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Using Intuitionistic Logic as a basis for Legal Ontologies Using Intuitionistic Logic as a basis for Legal Ontologies Edward Hermann Hausler Alexandre Rademaker Valeria de Paiva Departamento de Informatica - PUC-Rio - Brasil EPGE - FGV -

  1. Using Intuitionistic Logic as a basis for Legal Ontologies Using Intuitionistic Logic as a basis for Legal Ontologies Edward Hermann Hausler Alexandre Rademaker Valeria de Paiva Departamento de Informatica - PUC-Rio - Brasil EPGE - FGV - Brasil Curl Inc. - USA LOAIT 2010

  2. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  3. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  4. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  5. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  6. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  7. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  8. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What is an Ontology ? ◮ A declarative description of a domain. ◮ Ontology consistency is mandatory. ◮ Consistency means absence of contradictions. ◮ Negation is an essential operator. ◮ Concretely, an Ontology is a Knowledge Base: ◮ A set of Logical Assertions on a Domain that aim to describe it completely.

  9. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What does it mean the term “Law” ? ◮ What does count as the “unit of law” ? Open question, a.k.a. “The individuation problem”. ◮ (Raz1972) What is to count as one “complete law” ?

  10. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What does it mean the term “Law” ? ◮ What does count as the “unit of law” ? Open question, a.k.a. “The individuation problem”. ◮ (Raz1972) What is to count as one “complete law” ?

  11. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies What does it mean the term “Law” ? ◮ What does count as the “unit of law” ? Open question, a.k.a. “The individuation problem”. ◮ (Raz1972) What is to count as one “complete law” ?

  12. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Two main (distinct) approaches to the “Individuation problem”. ◮ Taking all (existing) legally valid statements as a whole. This totality is called “the law”. ◮ ✄ Legal Positivism tradition (Kelsen1991). Question: Natural coherence versus Knowledge Management resulted coherence. ◮ Taking into account all individual legally valid statement as individual laws. ◮ ✄ Facilitates the analysis of structural relationship between laws, viz. Primary and Secondary Rules. ◮ The second seems to be quite adequate to Legal AI .

  13. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Two main (distinct) approaches to the “Individuation problem”. ◮ Taking all (existing) legally valid statements as a whole. This totality is called “the law”. ◮ ✄ Legal Positivism tradition (Kelsen1991). Question: Natural coherence versus Knowledge Management resulted coherence. ◮ Taking into account all individual legally valid statement as individual laws. ◮ ✄ Facilitates the analysis of structural relationship between laws, viz. Primary and Secondary Rules. ◮ The second seems to be quite adequate to Legal AI .

  14. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Two main (distinct) approaches to the “Individuation problem”. ◮ Taking all (existing) legally valid statements as a whole. This totality is called “the law”. ◮ ✄ Legal Positivism tradition (Kelsen1991). Question: Natural coherence versus Knowledge Management resulted coherence. ◮ Taking into account all individual legally valid statement as individual laws. ◮ ✄ Facilitates the analysis of structural relationship between laws, viz. Primary and Secondary Rules. ◮ The second seems to be quite adequate to Legal AI .

  15. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Two main (distinct) approaches to the “Individuation problem”. ◮ Taking all (existing) legally valid statements as a whole. This totality is called “the law”. ◮ ✄ Legal Positivism tradition (Kelsen1991). Question: Natural coherence versus Knowledge Management resulted coherence. ◮ Taking into account all individual legally valid statement as individual laws. ◮ ✄ Facilitates the analysis of structural relationship between laws, viz. Primary and Secondary Rules. ◮ The second seems to be quite adequate to Legal AI .

  16. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Two main (distinct) approaches to the “Individuation problem”. ◮ Taking all (existing) legally valid statements as a whole. This totality is called “the law”. ◮ ✄ Legal Positivism tradition (Kelsen1991). Question: Natural coherence versus Knowledge Management resulted coherence. ◮ Taking into account all individual legally valid statement as individual laws. ◮ ✄ Facilitates the analysis of structural relationship between laws, viz. Primary and Secondary Rules. ◮ The second seems to be quite adequate to Legal AI .

  17. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Two main (distinct) approaches to the “Individuation problem”. ◮ Taking all (existing) legally valid statements as a whole. This totality is called “the law”. ◮ ✄ Legal Positivism tradition (Kelsen1991). Question: Natural coherence versus Knowledge Management resulted coherence. ◮ Taking into account all individual legally valid statement as individual laws. ◮ ✄ Facilitates the analysis of structural relationship between laws, viz. Primary and Secondary Rules. ◮ The second seems to be quite adequate to Legal AI .

  18. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Why we do not consider Deontic Modal Logic ? ◮ Deontic Logic does not properly distinguish between the normative status of a situation from the normative status of a norm (rule). (Valente1995) ◮ Norms should not have truth-value, they are not propositions. (Kelsen1991)

  19. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Why we do not consider Deontic Modal Logic ? ◮ Deontic Logic does not properly distinguish between the normative status of a situation from the normative status of a norm (rule). (Valente1995) ◮ Norms should not have truth-value, they are not propositions. (Kelsen1991)

  20. Using Intuitionistic Logic as a basis for Legal Ontologies Jurisprudence Motivation Considerations on Legal Ontologies Why we do not consider Deontic Modal Logic ? ◮ Deontic Logic does not properly distinguish between the normative status of a situation from the normative status of a norm (rule). (Valente1995) ◮ Norms should not have truth-value, they are not propositions. (Kelsen1991)

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