A logic for legal hierarchies

ABSTRACT

The theory of non-monotonic reasoning has interesting applications for the formalization and automated use of legal concepts, specially: • drawing conclusions from a logically inconsistent, but hierarchic, regulations [1, 30]; • similarly, establishing facts from a set of inconsistent testimonies, partially ranked by confidence; • using presumptions (such as the presumption of innocence) in the face of possibly contradictory evidence. In this paper, we use a logic [37, 38], that ranks contradictory formulae using two new paraconsistent variants of conjunction: “but” and “on the other hand”. Its algebraic proof theory is presented.

REFERENCES

• 1: C. AJchourron and D. Makinson. Hierachies of regulations and their logic. In R. Hilpinen, editor, New Studies in Deontic Logic, pages 123-148. Reidel, 1981.
• 2: L. Bachmair and H. Ganzinger. Perfect model semantics for logic programs with equality. In Proc. 8th Intl. Conf. on Logic Programming. MIT Press, 1991.
• 3: M. Bicloit and G. Bemot. Proving correctness of algebraically specified software: Modularity and observability issues. In M. Nivat, C. Rattray, T. Rus, and G. Scollo, editors, AMAST'gl, Worskshops in Computing, pages 139-161. Springer-Verlag, 1992.
• 4: N. Bobbio. Des crit~res pour rtsoudre des antinomies. In C. Perelman, editor, Les Antinomies en Droit, Travaux du Centre National de Recherches de Logique. Bmylant, 1965.
• 5: G. Brewka. Nonmonotonic reasoning. Cambridge Univ. Press, 1991.
• 6: M. Dalai. Investigations into a theory of knowledge base revision: preliminary report. In Proc. of the 7th Nat. Conf. onArt. Int. (AAAI-88), pages 475--479,1988.
• 7: James R. Delgrande, An approach to default reasoning based on a first-order conditional logic: revised report, Artificial Intelligence, v.36 n.1, p.63-90, August 1988 [doi>10.1016/0004-3702(88)90079-3]
• 8: R. Ducournau , M. Habib, Masking and conflicts, or to inherit not to own!, Inheritance hierarchies in knowledge representation and programming languages, John Wiley and Sons Ltd., Chichester, UK, 1991
• 9: R. V. Elst. Antinomies en droit international privY. In C. Perelman, editor, Les Antinomies en Droit, Travaux du Centre National de Recherches de Logique. Bmylant, 1965.
• 10: J. Fiadeiro and T. Maibaum. Temporal reasoning over deontic specifications. J. Logic Computat., 1(3):357- 395, 1991.
• 11: P. Gardenfors. Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT press, 1988.
• 12: Joseph A. Goguen , Rod M. Burstall, Institutions: abstract model theory for specification and programming, Journal of the ACM (JACM), v.39 n.1, p.95-146, Jan. 1992 [doi>10.1145/147508.147524]
• 13: T. F. Gordon, An abductive theory of legal issues, International Journal of Man-Machine Studies, v.35 n.1, p.95-118, July 1991 [doi>10.1016/S0020-7373(07)80009-5]
• 14: B. Grosof. Generalizing prioritization. In Proc. of the 2nd Intl. Conf. on Knowledge Representation and Reasoni$ (KR'91), pages 289-300, 1991.
• 15: S. Hansson. New operators fortheory change. Theoria, 55(2), 1989.
• 16: A. Jones and M. Sergot. Deontic logic in the representation of law: towards a methodology. Artificial Intelligence and Law, i(1), 1992.
• 17: S. Kaplan, Positive/negative conditional rewriting, 1st international workshop on Conditional Term Rewriting Systems, p.129-143, August 1988, Orsay, France
• 18: H. Kelsen. The pure theory of law. Law Quarterly Review, 51:517-535, 1935.
• 19: Sarit Kraus , Daniel Lehmann , Menachem Magidor, Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, v.44 n.1-2, p.167-207, July 1990 [doi>10.1016/0004-3702(90)90101-5]
• 20: David Makinson, General patterns in nonmonotonic reasoning, Handbook of logic in artificial intelligence and logic programming (vol. 3): nonmonotonic reasoning and uncertain reasoning, Oxford University Press, Inc., New York, NY, 1994
• 21: John McCarthy, Applications of circumscription to formalizing common-sense knowledge, Artificial Intelligence, v.28 n.1, p.89-116, Feb. 1986 [doi>10.1016/0004-3702(86)90032-9]
• 22: Robert C. Moore, Semantical considerations on nonmonotonic logic, Artificial Intelligence, v.25 n.1, p.75-94, Jan. 1985 [doi>10.1016/0004-3702(85)90042-6]
• 23: J. Pollock. A refined theory ofcounterfactuals. Journal of Philosophical Logic, 10:239-266, 1981.
• 24: David Poole, A logical framework for default reasoning, Artificial Intelligence, v.36 n.1, p.27-47, August 1988 [doi>10.1016/0004-3702(88)90077-X]
• 25: H. Prakken. Logical Tools for Modelling Legal Argument. PhD thesis, Vrije Univ. Amsterdam, 1993.
• 26: P. Rathmann and M. Winslett. Circumscribing equality. In Proc. of the 8th Nat. Conf. on Art. Int. (AAAI-89), pages 468-473, 1989.
• 27: J. Ray. Essai sur la Structure Logique du Code Civil Francais. F. Alcan, 1926.
• 28: R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81-132, 1980.
• 29: T. Routen, Hierarchically organised formalisations, Proceedings of the 2nd international conference on Artificial intelligence and law, p.242-250, May 1989, Vancouver, British Columbia, Canada [doi>10.1145/74014.74045]
• 30: M. Ryan. Defaults and revision in structured theories. In Proceedings, Sixth Annual IEEE Symposium on Logic in Computer Science, pages 362-373. IEEE Computer Society Press, 1990.
• 31: M. Ryan and P.-Y. Schobbens. Laws of generaiised prioritization. Technical report, FUNDP, Namur, 1993.
• 32: Giovanni Sartor, The structure of norm conditions and nonmonotonic reasoning in law, Proceedings of the 3rd international conference on Artificial intelligence and law, p.155-164, May 1991, Oxford, England [doi>10.1145/112646.112665]
• 33: G. Sartor. Artificial Intelligence and Law: Legal Philosophy and Legal Theory. Tano, 1993.
• 34: A. Schmidt. Die zul'fissigkeit tier behandlung mehrsortiger theorien mittels tier tiblichen einsortigen pr~idikatenlogik. Math. Ann., 123:187-200, 1951.
• 35: P.-Y. Schobbens. Inheritance with exceptions for software specification: On the meaning of but. Technical report, RR-89-08, Universit6 Catholique de Louvain, Unit6 d'infonnatique, Feb. 1989.
• 36: P.-Y. Schobbens. Equality circumscription revisited: surjective circumscription. Technical report, CRiN, Nancy, 1992.
• 37: P.-Y. Schobbens. Exceptions in Algebraic Specifications. PhD thesis, Univ. Cath. de Louvain, 1992.
• 38: P.-Y. Schobbens. On the meaning of "but". Science of Computer Programming, March/April 1993.
• 39: M. J. Sergot , F. Sadri , R. A. Kowalski , F. Kriwaczek , P. Hammond , H. T. Cory, The British Nationality Act as a logic program, Communications of the ACM, v.29 n.5, p.370-386, May 1986 [doi>10.1145/5689.5920]
• 40: Y. Shoham. Reasoning about Change. Electrical Engineering and Computer Science Serie. The MIT Press, 1988.
• 41: Marianne Winslett, Updating logical databases, Cambridge University Press, New York, NY, 1991

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.1 Applications and Expert Systems
          Subjects: Law

Additional Classification:
  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES

  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.3 Deduction and Theorem Proving
          Subjects: Nonmonotonic reasoning and belief revision
      I.2.4 Knowledge Representation Formalisms and Methods
          Subjects: Representations (procedural and rule-based)

General Terms:
Languages, Legal Aspects, Reliability, Theory, Verification