systems: OTM 2009 workshops. Berlin: Springer.

  • Casini, G., Meyer, T., Moodley, K., Sattler, U., & Varzinczak, I. (2015). Introducing defeasibility into owl ontologies. In R. Meersman, P. Herrero, & T. Dillon (Eds.), Proceedings of international semantic Web conference (ISWC).

  • Davidson, D. (1967). The logical form of action sentences. In N. Rescher (Ed.), The logic of decision and action. Pittsburgh: University of Pittsburgh Press.

    Google Scholar 

  • Dimyadi, J., Governatori, G., & Amor, R.. (2017). Evaluating legaldocml and legalruleml as a standard for sharing normative information in the aec/fm domain. In Proceedings of joint conference on computing in construction (JC3), Vol. 1, Heraklion, Greece.

  • Galton, A. (2006). Operators vs. arguments: The ins and outs of reification. Synthese, 150(3), 415–441.

    Google Scholar 

  • Governatori, G. (2015). Thou shalt is not you will. In Proceedings of the 15th international conference on artificial intelligence and law, ICAIL 2015 (pp. 63–68), ACM, New York, NY, USA.

  • Governatori, G., & Rotolo, A. (2006) Logic of violation: A Gentzen system for reasoning with contrary-to-duty obligations. Australasian Journal of Logic, (426).

  • Governatori, G., Padmanabhan, V., Rotolo, A., & Sattar, A. (2009). A defeasible logic for modelling policy-based intentions and motivational attitudes. Logic Journal of the IGPL, 17(3), 227.

    Google Scholar 

  • Governatori, G., Olivieri, F., Rotolo, A., & Scannapieco, S. (2013). Computing strong and weak permissions in defeasible logic. Journal of Philosophical Logic, 6(42), 799–829.

    Google Scholar 

  • Governatori, G., & Rotolo, A. (2008). Bio logical agents: Norms, beliefs, intentions in defeasible logic. Autonomous Agents and Multi-Agent Systems, 17(1), 36–69.

    Google Scholar 

  • Hansen, J. (2008). Prioritized conditional imperatives: Problems and a new proposal. Autonomous Agents and Multi-Agent Systems, 17(1), 11–35.

    Google Scholar 

  • Hobbs, J. R. (1998). The logical notation: Ontological promiscuity. In Chapter 2 of discourse and inference. Available at http://www.isi.edu/~hobbs/disinf-tc.html.

  • Hobbs, J. R. (2001). Syntax and metonymy. In P. Bouillon & F. Busa (Eds.), The Language of word meaning (pp. 302–361). Cambridge: Cambridge University Press.

    Google Scholar 

  • Hobbs, J. R., & Gordon, A. S. (2017). A formal theory of commonsense psychology, how people think people think. Cambridge: Cambridge University Press.

    Google Scholar 

  • Horty, J. (2001). Agency and deontic logic. New York: Oxford University Press.

    Google Scholar 

  • Horty, J. (2012). Reasons as defaults. Oxford: Oxford University Press.

    Google Scholar 

  • Idelberger, F., Governatori, G., Riveret, R., & Sartor, G. (2016). Evaluation of logic-based smart contracts for blockchain systems. In RuleML, volume 9718 of Lecture Notes in Computer Science (pp. 167–183). Berlin: Springer.

  • Jörg, H. (2014). Reasoning about permission and obligation. In S. O. Hansson (Ed.), David Makinson on classical methods for non-classical problems (Vol. 3, pp. 287–333). Outstanding Contributions to Logic. Berlin: Springer.

  • Jørgensen, J. (1937). Imperatives and logic. Erkenntnis, 7, 288–296.

    Google Scholar 

  • MacCormick, N., & Summers, R. S. (1991). Interpreting statutes: A comparative study. Applied legal philosophy. Hanover: Dartmouth.

  • Makinson, D. & van der Torre, L. (2003b). What is input/output logic? In B. Lowe, W. Malzkorn, & T. Rasch (Eds.), Foundations of the formal sciences II: Applications of mathematical logic in philosophy and linguistics (pp. 163–174).

  • Makinson, D., & van der Torre, L. W. N. (2000). Input/output logics. Journal of Philosophical Logic, 29(4), 383–408.

    Google Scholar 

  • Makinson, D., & van der Torre, L. (2001). Constraints for input/output logics. Journal of Philosophical Logic, 30(2), 155–185.

    Google Scholar 

  • Makinson, D., & van der Torre, L. (2003a). Permission from an input/output perspective. Journal of Philosophical Logic, 32, 391–416.

    Google Scholar 

  • Malerba, A. (2017). Interpretive interactions among Legal systems and argumentation schemes. Ph.D. thesis, Joint International Doctoral (Ph.D.) Degree in Law, Science and Technology (LAST-JD).

  • Maranhão, J. S. A. (2017). A logical architecture for dynamic legal interpretation. In Proceedings of the 16th Edition of the international conference on articial intelligence and law, ICAIL ’17 (pp. 129–138). ACM, New York, NY, USA.

  • Maranhão, J., & de Souza, E. G.. (2018) Contraction of combined normative sets. In J. M. Broersen, C. Condoravdi, N. Shyam, & G. Pigozzi (Eds.), Deontic logic and normative systems - 14th international conference, DEON 2018, Utrecht, The Netherlands, July 3–6, 2018 (pp. 247–261). College Publications.

  • McCarthy, J. (1980). Circumscription: A form of nonmonotonic reasoning. Artificial Intelligence, 13, 27–39.

    Google Scholar 

  • Nute, D. (1994b). Defeasible prolog. In AAAI technical report FS-93-0. Oxford: Oxford University Press. Available at https://www.aaai.org/Papers/Symposia/Fall/1993/FS-93-01/FS93-01-015.pdf.

  • Nute, D. (1994a). Defeasible logic. In D. Gabbay, C. Hogger, & J. Robinson (Eds.), Handbook of logic in artificial intelligence and logic programming. Oxford: Oxford University Press.

    Google Scholar 

  • Nute, D. (1997). Defeasible deontic logic. Dordrecht: Kluwer.

    Google Scholar 

  • Palmirani, M., Martoni, M., Rossi, A., Bartolini, C., & Robaldo, L. (2018a). Legal ontology for modelling GDPR concepts and norms. In Legal knowledge and information systems - JURIX 2018: The thirty-first annual conference, Groningen, The Netherlands, 12–14 December 2018.

  • Palmirani, M., Martoni, M., Rossi, A., Bartolini, C., & Robaldo, L. (2018b). Pronto: Privacy ontology for legal compliance. In Proceedings of the 18th European conference on digital government (ECDG), October (Forthcoming).

  • Palmirani, M., Martoni, M., Rossi, A., Bartolini, C., & Robaldo, L. (2018c). Pronto: Privacy ontology for legal reasoning. In Proceedings of the 7th international conference on electronic government and the information systems perspective (EGOVIS): Technology-enabled innovation for democracy, government and governance, September (Forthcoming).

  • Palmirani, M., Martoni, M., Rossi, A., Bartolini, C., & Robaldo, L. (2018d). Pronto: Privacy ontology for legal reasoning. In Proceedings of the Internationales Rechtsinformatik Symposion (IRIS), February.

  • Palmirani, M. (2011). Legislative change management with Akoma-Ntoso (pp. 101–130). Dordrecht: Springer.

    Google Scholar 

  • Palmirani, M., & Vitali, F. (2011). Akoma Ntoso for legal documents (pp. 75–100). Dordrecht: Springer.

    Google Scholar 

  • Parent, X., & van der Torre, L. (2018). Input/output logics with a consistency check. In Proceedings of the 14th international conference on deontic logic and normative systems (DEON2018).

  • Parent, X., & van der Torre, L. (2014a). Aggregative deontic detachment for normative reasoning. In Principles of knowledge representation and reasoning: Proceedings of the fourteenth international conference, KR 2014, Vienna, Austria, July 20–24, 2014.

  • Parent, X., & van der Torre, L. W. N.. (2017). The pragmatic oddity in norm-based deontic logics. In Proceedings of the 16th edition of the international conference on articial intelligence and law, ICAIL 2017, London, United Kingdom, June 12–16, 2017 (pp. 169–178).

  • Parent, X. (2011). Moral particularism in the light of deontic logic. Artificial Intelligence and Law, 19(2–3), 75–98.

    Google Scholar 

  • Parent, X., & van der Torre, L. (2014). Sing and dance!. In F. Cariani, D. Grossi, J. Meheus, & X. Parent (Eds.), Deontic logic and normative systems (pp. 149–165). Berlin: Springer.

    Google Scholar 

  • Pnueli, A. (1977). The temporal logic of programs. In Proceedings of the 18th annual symposium on foundations of computer science, SFCS ’77 (pp. 46–57). IEEE Computer Society.

  • Prakken, H. (2005). Ai & law, logic and argument schemes. Argumentation, 19(3), 303–320.

    Google Scholar 

  • Ramakrishna, S., Gorski, L., & Paschke, A. (2016). A dialogue between a lawyer and computer scientist: The evaluation of knowledge transformation from legal text to computer-readable format. Applied Artificial Intelligence, 30(3),

  • Reiter, R. (1987). A logic for default reasoning. In M. L. Ginsberg (Ed.), Readings in nonmonotonic reasoning (pp. 68–93). Los Altos, CA: Kaufmann.

    Google Scholar 

  • Robaldo, L., & Sun, X. (2017). Reified input/output logic: Combining input/output logic and reification to represent norms coming from existing legislation. The Journal of Logic and Computation, 7.

  • Robaldo, L., Caselli, T., Russo, I., & Grella, M. (2011). From Italian text to TimeML document via dependency parsing. In Computational Linguistics and intelligent text processing - 12th international conference, CICLing 2011, Tokyo, Japan (pp. 177–187).

  • Robaldo, L. (2010a). Independent set readings and generalized quantifiers. The Journal of Philosophical Logic, 39(1), 23–58.

    Google Scholar 

  • Robaldo, L. (2010b). Interpretation and inference with maximal referential terms. The Journal of Computer and System Sciences, 76(5), 373–388.

    Google Scholar 

  • Robaldo, L. (2011). Distributivity, collectivity, and cumulativity in terms of (in)dependence and maximality. The Journal of Logic, Language, and Information, 20(2), 233–271.

    Google Scholar 

  • Robaldo, L., Szymanik, J., & Meijering, B. (2014). On the identification of quantifiers’ witness sets: A study of multi-quantifier sentences. The Journal of Logic, Language, and Information, 23(1), 53.

    Google Scholar 

  • Rotolo, A., Governatori, G., & Sartor, G. (2015). Deontic defeasible reasoning in legal interpretation: Two options for modelling interpretive arguments. In Proceedings of the 15th international conference on artificial intelligence and law (ICAIL). ACM, New York, NY, USA.

  • Sartor, G. (2005). Legal reasoning: A cognitive approach to the law. Treatise of legal philosophy and general jurisprudence / ed.-in-chief Enrico Pattaro. Berlin: Springer.

  • Satariano, A. (2018). What the G.D.P.R. Europe’s tough new data law, means for you, and for the Internet. Online article, May.

  • Schwarzentruber, F., & Caroline, S. (2014). STIT is dangerously undecidable. In T. Schaub, G. Friedrich, & B. O’Sullivan (Eds.), ECAI 2014-21st European conference on artificial intelligence, 18–22 August 2014, Prague, Czech Republic - Including prestigious applications of intelligent systems (PAIS 2014), volume 263 of Frontiers in artificial intelligence and applications. IOS Press.

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

    Google Scholar 

  • Sun, X., & Robaldo, L. (2015). Logic and games for ethical agents in normative multi-agent systems. In M. Rovatsos, G. A. Vouros, & V. Julián (Eds.), Multi-agent systems and agreement technologies - 13th European conference, EUMAS 2015, and third international conference, at 2015, Athens, Greece, December 17–18, 2015, Revised Selected Papers, volume 9571 of Lecture Notes in Computer Science (pp. 367–375). Berlin: Springer.

  • Sun, X., & van der Torre, L. W. N.. (2014). Combining constitutive and regulative norms in input/output logic. In F. Cariani, D. Grossi, J. Meheus, & X. Parent (Eds.), Deontic logic and normative systems - 12th international conference, DEON 2014, Ghent, Belgium, July 12–15, 2014. Proceedings, volume 8554 of Lecture Notes in Computer Science (pp. 241–257). Berlin: Springer.

  • Sun, X., & Robaldo, L. (2017). On the complexity of input/output logic. The Journal of Applied Logic, 25, 69–88.

    Google Scholar 

  • Walton, D., Sartor, G., & Macagno, F. (2016). An argumentation framework for contested cases of statutory interpretation. Artifical Intelligence and Law, 24(1), 51–91.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Livio Robaldo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Research supported by the Luxembourg national FNR-CORE project “DAPRECO: DAta Protection REgulation Compliance”, and by the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No 690974 for the project “MIREL: MIning and REasoning with Legal texts”. Arianna Rossi performed this work at CIRSFID (University of Bologna) and ICR (University of Luxembourg) while she was supported by LAST-JD, the Joint International Doctoral Degree in Law, Science, and Technology, financed by EACEA.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Robaldo, L., Bartolini, C., Palmirani, M. et al. Formalizing GDPR Provisions in Reified I/O Logic: The DAPRECO Knowledge Base. J of Log Lang and Inf 29, 401–449 (2020). https://doi.org/10.1007/s10849-019-09309-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10849-019-09309-z

Keywords

Navigation